Robust Hybrid Control Design for Stochastic Markovian Jump System via Fault Alarm Approach

Abstract

In this brief, the fault alarm-based hybrid control is developed for a class of stochastic Markovian jump systems subject to actuator faults, disturbances and time-varying delay. The main objective of this brief is to design a reliable state feedback controller such that the resulting closed-loop system is stochastically stable under a prescribed $H_{\infty }$ performance level $\gamma > 0$ in the presence of actuator faults. More precisely, an alarm signal is considered by designing suitable threshold to avoid false alarm, (i.e.,) to invoke the reliable controller and remove the estimated value of actuator failure. Based on the Lyapunov stability theory and the extended Wirtinger-based single integral inequality, a novel set of sufficient criteria is constructed in the form of linear matrix inequality (LMI) constraints to ensure the stochastic stability of the addressed system. Further, the control design parameters are calculated by solving the developed LMI constraints. Finally, two numerical examples including RLC series circuit with simulation results is provided to illustrate the effectiveness of the proposed control scheme.