The finite-time stability, H_∞$H_{\infty }$ boundedness, H_∞$H_{\infty }$ 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.