Guaranteed cost control for semi-Markovian jump systems by a conditionally mode-dependent controller

This article considers the guaranteed cost control problem of continuous-time semi-Markovian jump system. First, a conditionally mode-dependent controller is proposed, which includes mode-dependent and -independent controllers as special cases. Via exploiting a Lyapunov function method and enlarging techniques, sufficient LMI conditions are presented for solving such a controller directly. All the features such as conditional probability, sojourn time, and transition probability are involved. More extensions about general conditional probabilities such as uncertain and partially unknown cases are considered. Finally, a practical example is given to illustrate the effectiveness and superiority of the proposed methods.