Robust Invariant Control Synthesis for Discrete-Time Polytopic Uncertain Linear Hybrid Systems

In this paper, a class of discrete-time uncertain linear hybrid systems, which is affected by both parameter variations and exterior disturbances, is considered. The goal here is to synthesize a hybrid control law, which includes the continuous variable control law and the discrete event control signal, so as to guarantee the controlled invariance for a specific region in the hybrid state space. It turns out that the continuous variable control law is a piecewise linear state feedback control based on the partition of the given region’s continuous variable state space projection. A numerical example is given for illustration.