Cong Liu, Lijuan Xu, and Simon X. Yang
Markov jump systems, nonlinear systems, time delay, stochastically stable, PID, LMI
The robust proportional–integral–diﬀerential (PID) control strategy is extended to more complex nonlinear stochastic Markov jump systems with state and input delay in this paper. A new proposal of controller design is presented which can realize stochastic stability, robustness of the stochastic systems and favourable tracking performance of the system state. By adopting the Lyapunov stability
theory and the peak-to-peak measure, a PID tracking controller is built to ensure the stochastic stability and optimize the state tracking performance of the stochastic systems than a PI controller which can make the state vector track the given dynamic signal with zero steady-state error, and to enhance the ability of restraining
disturbance and the robustness of the stochastic systems. And by combining the improved convex linear matrix inequality) algorithms, the suﬃcient condition is given which can guarantee the solvability of the multiple objective control for the stochastic systems and
the controller gains can be computed. Finally, numerical examples are provided to demonstrate the eﬀectiveness of the presented approach.