Robust Non-Fragile Control of Positive Semi-Markovian Jump Systems With Actuator Saturation

Abstract

This paper is concerned with the non-fragile control problem of the positive semi-Markovian jump systems with actuator saturation. For the semi-Markovian process, a class of non-exponential distributions is considered as the probability distribution of the sojourn-time. First, a family of non-fragile controllers containing gain perturbation terms for the positive semi-Markovian jump systems with actuator saturation is designed using the matrix decomposition technique. By the virtue of linear programming, all obtained conditions guaranteeing the stochastic stability of the closed-loop systems can be directly computed. Then, the presented approach is extended to the systems with interval uncertainties. Under the designed controller, the robust stochastic stabilization of the positive semi-Markovian jump systems with actuator saturation is realized. In addition, an optimization problem is presented to estimate the maximum attraction domain of the system. Finally, a numerical example is provided to verify the effectiveness of the theoretical findings.