Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

In this paper, globally asymptotical stabilization problem for a class of planar switched nonlinear systems with an output constraint via smooth output feedback is investigated. To prevent output constraint violation, a common tangent‐type barrier Lyapunov function (tan‐BLF) is developed. Adding a power integrator approach (APIA) is revamped to systematically design state‐feedback stabilizing control laws incorporating the common tan‐BLF. Then, based on the designed state‐feedback controllers and a constructed common nonlinear observer, smooth output‐feedback controllers, which can make the system output meet the predefined constraint during operation, are proposed to deal with the globally asymptotical stabilization problem of planar switched nonlinear systems under arbitrary switchings. A numerical example is employed to verify the proposed method.     

Robust state‐feedback control of stochastic state‐multiplicative discrete‐time linear switched systems with dwell time

Linear discrete‐time switched stochastic systems are considered, where the problems of mean square stability, stochastic l₂‐gain and state‐feedback control design are treated and solved. Solutions are obtained for both nominal and polytopic‐type uncertain systems. In all these problems, the switching obeys a dwell time constraint. In our solution, to each subsystem of the switched system, a Lyapunov function is assigned that is nonincreasing at the switching instants. The latter function is allowed to vary piecewise linearly, starting at the end of the previous switch instant, and it becomes time invariant after the dwell. In order to guarantee asymptotic stability, we require the Lyapunov function to be negative between consecutive switchings. We thus obtain Linear Matrix Inequalities conditions. Based on the solution of the stochastic l₂‐gain problem, we derive a solution to the state‐feedback control design, where we treat a variety of special cases. Being affine in the system matrices, all the aforementioned solutions are extended to the uncertain polytopic case. The proposed theory is demonstrated by a practical example taken from the field of flight control. Copyright © 2015 John Wiley & Sons, Ltd.     

An improved sum‐of‐squares based approach to fuzzy tracking control design of nonlinear systems

In this paper, using a more general Lyapunov function, less conservative sum‐of‐squares (SOS) stability conditions for polynomial‐fuzzy‐model‐based tracking control systems are derived. In tracking control problems the objective is to drive the system states of a nonlinear plant to follow the system states of a given reference model. A state feedback polynomial fuzzy controller is employed to achieve this goal. The tracking control design is formulated as an SOS optimization problem. Here, unlike previous SOS‐based tracking control approaches, a full‐state‐dependent Lyapunov matrix is used, which reduces the conservatism of the stability criteria. Furthermore, the SOS conditions are derived to guarantee the system stability subject to a given H_∞ performance. The proposed method is applied to the pitch‐axis autopilot design problem of a high‐agile tail‐controlled pursuit and another numerical example to demonstrate the effectiveness and benefits of the proposed method.     

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

This paper studies the finite‐time stabilizing control problem for a class of switched stochastic nonlinear systems (SSNSs) in p‐normal form. The switched systems under consideration possess the powers of different positive rational numbers and the dead‐zone input nonlinearities. Based on the improving finite‐time stability theorem for SSNSs established in this paper, a general framework to address common state feedback for SSNSs is developed by adopting the common Lyapunov function–based adding a power integrator technique. It is proved that the proposed controller renders the trivial solution of the closed‐loop system uniformly finite‐time stable in probability under arbitrary switchings. Finally, simulation results are given to confirm the validity of the proposed approach.     

Sampling‐interval‐dependent stability for sampled‐data systems with state quantization

This paper is concerned with the stability of sampled‐data systems with state quantization. A new piecewise differentiable Lyapunov functional is first constructed by fully utilizing information about sampling instants. This functional has two features: one is that it is of the second order in time t and of every term being dependent on time t explicitly and the other is that it is discontinuous and is only required to be definite positive at sampling instants. Then, on the basis of this piecewise differentiable Lyapunov functional, a sampling‐interval‐dependent exponential stability criterion is derived by applying the technique of a convex quadratic function with respect to the time t to check the negative definiteness for the derivative of the piecewise differentiable Lyapunov functional. In the case of no quantization, a new sampling‐interval‐dependent stability criterion is also obtained. It is shown that the new stability criterion is less conservative than some existing one in the literature. Finally, two examples are given to illustrate the effectiveness of the stability criterion. Copyright © 2013 John Wiley & Sons, Ltd.     

A less conservative stability criterion for sampled‐data system via a fractional‐delayed state and its state‐space model

This paper introduces a state‐space model based on a fractional‐delayed state for a sampled‐data system described as a linear system under aperiodic sampling intervals. The new state‐space model exploits the information on the sampled‐data system and the fractional‐delayed state, which is defined on the sampling interval. The fractional‐delayed state and its state‐space model are utilized to construct the Lyapunov functional, which consists of the traditional Lyapunov function and a looped functional whose boundary conditions are zeros at sampling instants. Based on the Lyapunov functional, a stability criterion and a robust stability criterion are derived in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed criterion.     

Regional stability of two‐dimensional nonlinear polynomial Fornasini‐Marchesini systems

This paper addresses the problem of regional stability analysis of 2‐dimensional nonlinear polynomial systems represented by the Fornasini‐Marchesini second state‐space model. A method based on a polynomial Lyapunov function is proposed to ensure local asymptotic stability and provide an estimate of the domain of attraction of the system zero equilibrium point. The proposed results that build on recursive algebraic representations of the polynomial vector function of the system dynamics and Lyapunov function are tailored via linear matrix inequalities that are required to be satisfied at the vertices of a given bounded convex polyhedral region of the state space. Numerical examples demonstrate the effectiveness of the proposed method.     

Observer‐Based H∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

The paper investigates the observer‐based H_∞ synchronization for coronary artery time‐delay system under the state immeasurement and external uncertainty. A Luenberger‐like state observer, the observation system, is designed to realize the state reconstruction of the master system. Based on the Lyapunov stability theory and Lyapunov‐Krasovskii functional (LKF), the observer‐based synchronization control condition is derived for a coronary artery system subjected to the external uncertainty bounded by L₂ norm. By introducing the delay‐interval bounds and delay‐derivative limits in LKF, the time‐delays are handled by the delay‐range‐dependent strategy. The tighter upper bound of inequality can be obtained to reduce the conservation by employing further improved result of Jensen inequality and reciprocally convex approach. Furthermore, a decoupling technique is utilized to render the separate and simple controller and observer synthesis condition, which can be further solved by applying the cone complementary linearization approach respectively. Numerical simulations are listed to exhibit the effectiveness of the presented methodology.     

Finite‐time stability of switched positive linear systems

This brief paper addresses the finite‐time stability problem of switched positive linear systems. First, the concept of finite‐time stability is extended to positive linear systems and switched positive linear systems. Then, by using the state transition matrix of the system and copositive Lyapunov function, we present a necessary and sufficient condition and a sufficient condition for finite‐time stability of positive linear systems. Furthermore, two sufficient conditions for finite‐time stability of switched positive linear systems are given by using the common copositive Lyapunov function and multiple copositive Lyapunov functions, a class of switching signals with average dwell time is designed to stabilize the system, and a computational method for vector functions used to construct the Lyapunov function of systems is proposed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.     

Finite‐time H∞ bumpless transfer control for switched systems: A state‐dependent switching approach

This paper addresses the finite‐time H_∞ bumpless transfer control problem for switched systems. The main idea lies in designing a state‐feedback controller with amplitude limitation and a state‐dependent switching law to reduce control bumps caused by switching. First, a local bumpless transfer condition is proposed to limit the amplitude of switching controllers at switching points. Second, by introducing a state‐dependent switching law, a prescribed finite‐time H_∞ bumpless transfer control performance is attained even if it does not hold for each subsystem or system state remaining on a switching surface. Third, a sufficient condition verifying the solvability of finite‐time H_∞ bumpless transfer control problem is established by resorting to multiple Lyapunov function method. Finally, the effectiveness of developed method is illustrated by a numerical example.     

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.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach

In this paper, the problem of exponential H_∞ filter problem for a class of discrete‐time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete‐time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ‐dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode‐dependent full‐order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H_∞ performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.     

ℒ︁2‐Stabilization of continuous‐time linear systems with saturating actuators

This paper addresses the problem of controlling a linear system subject to actuator saturations and to ??₂‐bounded disturbances. Linear matrix inequality (LMI) conditions are proposed to design a state feedback gain in order to satisfy the closed‐loop input‐to‐state stability (ISS) and the closed‐loop finite gain ??₂ stability. By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition, which encompasses the classical sector‐nonlinearity condition considered in some previous works, and Finsler's Lemma, which allows to derive stabilization conditions which are adapted to treat multiple objective control optimization problems in a potentially less conservative framework. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust PID‐PSD Controller Design: BMI Approach

A new robust proportional‐integral‐derivative (PID)–proportional‐sum‐derivative (PSD) controller design method based on linear (bilinear) matrix inequalities (LMI, BMI) is proposed for uncertain affine linear system. The design procedure guarantees the parameter dependent quadratic stability, and guaranteed cost control with a new quadratic cost function (LQRS) including the derivative term for the state vector as a tool to influence the overshoot and response rate. The second approach to the PSD controller design procedure is based on a Lyapunov function with a special term corresponding to the time‐delay part of the control algorithm. The results obtained are illustrated on three examples to show the robust PID, PSD control design procedure and the influence of the choice of matrix S in the extended cost function.     

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

In this paper, an adaptive output‐feedback control problem is investigated for nonlinear strict‐feedback stochastic systems with input saturation and output constraint. A barrier Lyapunov function is used to solve the problem of output constraint. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. To overcome the difficulties in designing the control signal in the saturation, we introduce an auxiliary signal in the n + 1th step in the deduction. By combining Nussbaum technique and the adaptive backstepping technique, an adaptive output‐feedback control method is developed. The proposed control method not only overcomes the problem of the compensation for the nonlinear term from the input saturation but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified by the simulation results.     

Output feedback finite‐time stabilization of a class of nonlinear time‐delay systems in the p‐normal form

This article investigates the finite‐time output feedback stabilization problem for a class of nonlinear time‐varying delay systems in the p‐normal form. First, a reduced‐order state observer is designed to estimate the unmeasurable state. Then, an output feedback controller is constructed, with the help of the finite‐time Lyapunov stability theorem, it is proved that the state of the resulting closed‐loop system converges to the origin in finite time. Two simulation examples are given to verify the effectiveness of the proposed scheme.     

Exponential H∞ Filtering for Discrete‐Time Switched State‐Delay Systems Under Asynchronous Switching

The exponential H_∞ filtering problem of discrete‐time switched state‐delay systems under asynchronous switching is considered in this paper. The objective is to design a full‐order or reduced‐order switched filter guaranteeing the exponential stability with the weighted H_∞ performance of the filtering error system. A sufficient condition for the exponential stability with the weighted H_∞ performance of the filtering error system is provided based on delay‐dependent multiple Lyapunov‐Krasovskii functionals. The gains of the filter can be obtained by solving a set of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results.     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.