Stability analysis for discrete linear systems with state saturation by a saturation-dependent Lyapunov functional

This paper concerns the stability analysis problem of discrete linear systems with state saturation using a saturation-dependent Lyapunov functional.We introduce a free matrix characterized by the sum of the absolute value of each elements for each row less than 1,which makes the state with saturation constraint reside in a convex polyhedron.A saturation-dependent Lyapunov functional is then designed to obtain a sufficient condition for such systems to be globally asymptotically stable.Based on this stability criterion,the state feedback control law synthesis problem is also studied.The obtained results are formulated in terms of bilinear matrix inequalities that can be solved by the presented iterative linear matrix inequality algorithm.Two numerical examples are used to demonstrate the effectiveness of the proposed method.     

Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed using a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimization problem. Numerical examples are presented to show the effectiveness of the proposed method.