Robust non‐fragile H ∞ ∕ L2 − L ∞ control of uncertain linear system with time‐delay and application to vehicle active suspension

This paper presents an approach to design robust non‐fragile H _∞ ∕ L₂ ? L _∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H _∞ and L₂ ? L _∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H _∞ controller and L₂ ? L _∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite frequency H∞ control of singularly perturbed Euler‐Lagrange systems: An artificial delay approach

In this paper, we show that small artificial delays in the feedback loops operating in different time scales may stabilize singularly perturbed systems (SPSs). An artificial delay approach is proposed for the robust stabilization and L₂‐gain analysis of SPSs in the finite frequency domain. A two‐time‐scale delayed static output feedback controller is designed, in which the controller gains are formulated via a linear matrix inequality (LMI) algorithm. A distinctive feature of the proposed algorithm is setting controller parameters as free variables, which increases the degrees of freedom in controller design and leads to more flexibility in solving LMIs. Moreover, the proposed method is further extended to analyze the finite frequency system specifications of SPSs. The L₂‐gain performance analysis is conducted for parameter‐independent subsystems in their dominant frequency ranges, and the disturbance attenuation level of the original high‐order system is then estimated. Finally, the efficiency of the proposed design method is verified in an active suspension system subject to multiple finite frequency disturbance.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.     

Output‐Feedback Control for Continuous‐time Interval Positive Systems under L1 Performance

This paper is concerned with the design of an L₁‐induced output‐feedback controller for continuous‐time positive systems with interval uncertainties. A necessary and sufficient condition for stability and an L₁‐induced performance of interval positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust static output‐feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. For special single‐input‐multiple‐output (SIMO) positive systems, the problem of controller synthesis is completely solved with the help of an analytical formula for the L₁‐induced norm. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

Almost Disturbance Decoupling for a Class of Nonlinear Systems Subject to Time‐Delays Via Sampled‐Data Output Feedback Control

This paper considers the problem of almost disturbance decoupling (ADD) via sampled‐data output feedback control for a class of uncertain nonlinear systems subject to time‐delays. Based on output feedback domination approach, a sampled‐data output feedback controller is designed to globally stabilize the system under a lower‐triangular linear growth condition. Gronwall‐Bellman‐like inequality and inductive method are introduced to estimate the state growth in the presence of time‐delays, uncertain nonlinearities and unknown disturbances. The proposed controller can attenuate the influence of disturbances on the output to an arbitrary degree in the L₂ gain sense. Finally, simulation results show the effectiveness of the control method.     

Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties

This paper investigates the problem of robust ??_∞ static output feedback controller design for a class of discrete‐time piecewise‐affine systems with norm‐bounded time‐varying parametric uncertainties. The objective is to design a piecewise‐linear static output feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop system with a prescribed ??_∞ disturbance attenuation level. Based on a piecewise Lyapunov function combined with S‐procedure, Projection lemma, and some matrix inequality convexifying techniques, several novel approaches to the static output feedback controller analysis and synthesis are developed for the underlying piecewise‐affine systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a family of LMIs parameterized by one or two scalar variables, which are numerically efficient with commercially available software. Finally, three simulation examples are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.     

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

A robust dynamic output feedback controller synthesis algorithm considering H_∞/H₂ performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.     

Robust event‐triggered output feedback learning algorithm for voltage source inverters with unknown load and parameter variations

We consider the output feedback event‐triggered control of an off‐grid voltage source inverter (VSI) with unknown inductance‐capacitance (L ? C) filter dynamics and connected load in the presence of an input disturbance acting at the inverter. Due to uncertain dynamics and unmodeled parameters in the L ? C filter connected to the VSI, we use an adaptive observer to reconstruct the system's states by measuring only the voltage at the output. The control mechanism is constructed based on an impulsive actor/critic framework that approximates the cost, the event‐triggered controller, and the worst case disturbance and generates the desired AC output with the least energy dissipation. We provide rigorous stability proofs and illustrate the applicability of our results through a simulation example.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Robust output‐feedback control of state‐multiplicative noisy discrete‐time systems

Linear discrete‐time systems with stochastic and deterministic polytopic type uncertainties in their state‐space model are considered. A dynamic output‐feedback controller is obtained via a new approach that allows a derivation of a controller in spite of parameter uncertainty. In the proposed approach, the system is described via a difference equation and an augmented system is then used to obtain the output‐feedback controller parameters. The controller is obtained without assuming a specific structure to the quadratic Lyapunov function, and it is the first time that an output‐feedback controller is obtained for robust state‐multiplicative systems. The controller minimizes the stochastic L₂‐gain of the closed‐loop where a cost function is defined to be the expected value of the standard performance index with respect to the stochastic uncertainty. Two examples are given where the second of which demonstrates the applicability of our theory to a robot manipulator system. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

H∞ Guaranteed Cost Control for LPV Systems Subject to The Gain Constraint

This paper deals with the problem of H_∞ guaranteed cost control for linear parameter varying (LPV) systems subject to the gain constraint. Specifically, our main goal is to design a controller such that the closed‐loop system is exponentially stable with the H_∞ performance index, the quadratic performance index, and the gain within the desired constraints over the entire parameter region. In order to achieve this goal, less conservative and more practical sufficient conditions for the existence of the state feedback controller are proposed by introducing the parameter dependent Lyapunov function and many extra freedom degrees in terms of linear matrix inequalities and a free parameter matrix. The parameter matrix aspecially can regulate the gain freely without the influence of the desired performance to meet the additional design criteria enhancing the practicability and the design flexibility. As a special case, relevant results are extended to design a static output feedback controller. One numerical example is used to show advantages of the proposed approach.     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

Almost disturbance decoupling for a class of nonlinear systems via sampled‐data output feedback control

This paper addresses the problem of almost disturbance decoupling (ADD) using sampled‐data output feedback control for a class of continuous‐time nonlinear systems. Under a lower‐triangular linear growth condition, a sampled‐data output feedback controller is constructed based on the output feedback domination approach, and a Gronwall–Bellman‐like inequality is established in the presence of disturbances. Even though a sampled‐data controller is employed for easy computer implementation, the proposed controller is still able to achieve ADD under the commonly used continuous‐time requirement, that is, the disturbances' effect on the output is attenuated to an arbitrary degree of accuracy in the L₂ gain sense. Copyright © 2015 John Wiley & Sons, Ltd.     

A Simultaneous Mixed LQR/H∞ Control Approach to the Design of Reliable Active Suspension Controllers

This paper is concerned with the synthesis of reliable controllers for quarter‐car active suspension systems. By a simultaneous mixed LQR/H_∞ control approach, a static output feedback controller is derived for guaranteeing good suspension performance under possible sensor fault or suspension component breakdown. The considered simultaneous mixed LQR/H_∞ control problem is a nonconvex optimization problem; therefore, the linear matrix inequality approach is not applicable. Based on the barrier method, we solve an auxiliary minimization problem to get an approximate solution for the simultaneous mixed LQR/H_∞ control problem. Necessary conditions for the local optimum of the auxiliary minimization problem are derived. Moreover, a three‐stage solution algorithm is developed for solving the auxiliary minimization problem. The simulation shows that the obtained static output feedback suspension controllers can improve suspension performance in nominal mode and all considered failure modes.     

L1‐Gain Analysis and Control for Switched Positive Systems with Dwell Time Constraint

This paper studies the problems of L₁‐gain analysis and control for switched positive systems with dwell time constraint. The state‐dependent switching satisfies a minimal dwell time constraint to avoid possible arbitrary fast switching. By constructing multiple linear co‐positive Lyapunov functions, sufficient conditions of stability and L₁‐gain property are derived under the proposed switching strategy. Then, an effective state feedback controller is designed to ensure the positivity and L₁‐gain property of the closed‐loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.