We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switc...

In this paper piecewise quadratic stability of closed-loop affine Takagi-Sugeno (ATS) fuzzy systems with linear state-space submodels in the consequent of rules is addressed. The control law is assumed in the form of Parallel Distributed Compensation (PDC). Stability analysis of the closed-loop system is based on piecewise quadratic Lyapunov functions. This technique reduces conservatism of cla...

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable und...

This paper presents a new approach for the stability analysis of TakagiSugeno (T-S) fuzzy systems. An idea is investigated to use piecewise quadratic Lyapunov function with low amount of computations. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov function, we derive stability conditions that...

in this paper, stabilization conditions and controller design for a class of nonlinear systems are proposed. the proposed method is based on the nonlinear feedback, quadratic lyapunov function and heuristic slack matrices definition. these slack matrices in null products are derived using the properties of the system dynamics. based on the lyapunov stability theorem and sum of squares (sos) dec...