Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 31561, 26 pages
Research Article

Multiobjective Output Feedback Control of a Class of Stochastic Hybrid Systems with State-Dependent Noise

S. Aberkane, J. C. Ponsart, and D. Sauter

Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS), UMR 7039, Université Henri Poincaré, Nancy 1, BP 239, Vandœuvre-lès-Nancy Cedex 54506, France

Received 27 March 2006; Revised 12 January 2007; Accepted 9 March 2007

Academic Editor: Nahum Shimkin

Copyright © 2007 S. Aberkane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP) and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI) process. The specifications and objectives under consideration include stochastic stability, 2 and (or more generally, stochastic integral quadratic constraints) performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.