Stochastic Stability of a Class of Stochastic Bilinear Hybrid systems: Convex Analysis and Synthesis

This paper deals with the problem of local exponential stochastic stabilization of continuous time Bilinear Active Fault Tolerant Control Systems with Markovian Parameters (BAFTCSMP). The design technique is based on a differential inclusion of the bilinear term for a restricted domain of the state space. The above problematic is addressed under a convex programming approach. Indeed, conditions for local stochastic stability of the BAFTCSMP are derived and formulated through some matrix inequalities. The implicit problem being to maximize the region in which the closed-loop stability can be ensured, some convex optimization problems with LMI (linear matrix inequalities) relaxations schemes are stated. A numerical example is presented to illustrate the theoretical results.