Robust finite-time H∞ control for a class of uncertain switched neutral systems

This paper investigates the robust finite-time H_∞ control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance. The uncertainties under consideration are norm bounded. By using the average dwell time approach, a sufficient condition for finite-time boundedness of switched neutral systems is derived. Then, finite-time H_∞ performance analysis for switched neutral systems is developed, and a robust finite-time H_∞ state feedback controller is proposed to guarantee that the closed-loop system is finite-time bounded with H_∞ disturbance attenuation level γ. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.     

Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems

This paper studies the robust and resilient finite-time H_∞ control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H_∞ finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H_∞ finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H_∞ finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples.     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

Finite-time L1 control for positive switched linear systems with time-varying delay

This paper is concerned with the problem of finite-time L₁ control for a class of positive switched linear systems with time-varying delay. Firstly, by using the average dwell time approach, sufficient conditions which can guarantee the L₁ finite-time boundedness of the underlying system are given. Then, in virtue of the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with L₁-gain performance. All the obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be solved conveniently. Finally, an example is given to illustrate the efficiency of the proposed method.     

Robust finite-time H∞ control of singular stochastic systems via static output feedback

This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H_∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H_∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.     

H ∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty

This paper studies the problem of H -control for linear systems with Markovian jumping parameters. The jumping parameters considered here are two separable continuous-time, discrete-state Markov processes, one appearing in the system matrices and one appearing in the control variable. Our attention is focused on the design of linear state feedback controllers such that both stochastic stability and a prescribed H -performance are achieved. We also deal with the robust H -control problem for linear systems with both Markovian jumping parameters and parameter uncertainties. The parameter uncertainties are assumed to be real, time-varying, norm-bounded, appearing in the state matrix. Both the finite-horizon and infinite-horizon cases are analyzed. We show that the control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of coupled differential Riccati equations for the finite-horizon case or algebraic Riccati equations for the infinite-horizon case. Particularly, robust H -controllers are also designed when the jumping rates have parameter uncertainties.     

An H2-Type Norm of a Discrete-Time Linear Stochastic System with Periodic Coefficients Simultaneously Affected by an Infinite Markov Chain and Multiplicative White Noise Perturbations

This article investigates the problem of the definition and computation of an H₂-type norm for discrete-time time-varying periodic stochastic linear systems simultaneously affected by multiplicative white noise perturbations and random jumping according to a Markov chain with an infinite countable number of states. Also, we solve an optimization problem that contains, as a special case, the H₂ optimal control problem for the considered class of stochastic systems under the assumption of perfect state measurements.     

Delay-Dependent Nonfragile <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Observer-Based Control for Neutral Systems with Time Delays in the State and Control Input

The problem of the delay-dependent nonfragile H _∞ observer-based control for a class of neutral systems with time delays is investigated. The additive gain variations under consideration are contained in both the controller gain and the observer gain. Novel delay-dependent criteria are derived to guarantee the stability of the nonfragile H _∞ observer-based control system using the Lyapunov function approach combined with linear matrix inequalities (LMI). The controller and observer gains are given from the LMI feasible solutions. Based on the result of this paper, the constraint of matrix equality is not necessary for designing a nonfragile H _∞ observer-based control. The computer software Matlab can be applied to solve the proposed problems. Finally, a numerical example is given illustrating the design of the nonfragile H _∞ observer-based control. The research was supported by the National Science Council of Taiwan, ROC under Grant NSC 96-2221-E-507-003.     

Robust H∞ control for a class of switched nonlinear cascade systems via multiple Lyapunov functions approach

This paper addresses the problem of robust H_∞ control for a class of switched nonlinear cascade systems with parameter uncertainty using the multiple Lyapunov functions (MLFs) approach. Each subsystem under consideration is composed of two cascade-connected parts. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi equations, sufficient conditions for the solvability of the robust H_∞ control problem are presented. As an application, the hybrid robust H_∞ control problem for a class of uncertain non-switched nonlinear cascade systems is solved when no single continuous controller is effective. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method.