Non-fragile compensation controller design for linear time-invariant systems with adaptive mechanism

This paper presents an adaptive control design method to solve the non-fragile compensation problem for linear time-invariant systems. A state-feedback control gain with time-varying bounded additive gain variations is designed to guarantee the stability of the system. When the bounds of gain variations are unknown, some adaptive laws are constructed in adaptive mechanism to estimate the bounds for eliminating the effects of gain variations. Then the designed control gain and adaptive laws are composed as a non-fragile controller to ensure such that the closed-loop system is asymptotically stable with respect to the controller gain variations. A numerical example is given to illustrate the design methods.