A generalized robust H ∞ filtering for singular Markovian jump systems and its applications

In this paper, a generalized robust H _∞ filtering method is proposed for a class of singular Markovian jump systems, whose generality is mainly embodied that the desired filter could bear perturbances in terms of uncertainties on its parameter matrices. Firstly, an LMI condition of robust mode‐dependent filter is developed. Based on the given result, a new approach to mode‐independent H _∞ filter is presented, which establishes a direct connection between mode‐dependent and mode‐independent filters. Secondly, when the transition rate matrix is with elementwise bounded uncertainties or partially unknown, sufficient conditions of such robust mode‐dependent and mode‐independent filters are all developed within LMI frameworks. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Robust H ∞ filtering for singular time‐delayed systems with uncertain Markovian switching probabilities

This paper is concerned with the robust H _∞ filter design for a class of uncertain singular time‐delayed Markovian jump systems, whose transition rate matrix has elementwise bounded uncertainties. By the LMI approach, a novel bounded real lemma is proposed such that the singular Markovian jump system is robustly exponentially mean‐square admissible with a prescribed H _∞ performance index. Based on this, a sufficient condition for the existence of a robust H _∞ filter is developed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

H ∞ control for discrete‐time nonlinear Markov jump systems with multiplicative noise and sector constraint

This paper addresses the finite horizon H _∞ control problem for a class of discrete‐time nonlinear Markov jump systems with multiplicative noise and nonlinear feedback device. The system nonlinearity occurs in a random way specified by a Bernoulli process, whereas the actuator and sensor nonlinearities are restricted to a sector region. Both the state and the dynamic output feedback H _∞ controllers are devised in terms of difference LMIs. The proposed approach not only allows the resulting system to achieve a prescribed disturbance attenuation level, but also enables the output of actuator/sensor to meet the designated sector condition. Moreover, it is also shown that our approach is well‐adapted for dealing with the discrete‐time Markov jump systems with saturated actuator and sensor. Finally, a backward iterative algorithm is provided to solve the obtained difference LMIs and a numerical example is presented to verify the efficiency of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

New approach to H ∞ filtering of two‐dimensional T‐S fuzzy systems

This paper is concerned with the H _∞ filtering problem for two‐dimensional T‐S fuzzy systems. Sufficient conditions for the solvability of this problem are obtained by using basis‐dependent Lyapunov functions. By considering the measured output as an independent variable with respect to the state variable and the disturbance input, a new method for designing two‐dimensional H _∞ filters is presented. Moreover, it has been shown that the proposed method is equivalent to the conventional one. Therefore, the proposed method does not lead to any conservativeness that may be caused by separately considering the measured output, the state variable, and the disturbance input. In converting the parameterized linear matrix inequalities (PLMI) into LMI constraints, attention is focused on the reduction of the number of LMI‐based conditions. On the basis of the proposed theorem, the number of LMI‐based conditions is reduced to r³ from r³(r + 1)² ∕ 4 by the conventional method. Thus, the computational advantage is obvious for fuzzy systems with large number of fuzzy rules. Simulation results have demonstrated the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

In this paper, the problem of finite‐time H _∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H _∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H _∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H _∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H _∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based H ∞ control for networked systems with bounded random delays and consecutive packet dropouts

This paper is concerned with the H _∞ control problem for a class of systems with bounded random delays and consecutive packet dropouts that exist in both sensor‐to‐controller channel and controller‐to‐actuator channel during data transmission. A new model is developed to describe possible random delays and packet dropouts by two groups of Bernoulli distributed stochastic variables. To avoid the state augmentation, a full‐order observer‐based feedback controller is designed via LMI approach. Based on the Lyapunov theory, a sufficient condition is provided to guarantee the closed‐loop networked system to be asymptotically mean‐square stable and achieve the prescribed H _∞ disturbance‐rejection‐attenuation level. The simulation examples illustrate the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliable H ∞ filter design for T–S fuzzy model‐based networked control systems with random sensor failure

This paper investigates robust and reliable H _∞ filter design for a class of nonlinear networked control systems: (i) a T‐S fuzzy model with its own uncertainties is used to approximate the nonlinear dynamics of the plant, (ii) a new sensor failure model with uncertainties is proposed, and (iii) the signal transfer of the closed‐loop system is under a networked communication scheme and therefore is subject to time delay, packet loss, and/or packet out of order. Four new theorems are proved to cover the conditions for the robust mean square stability of the systems under study in terms of LMIs, and a decoupling method for the filter design is developed. Two examples, one of them is based on a model of an inverted pendulum, are provided to demonstrate the design method. Copyright © 2011 John Wiley & Sons, Ltd.     

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 H ∞ control of discrete‐time Markovian jump systems in the presence of incomplete knowledge of transition probabilities and saturating actuator

This paper deals with the problem of robust H _∞ control for a class of discrete‐time Markovian jump systems subject to both actuator saturation and incomplete knowledge of transition probability. Different from the previous results where the transition probability is completely known, a more general situation where only partial information on the exact values of elements in transition probability matrix is considered. By introducing some free parameters to express the relationship for the known and the unknown elements of transition probability matrix in stability analysis, a criterion is established to guarantee the stochastic stability of the closed‐loop system as well as an H _∞ performance index. The concept of domain of attraction in mean square sense is used to analyze the closed‐loop stability, and the mode‐dependent H _∞ state‐feedback controller is designed. It is shown that, even in the absence of actuator saturation, the obtained result is less conservative than the existing one. A numerical example is provided to illustrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Exponential H ∞ filtering for stochastic Markovian jump systems with time delays

This paper investigates the problem of exponential H _∞ filtering for stochastic systems with time delays and Markovian jumping parameters. On the basis of Lyapunov–Krasovskii functional theory and generalized Finsler lemma, a delay‐dependent bounded real lemma is established without using any model transformations, bounding techniques for cross terms, or additional free matrix variables. The obtained bounded real lemma guarantees that the filtering error system is both mean‐square exponentially stable and almost surely exponentially stable with a prescribed H _∞ noise attenuation level. Then an exponential H _∞ filter is designed for stochastic retarded Markovian jump systems in terms of a set of LMIs. Meanwhile, the mathematical equivalence of the proposed method to one recent method is presented, but our proposed method is more computationally efficient with fewer matrix variables than that recent method. The validity of the method is verified by a numerical example.Copyright © 2012 John Wiley & Sons, Ltd.     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

On designing network‐based H ∞ controllers for stochastic systems

This paper is concerned with network‐based H _∞ stabilization for stochastic systems, where network‐induced delays, packet dropouts, and packet disorders are taken into account simultaneously. The packet disorders arising from both the sampler‐to‐controller channel and the controller‐to‐actuator channel are considered by introducing a logic controller and a logic zero‐order hold. The network‐induced delays and packet dropouts are modeled as a constant delay plus a non‐differentiable time‐varying delay in the input. By employing Lyapunov–Krasovskii functional approach, we establish results that parallel well‐known bounded real Lemmas. More specifically, these results provide conditions to bound the H _∞ level of the system, which means the worst case energy of the output of the system when subjected to a unitary norm deterministic disturbance signal. On the basis of these results, suitable network‐based H _∞ controllers are designed by using cone complementary linearization method. An air vehicle system is finally taken as an example to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based H ∞ output tracking control for networked control systems

This paper is concerned with observer‐based H _∞ output tracking control for networked control systems. An observer‐based controller is implemented through a communication network to drive the output of a controlled plant to track the output of a reference model. The inputs of the controlled plant and the observer‐based tracking controller are updated in an asynchronous way because of the effects of network‐induced delays and packet dropouts in the controller‐to‐actuator channel. Taking the asynchronous characteristic into consideration, the resulting closed‐loop system is modeled as a system with two interval time‐varying delays. A Lyapunov–Krasovskii functional, which makes use of information about the lower and upper bounds of the interval time‐varying delays, is constructed to derive a delay‐dependent criterion such that the closed‐loop system has a desired H _∞ tracking performance. Notice that a separation principle cannot be used to design an observer gain and a control gain due to the asynchronous inputs of the plant and the controller. Instead, a novel design algorithm is proposed by applying a particle swarm optimization technique with the feasibility of the stability criterion to search for the minimum H _∞ tracking performance and the corresponding gains. The effectiveness of the proposed method is illustrated by an example. Copyright © 2013 John Wiley & Sons, Ltd.     

Decentralized state feedback robust H ∞ control using a differential evolution algorithm

This paper presents a new method to synthesize a decentralized state feedback robust H ^∞ controller for a class of large‐scale linear uncertain systems satisfying integral quadratic constraints. The decentralized controller is constructed by taking only block‐diagonal elements of a nondecentralized state feedback controller and treating neglected off‐diagonal blocks as uncertainties. A solution to this controller synthesis problem is given in terms of a stabilizing solution to a parametrized algebraic Riccati equation where the parameters are obtained using a differential evolution algorithm.Copyright © 2012 John Wiley & Sons, Ltd.     

H ∞ output tracking control for discrete‐time switched systems via output feedback

This paper studies the problem of H _∞ output tracking control for a class of discrete‐time switched systems. Neither the measurability of the system state nor the solvability of the output tracking control problem for each individual subsystem is required. We design controllers for subsystems and a switching law to solve the H _∞ output tracking problem for the switched system. The designed controllers use only the measured output feedback, and the switching law is based on the measured output tracking error. In addition, the quadratic function corresponding to each subsystem is not required to be positive definite. A numerical example is provided to demonstrate the feasibility and validity of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust H ∞ control of stochastic linear switched systems with dwell time

The theory of H _∞ control of switched systems is extended to stochastic systems with state‐multiplicative noise. Sufficient conditions are obtained for the mean square stability of these systems where dwell time constraint is imposed on the switching. Both nominal and uncertain polytopic systems are considered. A Lyapunov function, in a quadratic form, is assigned to each subsystem that is nonincreasing at the switching instants. During the dwell time, this function varies piecewise linearly in time following the last switch, and it becomes time invariant afterwards. Asymptotic stochastic stability of the set of subsystems is thus ensured by requiring the expected value of the infinitesimal generator of this function to be negative between switchings, resulting in conditions for stability in the form of LMIs. These conditions are extended to the case where the subsystems encounter polytopic‐type parameter uncertainties. The method proposed is applied to the problem of finding an upper bound on the stochastic L₂‐gain of the system. A solution to the robust state‐feedback control problem is then derived, which is based on a modification of the L₂‐gain bound result. Two examples are given that demonstrate the applicability of the proposed theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential H ∞ filtering for singular systems with Markovian jump parameters

This paper is concerned with the H _∞ filter design for continuous‐time singular systems with Markovian jump parameters, whose system mode is transmitted through an unreliable network. In contrast to the traditionally mode‐dependent or mode‐independent filtering method, a new partially mode‐dependent filter is established via using a mode‐dependent Lyapunov function, where the stochastic property of mode available to a filter is considered. Sufficient conditions for the existence of H _∞ filter are obtained as strict linear matrix inequalities. Finally, numerical examples are used to show the effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.