Non-fragile delay-dependent H ∞ control of linear time-delay system with uncertainties in state and control input

Abstract

The problem of designing a non-fragile delay-dependent H ∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral inequality method and Lyapunov-Krasovskii stability theory were used to derive new delay-dependent bounded real lemmas for a non-fragile state-feedback controller containing additive or multiplicative uncertainties. They ensure that the closed-loop system is internally stable and has a given H ∞ disturbance attenuation level. Then, methods of designing a non-fragile H ∞ state feedback controller were presented. No parameters need to be tuned and can be easily determined by solving linear matrix inequalities. Finally, the validity of the proposed methods was demonstrated by a numerical example with the asymptotically stable curves of system state and controller output under the initial condition of x(0)=[1 0 −1]T and h=0.8 time-delay boundary.