A Delta-operator Approach to Robust Stabilization for Uncertain Time-delay Systems with Jumping Parameter

Abstract

This paper deals with the robust stabilization for a class of linear Delta-operator formulated uncertain systems with state delays and jumping parameters. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The class of systems is a hybrid class of systems with two components in the vector state. The first component refers to the mode and the second one to the state. The mode is described by a continuous Markov process with finite state space. The state in each mode is denoted by a stochastic differential equation. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust stabilizing control law is derived. Based on this condition, a robust memoryless stabilizing control law is designed in terms of a set of linear matrix inequalities. A numerical example demonstrates the effect of the proposed design approach.