Search results for " Lyapunov function"

Fault detection for continuous-time switched systems under asynchronous switching

2013

In this chapter, the problem of FD for continuous-time switched systems under asynchronous switching is investigated. The designed FD filter is assumed to be asynchronous with the original systems. Attention is focused on designing a FD filter such that the estimation error between the residual and the fault is minimized in the sense of H ∞ norm. By employing piecewise Lyapunov function and ADT techniques, a sufficient condition for the existence of such a filter is exploited in terms of certain LMIs. Finally, an example is provided to illustrate the effectiveness of the proposed approach.

Robust reliable passive control of uncertain stochastic switched time-delay systems

2014

This paper investigates the problem of robust reliable passive control for a class of uncertain stochastic switched time-delay systems with actuator failures. The multiple Lyapunov functions (MLFs) technique is exploited to derive a delay-dependent sufficient condition for the stochastic switched time-delay systems to be passive and exponentially stable under a state-based switching law. Moreover, the proposed approach is extended to investigate stochastic switched systems with structured uncertainties. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.

Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits

2014

In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedb…

Stability and l1-gain analysis for positive 2D T–S fuzzy state-delayed systems in the second FM model

2014

This paper considers the problems of delay-dependent stability and l"1-gain analysis for a class of positive two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy linear systems with state delays described by the second FM model. Firstly, the co-positive type Lyapunov function method is applied to establish sufficient conditions of asymptotical stability for the addressed positive 2D T-S fuzzy system. Then, the l"1-gain performance analysis for the positive 2D T-S fuzzy delayed system is studied. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the p…

Stability of a stochastic SIR system

2005

Abstract We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found.

Robust fault detection for switched systems with time-varying delay using delta operator approach

2014