Composite hierarchical control for Markovian jump systems with multiple disturbances and time-varying fault

Abstract

We investigate a robust fault-tolerant control problem for continuous-time Markovian jump systems with an actuator fault and multiple disturbances (one is norm-bounded, whereas the other can be modelled by an exogenous system). Our aim is to construct, simultaneously, a model-dependent disturbance observer for modelling the disturbance estimate and a model-dependent fault diagnosis observer for the time-varying fault estimate and then propose a composite hierarchical control scheme by integrating the fault and disturbance estimates using a state feedback control strategy. Application of the ${\mathcal{H}}_{\infty }$ control methodology ensures stochastic stability of the resulting composite system with fault compensation, disturbance attenuation and rejection performances. On the basis of Lyapunov stability theory, the existence conditions of the disturbance observer, fault diagnosis observer and composite controller are derived from the solution to a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed techniques.