Robust variance-constrained fault-tolerant control for a class of nonlinear stochastic systems

This paper is concerned with the variance-constrained controller design problem for a class of uncertain nonlinear stochastic systems with possible actuator faults. The stochastic nonlinearities described by statistical means are quite general that include several well-studied classes of nonlinearities as special cases. A model of actuator failures is adopted which is more practical than the traditional outage one. A linear matrix inequality (LMI) approach is proposed to solve the multiobjective fault-tolerant controller design problem, where both the exponential stability and the steady-state state variance indices are simultaneously guaranteed. Within the developed LMI framework, a sufficient condition for the solvability of the robust control problem is obtained. The explicit expression of the desired controllers is also parameterized and a single degree-of-freedom (SDOF) model is used to demonstrate the effectiveness and applicability of the proposed design approach.