Reliable Finite-Time Robust Control for Sampled-Data Mechanical Systems under Stochastic Actuator Failures

This paper considers the problem of reliable finite-time robust control for uncertain mechanical systems with stochastic actuator failures and aperiodic sampling. A novel model of actuator failure capable of depicting various faulty modes is developed on the basis of homogenous Markov variable. To guarantee the finite-time stability (FTS) and boundedness, a novel fault-tolerant switching controller is developed by virtue of Lyapunov-Krasovskii functional and stochastic analysis technique, simultaneously, the finite-time H_∞ performance is also ensured to attenuate the mechanical vibration caused by external disturbances. With convex optimization algorithm, the anticipated controller can be procured by solving a set of linear matrix inequalities (LMIs). Finally, two practical examples of mechanical systems, one of which is governed by lumped parameters and the other is described by distributed parameters, are proposed to prove the effectiveness of the theoretical developments of this study.