Stability of delay impulsive systems with application to networked control systems

Abstract

We establish asymptotic and exponential stability theorems for delay impulsive systems by employing Lyapunov functionals with discontinuities. Our conditions have the property that when specialized to linear delay impulsive systems, the stability tests can be formulated as Linear Matrix Inequalities (LMIs). Then we consider Networked Control Systems (NCSs) consisting of an LTI process and a static feedback controller connected through a communication network. Due to the shared and unreliable channels, sampling intervals become uncertain and variable. Moreover, samples may be dropped or experience uncertain and variable delays before arriving at the destination. We show that the resulting NCSs can be modelled by linear delay impulsive systems and we provide conditions for stability of the closed-loop system in terms of LMIs. By solving these LMIs, one can find a positive constant that determines an upper bound between each sampling time and the subsequent input update time, for which stability of the closed-loop system is guaranteed.