Analysis Of Stability For Switched Normal Symtems With Perturbed Term

In this paper, we study the stability property for a class of switched linear systems with nonlinear perturbed term whose subsystems are normal. Firstly, we discuss the stability property of discrete-time switched normal systems with perturbed term. when all subsystems are Schur stable and the perturbed term satisfies a certain condition, we show that the discrete-time switched system is uniform ultimate boundedness under arbitrary switching. Then we show that when all subsystems are Hurwitz stable and the perturbed term satisfies a certain condition, the continuous-time switched normal system is uniform ultimate boundedness under arbitrary switching. secondly, we discuss a class of hybrid switched normal system with perturbed term whose subsystems can be continuous-time or discrete-time. When this switched system satisfies a couple of assumptions, we show that the switched normal systems are exponentially stable under arbitrary switching by using common Lyapunov function. Finally, when unstable subsystems are involved, a time-controlled switching law is designed such that the switched system is exponentially stable under this switching law.