Randomized algorithms for robust stability and control of stochastic hybrid systems with uncertain switching policies

Abstract

It has been suggested that the probabilistic approach may offer some numerical advantages when applied to robust control problems. This paper investigates new possibilities which this approach may offer in relation to robust stability and control of hybrid systems with uncertain switching policies. We consider a hybrid system modeled as a linear continuous-time system with random structure. The changes in the system structure,are governed by a discrete state Markov process which has an uncertain transition probability law. We show that a quadratic Lyapunov function for the system can be efficiently constructed using a combination of randomization techniques and convex optimization. This leads to tractable methodologies for robust stability analysis and robust control design for the class of uncertain hybrid systems under consideration.