Robust Static Output Feedback H_{infinity} Control of a Class of Stochastic Hybrid Systems in Noisy Environment: LMI Formulation

Samir Aberkane (1) , Jean-Christophe Ponsart (1) , Frédéric Hamelin (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

In this paper, we address the robust static output feedback control problem of continuous time active fault tolerant control system with Markovian parameters (AFTCSMP) subject to structured parameter uncertainties, in noisy environnement. We will first derive a necessary and sufficient condition for the robust internal exponential stability in the mean square of the uncertain AFTCSMP in terms of nonlinear matrix inequalities. Then, an LMI relaxation scheme is presented to eliminate the nonlinearities, yielding a new easily tractable sufficient condition. Having obtained this result, we can move on the control problem and write the robust output feedback H_{infinity} control problem of the uncertain continuous time AFTCSMP in terms of an LMI optimization problem. The convex approach naturally leads to powerful numerical algorithms to solve these problematic. A numerical example is presented to illustrate the theoretical results.

Mots clés: LMI; Active Fault Tolerant Control; Stochastic Hybrid systems; Markovian jumping parameters; H_{infinity} control; Output Feedback; Structured Uncertainties; Wiener Process; Lyapunov stability; LMI.

Domaines: Automatique / Robotique

Samir Aberkane, Jean-Christophe Ponsart, Frédéric Hamelin. Robust Static Output Feedback H_{infinity} Control of a Class of Stochastic Hybrid Systems in Noisy Environment: LMI Formulation. Aug 2006, pp.1495-1500. ⟨hal-00121661⟩