Gain-scheduled state-feedback control for LPV time-delay systems based on multiple performances

This paper is concerned with the gain-scheduled control problem for continuous-time linear parameter-varying (LPV) systems with time-varying delays and energy-bounded disturbances. Attention is focused on the design of state-feedback controllers with the controller gains depending on the time-varying parameters, such that the resulting closed-loop system is asymptotically stable and the controlled output and disturbance input satisfy a prescribed performance inequality. The performance inequality introduced in this paper covers the well-known H_∞ performance, L₂-L_∞ performance, passivity and disspativity as special cases. Delay-dependent conditions for the existence of desired controllers are obtained by using a parameter-dependent Lyapunov-Krasovskii functional together with a recently developed integral inequality. When the obtained conditions are feasible, the desired controller gains can be constructed by using the feasible solutions to those conditions. Moreover, the obtained conditions are further converted into linear matrix inequalities (LMIs) for the particular case where the system coefficients are assumed to take a polytopic form.