Robust non-fragile hybrid control for delayed uncertain singular impulsive jump systems based on improved impulse instant-dependent auxiliary functions method

This article researches the issue of robust non-fragile hybrid control for delayed uncertain singular impulsive jump systems (USIMJSs). The key aim is to design non-fragile hybrid state feedback controllers (including a non-fragile normal state feedback controller and a non-fragile impulsive state feedback controller), which are insensitive to the uncertainties of gains of controllers and can provide sufficient tuning margins. The non-fragile normal state feedback controller can eliminate the internal impulses and overcome the external disturbances; the non-fragile impulsive state feedback controller can suppress the interference of external unstable impulses and restrain the instantaneous jumps caused by Markovian modes switching. By introducing impulse instant-dependent auxiliary functions, the improved impulse-time-dependent Lyapunov–Krasovskii functional is constructed, which can capture the information of the impulse instants and Markovian jump modes. Novel criteria of robust admissibilization for delayed USIMJSs are acquired under linear matrix inequalities framework. Lastly, the effectiveness of the derived algorithm and designed method is confirmed by simulation examples including a direct current motor-controlled inverted pendulum device and a Quarter-Car active suspension model.