Zhengzhi Han

Robust Stabilization of Discrete-Time Positive Switched Systems with Uncertainties and Average Dwell Time Switching

This paper studies robust problems of a class of discrete-time positive switched systems with uncertainties. The uncertainties refer to interval and polytopic uncertainties. By means of the multiple linear copositive Lyapunov functions approach, the robust stability of autonomous systems with average dwell time is solved. Then, the control synthesis of non-autonomous systems with average dwell time is discussed. State-feedback and output-feedback controllers are designed to guarantee the robust stabilization of the considered systems, respectively. All present conditions are solvable in terms of linear programming. Finally, several simulation examples are given to illustrate the validity of the design.

Absolute exponential stability and stabilization of switched nonlinear systems

Abstract This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings.

L1-gain analysis and control synthesis of positive switched systems

This paper investigates the problems of L1-gain analysis and control synthesis of positive switched systems. Linear supply rates and L1-gain notations are introduced to analyse the performance of the underlying systems. Stability with a weighted L1-gain for autonomous systems are solved by using multiple linear copositive Lyapunov functions incorporated with the average dwell time approach. Then, state-feedback and output-feedback controllers are designed to guarantee the stabilisation with a weighted L1-gain for non-autonomous systems. All present conditions are solvable in terms of linear programming. Finally, a practical example is given to illustrate the validity of theoretical findings.

Globally uniformly asymptotical stabilisation of time-delay nonlinear systems

Globally uniformly asymptotical stabilisation of nonlinear systems in feedback form with a delay arbitrarily large in the input is dealt with based on the backstepping approach in this article. The design strategy depends on the construction of a Lyapunov–Krasovskii functional. A continuously differentiable control law is obtained to globally uniformly asymptotically stabilise the closed-loop system. The simulation shows the effectiveness of the method.

L1/ℓ1-Gain analysis and synthesis of Markovian jump positive systems with time delay.

This paper is concerned with stability analysis and control synthesis of Markovian jump positive systems with time delay. The notions of stochastic stability with L1- and ℓ1-gain performances are introduced for continuous- and discrete-time contexts, respectively. Using a stochastic copositive Lyapunov function, sufficient conditions for the stability with L1/ℓ1-gain performance of the systems are established. Furthermore, mode-dependent controllers are designed to achieve the stabilization with L1/ℓ1-gain of the resulting closed-loop systems. All proposed conditions are formulated in terms of linear programming. Numerical examples are provided to verify the effectiveness of the findings of theory.

Robust model predictive control with ℓ1-gain performance for positive systems

Abstract This paper is concerned with robust model predictive control for positive systems. The technique of model predictive control is extended to the context of positive systems. By using the linear copositive Lyapunov function approach, a robust model predictive controller for positive systems is first constructed. Being unlike the classic robust control with l 2 -gain performance, the robustness of the underlying systems is guaranteed by means of l 1 -gain performance. In order to increase the feasibility of the present conditions, a multi-step control strategy is then utilized. Accordingly, a cone invariant set is addressed to satisfy the recursive feasibility of the present design. All present conditions can be described by linear programming. Meanwhile, the main computation of these conditions is completely off-line, by which the computational burden is reduced. Finally, an illustrative example is given to show the effectiveness of the design.

Uniformly ultimately bounded tracking control of linear differential inclusions with stochastic disturbance

Abstract: The tracking control of linear differential inclusions with stochastic disturbance is considered. The feedback law is constructed by the convex hull Lyapunov function. The design objective is to make the error system uniformly ultimately bounded in mean square. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.

Global asymptotic stabilisation for switched planar systems

This paper studies the stabilisation problem of a class of switched planar systems. The present method is different from the existing one designing directly controllers for the underlying systems. The controllers are constructed through two steps. Firstly, by means of the backstepping approach, homogeneous controllers stabilising the nominal systems are obtained. Secondly, the controllers stabilising the planar subsystems are attained by modifying the obtained homogeneous controllers. The controllers depend on perturbations of the switched systems. Finally, by using the multiple Lyapunov functions approach, a sufficient condition of the stabilisation for switched planar systems is given. The conclusions are extended to multiple dimensional switched systems. An illustrative example verifies the validity of the design.

Robust Stability for Nonlinear Discrete-time Systems with Interval Time-varying Delay

This paper considers the robust stability of linear discrete-time systems with nonlinear perturbations and interval time-varying delay in the state. By using a finite sum inequality approach, new delay-range-dependent stability criteria are developed in terms of linear matrix inequalities (LMIs). It is shown that the proposed criteria can provide less conservative results than some existing ones. A numerical example is included to demonstrate the effectiveness of the proposed approach.

Chaotification via system immersion

By introducing a definition of partially chaotic for a kind of generalized chaotic system, this paper discusses the chaotification problem with a new approach based on (system) immersion and (manifold) invariance. The basic idea is to immerse the plant system into a reduced-order chaotic system. The proposed approach is also applied to chaotify systems with uncertain parameters. Illustrative examples with simulation results are presented to validate the proposed chaotification schemes.