Finite-time fault tolerant control of uncertain singular Markovian jump systems with bounded transition probabilities

This paper is concerned with the problem of finite-time fault-tolerant control for one family of uncertain singular Markovian jump with bounded transition probabilities and nonlinearities systems. The actuator faults are presented as a more general and practical continuous fault model. Partially known transition rate parameters have given lower and upper bounds. Firstly, the resulting closed-loop error system is constructed based on a state estimator; sufficient criteria are provided to guarantee that the augmented system has singular stochastic finite-time boundedness and singular stochastic \(H_\infty \) finite-time boundedness in both normal and fault cases. Then, by employing a decoupling technique, the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to demonstrate the effectiveness of the proposed design approach.