Common stabilizers for linear control systems in the presence of actuators outage

Issue concerning the existence of common stabilizers for a linear control system experiences actuators’ outage are presented. The possible outage of actuators examined in this study are not restricted to a pre-specified set. By finding common quadratic-type Lyapunov functions, we obtain sufficient conditions for the existence of common stabilizers. For cases of which all the possible failed actuators belonged to a pre-specified set, the results presented in this paper agree with those obtained by Veillette in 1995. The control gain of common stabilizer for non-nested case is explicitly derived to guarantee system stability. A simplified checking condition for the existence of common stabilizers is also obtained for the extreme case when only single actuator can normally operate.