Adaptive Reliable $H_\infty $ Static Output Feedback Control Against Markovian Jumping Sensor Failures

This paper investigates the adaptive H
_∞
static output feedback (SOF) control problem for continuous-time linear systems with stochastic sensor failures. A multi-Markovian variable is introduced to denote the failure scaling factors for each sensor. Different from the existing results, the failure parameters are stochastically jumping and their bounds of are unknown. An adaptive reliable H
_∞
SOF control method is proposed, where the controller parameters are updated automatically to compensate for the failure effects on systems. A novel cubic absolute Lyapunov function is proposed to design adaptive laws only using measured output with sensor failures, and the convergence of jumping adaptive parameters is ensured by a trajectory initialization approach. The resultant designs can guarantee the asymptotic stability with an adaptive H
_∞
performance of closed-loop systems regardless of sensor failures. Finally, the simulation results on the “Raptor-90” helicopter are given to show the effectiveness of the proposed approaches.