Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions

This paper addresses the robust H_∞ static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainH_∞ performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.     

An augmented system approach to static output‐feedback stabilization with ℋ︁∞ performance for continuous‐time plants

This paper revisits the static output‐feedback stabilization problem of continuous‐time linear systems from a novel perspective. The closed‐loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ??_∞ performance of the closed‐loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output‐feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output‐feedback ??_∞ control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust delay‐dependent ℋ︁∞ control of time‐delay systems with state and input delays

This paper studies the design problem of robust delay‐dependent ??_∞ controller for a class of time‐delay control systems with time‐varying state and input delays, which are assumed to be noncoincident. The system is subject to norm‐bounded uncertainties and ??₂ disturbances. Based on the selection of an augmented form of Lyapunov–Krasovskii (L‐K) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time‐delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay‐dependent criteria are developed for a stabilizing ??_∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm‐bounded uncertainties, both the BRL and ??_∞ stabilization criteria are easily extended by employing a well‐known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐based controller design of discrete‐time piecewise affine systems

This paper presents a novel observer‐based controller design method for discrete‐time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed‐loop system. During the controller design, the piecewise‐quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Dynamic output feedback H ∞ control for affine fuzzy systems

This article investigates the problem of designing H _∞ dynamic output feedback controllers for nonlinear systems, which are described by affine fuzzy models. The system outputs have been chosen as premise variables, which can guarantee that the plant and the controller always switch to the same region. By using a piecewise Lyapunov function and adding slack matrix variables, a piecewise-affine dynamic output feedback controller design method is obtained in the formulation of linear matrix inequalities (LMIs), which can be efficiently solved numerically. In contrast to the existing work, the proposed approach needs less LMI constraints and leads to less conservatism. Finally, numerical examples illustrate the effectiveness of the new result.     

Novel Optimal Design Approach for Output‐Feedback H∞ Control of Vehicle Active Seat‐Suspension System

In this paper, the output‐feedback control problem of a vehicle active seat‐suspension system is investigated. A novel optimal design approach for an output‐feedback H_∞ controller is proposed. The main objective of the controller is to minimize the seat vertical acceleration to improve vehicle ride comfort. First, the human body and the seat are considered in the modeling of a vehicle active suspension system, which makes the model more precise. Other constraints, such as tire deflection, suspension deflection and actuator saturation, are also considered. Then the output‐feedback control strategy is adopted since some state variables, such as body acceleration and body deflection, are unavailable. A concise and effective approach for an output‐feedback H_∞ optimal control is presented. The desired controller is obtained by solving the corresponding linear matrix inequalities (LMIs) and by the calculation of equations proposed in this paper. Finally, a numerical example is presented to show the effectiveness and advantages of the proposed controller design approach.     

Gain‐scheduled dynamic output feedback control for discrete‐time LPV systems

This paper presents synthesis conditions for the design of gain‐scheduled dynamic output feedback controllers for discrete‐time linear parameter‐varying systems. The state‐space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective ??_∞ and ??₂ gain‐scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real‐time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter‐dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete‐time mixed ℋ︁2/ℋ︁∞ nonlinear filtering

In this paper, we consider the discrete‐time mixed ??₂/??_∞ filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled discrete‐time Hamilton–Jacobi‐Isaac's equations (DHJIE) with some side‐conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete‐time algebraic‐Riccati‐equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite‐horizon and infinite‐horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Mixed Event/Time‐Triggered Static Output Feedback L2‐Gain Control for Networked Control Systems

This paper considers the design of mixed event/time‐triggered controllers for networked control systems (NCSs) under transmission delay and possible packet dropout. Assuming that a conventional delayed static output feedback L₂‐gain controller exists, we propose an output‐based mixed event/time‐triggered communication scheme for reducing the network traffic in a NCS. Moreover, we show that a conventional delayed static output feedback L₂‐gain controller can be obtained by solving a linear matrix inequality with a matrix equality constraint. A numerical example is proposed for demonstrating the theoretical results.     

New results on static output feedback H ∞ control for fuzzy singularly perturbed systems: a linear matrix inequality approach

This paper presents the novel approaches of designing robust fuzzy static output feedback H _∞ controller for a class of nonlinear singularly perturbed systems. Specifically, the considered system is approximated by a fuzzy singularly perturbed model. With the use of linear matrix inequality (LMI) methods, two methods are provided to design fuzzy static output feedback H _∞ controllers. The resulted controllers can guarantee that the closed‐loop systems are asymptotically stable and satisfy H _∞ performances for sufficiently small ?. In contrast to the existing results, the proposed approaches have two advantages: (i) the gains of controller are solved directly by a set of ?‐independent LMIs, and therefore, the problem of selecting the initial values in iterative LMIs algorithm can be avoided, and (ii) the smaller control input efforts are needed. The given methods are easy to implement and can be applied to both standard and nonstandard nonlinear singularly perturbed systems. Two numerical examples are provided to illustrate the effectiveness of the developed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust filter design for piecewise discrete‐time systems with time‐varying delays

A novel delay‐dependent filtering design approach is developed for a class of linear piecewise discrete‐time systems with convex‐bounded parametric uncertainties and time‐varying delays. The time‐delays appear in the state as well as the output and measurement channels. The filter has a linear full‐order structure and guarantees the desired estimation accuracy over the entire uncertainty polytope. The desired accuracy is assessed in terms of either ??_∞‐performance or ??₂–??_∞ criteria. A new parametrization procedure based on a combined Finsler's Lemma and piecewise Lyapunov–Krasovskii functional is established to yield sufficient conditions for delay‐dependent filter feasibility. The filter gains are determined by solving a convex optimization problem over linear matrix inequalities. In comparison to the existing design methods, the developed methodology yields the least conservative measures since all previous overdesign limitations are almost eliminated. By means of simulation examples, the advantages of the developed technique are readily demonstrated. Copyright © 2009 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 H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

In this paper, we present a new scheme for designing a H_∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented.     

ℋ︁∞‐filtering for singularly perturbed nonlinear systems

In this paper, we consider the ??_∞‐filtering problem for singularly perturbed (two time‐scale) nonlinear systems. Two types of filters are discussed, namely, (i) decomposition and (ii) aggregate, and sufficient conditions for the solvability of the problem in terms of Hamilton–Jacobi–Isaac's equations (HJIEs) are presented. Reduced‐order filters are also derived in each case, and the results are specialized to linear systems, in which case the HJIEs reduce to a system of linear‐matrix‐inequalities (LMIs). Based on the linearization of the nonlinear models, upper bounds ε^* of the singular parameter ε that guarantee the asymptotic stability of the nonlinear filters can also be obtained. The mixed ??₂/??_∞‐filtering problem is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

H∞ Control Synthesis for Lurie Networked Control Systems with Multiple Delays Based on the Non‐Uniform Characteristic

This paper investigates the H _∞ control synthesis problem for Lurie networked control systems (NCSs) with multiple time‐varying delays. With the consideration of both network‐induced delays and data packet dropout, Lurie NCSs discussed in this work can effectively be transformed into Lurie control systems with multiple time‐varying delays. In addition, with the non‐uniform distribution characteristics of network delays, based on the delay probability distribution, the stable controller design, and H _∞ synthesis, approaches are derived in the form of linear matrix inequalities (LMIs). Finally, a set of numerical examples are studied, and the results demonstrate the applicability and effectiveness of the suggested approaches.