Delay‐dependent exponential H ∞ filtering for discrete‐time switched delay systems

In this paper, the problem of delay‐dependent exponential H _∞ filtering for discrete‐time switched delay systems is investigated under average dwell time switching signals. Time delay under consideration is interval time‐varying in the states. By introducing a proper factor to construct a novel Lyapunov‐Krasovskii function and using average dwell time approach, sufficient conditions for the solvability of this problem, dependent on the upper and lower bounds of time‐varying delay, are obtained in terms of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results. Copyright © 2011 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.     

Stability,L2‐gain and asynchronous H ∞ control for continuous‐time switched systems

This paper is concerned with the stability and L₂‐gain problems for a class of continuous‐time linear switched systems with the existed asynchronous behaviors, where ‘asynchronous’ means that the switching of the controllers to be designed has a lag to the switching of the system modes. Firstly, a new sufficient condition on the asymptotic stability and weighted L₂‐gain analysis is obtained by using multiple Lyapunov functions combined with the average dwell time technique. Moreover, a result that is formulated in form of linear matrix inequalities is derived for the problem of asynchronous H _∞ control. Based on the result, the mode‐dependent controllers can be designed. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results.Copyright © 2013 John Wiley & Sons, Ltd.     

Local input‐to‐state stabilization and ℓ ∞ ‐induced norm control of discrete‐time quadratic systems

This paper addresses the problems of local stabilization and control of open‐loop unstable discrete‐time quadratic systems subject to persistent magnitude bounded disturbances and actuator saturation. Firstly, for some polytopic region of the state‐space containing the origin, a method is derived to design a static nonlinear state feedback control law that achieves local input‐to‐state stabilization with a guaranteed stability region under nonzero initial conditions and persistent bounded disturbances. Secondly, the stabilization method is extended to deliver an optimized upper bound on the ? _∞ ‐induced norm of the closed‐loop system for a given set of persistent bounded disturbances. Thirdly, the stabilization and ? _∞ designs are adapted to cope with actuator saturation by means of a generalized sector bound constraint. The proposed controller designs are tailored via a finite set of state‐dependent linear matrix inequalities. Numerical examples are presented to illustrate the potentials of the proposed control design methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time boundedness and L2‐gain analysis for switched positive linear systems with multiple time delays

In this paper, we study the finite‐time boundedness, stabilization, and L₂‐gain for switched positive linear systems (SPLS) with multiple time delays. Using multiple linear copositive Lyapunov functions, sufficient conditions in terms of linear matrix inequalities are obtained for the problems of finite‐time boundedness and stabilization and the design of state feedback controllers for SPLS. Under asynchronous switching, L₂‐gain analysis is developed for SPLS under the constraint of average dwell time. Numerical examples are given to illustrate our theoretical results. Copyright © 2017 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 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.     

Exponential H∞ filtering for switched linear systems with interval time‐varying delay

This paper deals with the problem of exponential H_∞ filtering for a class of continuous‐time switched linear system with interval time‐varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay‐derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H_∞ noise attenuation level. Based on the free‐weighting matrix approach and the average dwell technology, delay‐dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results. Copyright © 2008 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.     

Non‐fragile H ∞ control for switched stochastic delay systems with application to water quality process

In this paper, the problem of non‐fragile observer‐based H _∞ control for discrete‐time switched delay systems is investigated. Both data missing and time delays are taken into account in the links from sensors to observers and from controllers to actuators. Because data missing satisfies the Bernoulli distribution, such problem is transformed into an H _∞ control problem for stochastic switched delay systems. Average dwell time approach is used to obtain sufficient conditions on the solvability of such problems. A numerical example and a real example for water quality control are provided to illustrate the effectiveness and potential applications of the proposed techniques. Copyright © 2013 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.     

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.     

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.     

Nonlinear H ∞ output feedback control with integrator for polynomial discrete‐time systems

This paper investigates the problem of designing a nonlinear H _∞ output feedback controller for a class of polynomial discrete‐time systems. In general, this problem is hard to be formulated in a convex form because the relation between the control input and the Lyapunov function is always not jointly convex. Therefore, the problem cannot be solved via semidefinite programming (SDP). On the basis of the sum of squares (SOS) approach and incorporation of an integrator into the controller, sufficient conditions for the existence of a nonlinear H _∞ output feedback controller are given in terms of SOS conditions, which can be solved by an SDP solver. In contrast to the existing methods, a less conservative result is obtained. Finally, numerical examples are used to demonstrate the validity of this integrator approach. Copyright © 2013 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.     

Observer‐based H ∞ control on nonhomogeneous Markov jump systems with nonlinear input

This paper considers the problem of observer‐based H _∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H _∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

H∞ Filtering for Spatially Interconnected Time‐Delay Systems with Interconnected Chains in Finite Frequency Domains

This paper deals with the problem of delay‐dependent H_∞ filtering for spatially interconnected time‐delay systems (SITSs) with interconnected chains in finite frequency domains. First, a multidimensional (N‐D) hybrid time‐delay Roesser model and a delay‐dependent finite frequency bounded ream lemma (BRL) for SITSs with interconnected chains are proposed. Then, using the obtained delay‐dependent finite frequency BRL, a finite frequency H_∞ filter design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, a practical example is provided to clearly demonstrate the effectiveness of the proposed method.