Robust stabilization and optimization of fault tolerant linear systems

The piecewise deterministic linear systems represent an interesting class of systems which can describe a large variety of processes. One of the most important area is in design of fault prone systems (see e.g. [A. Swierniak et al., 1998], [D.D. Siljak, 1980], [D.D. Sworder], where real world practical systems are discussed). In this paper. we consider the continuous time linear systems with abrupt changes of parameters modelled by discrete-state Markov processes. The changes may result from faults of actuators or sensors in the system and are localized by diagnostic equipment. Under the assumption of the existence of a suitable control law, we give the necessary and sufficient conditions for the stochastic stabilizability of the nominal model of this class of systems and optimality of the control law. Moreover assuming that the parameters of the real system may differ from their nominal values we present sufficient conditions of the robustness for the real systems.