Reliable H∞ Control of Static Output Feedback against Sensor Failure

In this study, the design of a reliable H
_∞
controller with static output feedback is studied for a linear steady-state system with continuous gain and single fault of the sensor. First, the necessary and sufficient conditions and design methods for the existence of a normal H
_∞
controller are given. When the sensor has a single continuous gain failure, the system cannot maintain stability. Then, using the linear matrix inequality (LMI) method and the convex combination processing of the continuous gain fault model, the necessary and sufficient conditions and design methods for the existence of a reliable H
_∞
controller are given. The obtained reliable controller enables the closed-loop system to maintain asymptotic stability and H
_∞
performance indicators regardless of whether components fail. Finally, the validity and feasibility of the design method are verified by numerical simulation.