Exponential Stability Analysis and Controller Design for LTI Positive System with Controller Failure

This paper studies exponential stability and fault tolerant control for linear time-invariant (LTI) positive system with controller failure. Through dwell time (DT) and mode-dependent average dwell time (MDADT) approach, sufficient conditions of globally uniformly exponential stability (GUES) are proposed. We treat the mode changing between controller work and failure as a switch. The main idea is using switching behavior to compensate the increment of Lyapunov function (LF) produced by controller failure, introducing the multiple linear copositive Lyapunov function (MLCLF) method to obtain less conservative results. By solving the linear programming problem, the switched positive system can be GUES under the constraint of DT and MDADT. On this basis, a fault tolerant controller is designed. Numerical examples are provided to show the effectiveness of the results.