Robust control design for hybrid systems based on Markovian jumping models

A. class of hybrid systems, which represented as a finite family of stochastic differential models is considered. Each model of this family describes the individual regime of the system. The transitions between these regimes are modelled by a homogeneous Markov chain. Both state and output feedback control laws are obtained, which guarantee stability in the mean square of closed-loop hybrid system for arbitrary transitions intensity and at the same time minimize a quadratic cost functional. An application to autopilot synthesis for high maneuvering aircraft is also given.