Abstract: The synthesis problem of reliable robust control for a class of dynamic systems is considered. A practical and general faults model with sensor, actuator is addressed. A necessary and sufficient condition of D -stability is presented, based on which a sufficient condition of existence of the reliable H_∞ controller is given for the case of sensor, actuator failures. The reliable H_∞ controller is designed in terms of linear matrix inequalities (LMIs), which guarantees the closed-loop to be D -stable and possesses H_∞ performance when all control components are operational as well as some control components experience failures. Finally, a numerical example is given to illustrate the design procedures and the effectiveness.

Key words: Dynamic systems, D -stability, Reliable control, Linear matrix inequality (LMI).