Research ArticleObserver-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate

- The finite-time stability, H∞ boundedness, H∞ state feedback stabilization and SMC problems are investigated for the first time.
- The condition that all the transition rates among modes are known and all states are observable are relaxed.
- A component observer-based robust finite-time SMC is designed to cope with the effect of partially unknown transition rate and unmeasured state.
- Some less conservative sufficient conditions are provided to illustrate the stability properties of sliding mode dynamics.

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem.