Fubo Zhu

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.

Stability analysis of stochastic differential equations with Markovian switching

Abstract This paper discusses the asymptotic stability of the nonlinear stochastic differential equations with Markovian switching (SDEWMSs). The equations under consideration are more general, whose transition jump rates matrix Q is not precisely known. By using the switching process jump times to subdivide the “time” and then investigate the related sequence, we provide sufficient conditions for asymptotic stability of SDEWMSs when each subsystem is stable and a certain “slow switching” condition holds. For the general multi-dimensional linear SDEWMSs, sufficient conditions via bi-linear matrix inequalities are also proposed for the design of robust stabilization. Some examples are given to illustrate the effectiveness of our results.

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.

Moment exponential stability analysis of Markovian jump stochastic differential equations with uncertain transition jump rates

This paper is concerned with the moment exponential stability analysis of Markovian jump stochastic differential equations. The equations under consideration are more general, whose transition jump rates matrix Q is not precisely known. Sufficient conditions for testing the stability of such equations are established, and some numerical examples to illustrate the effectiveness of our results are presented.