Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

Abstract

AbstractThis paper investigates the non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults. First, a novel fault model consisting of linear and nonlinear terms is established for the systems. By constructing a stochastic co‐positive Lyapunov function, the non‐fragile reliable controller is designed for the systems with additive gain perturbations using matrix decomposition technique. Then, the proposed design is extended for dealing with multiplicative gain perturbations and variable gain perturbations. Under the designed controllers, the resulting closed‐loop systems are positive and stochastically stable. All presented conditions are solvable in terms of linear programming. Finally, two illustrative examples are provided to verify the effectiveness of the theoretical results.