Abstract
In this paper, we deal with the problem of stability and stabilization for linear parameter-varying (LPV) systems with time-varying time delays. The uncertain parameters are assumed to reside in a polytope with bounded variation rates. Being main difference from the existing achievements, the representation of the time derivative of the time-varying parameter is under a polytopic structure. Based on the new representation, delay-dependent sufficient conditions of stability and stabilization are, respectively, formulated in terms of linear matrix inequalities (LMI). Simulation examples are then provided to confirm the effectiveness of the given approach.
Highlights
Linear time-varying (LPV) systems, which depend on unknown but measurable time-varying parameters, have received much attention
In [18], by using parameterdependent Lyapunov functionals and interior-point algorithms, the stability, H∞ gain performance, L2 gain performance, and L2-to-L∞ gain performance are explored for linear parameter-varying (LPV) systems with parameter-varying time delays
Let us consider a polytopic system in the form of (1a) with u(t) = 0
Summary
Linear time-varying (LPV) systems, which depend on unknown but measurable time-varying parameters, have received much attention. The difficulty of using a parameter-dependent Lyapunov function is that if the parameter is time-varying, the rate of variation needs to be taken into account. In [18], by using parameterdependent Lyapunov functionals and interior-point algorithms, the stability, H∞ gain performance, L2 gain performance, and L2-to-L∞ gain performance are explored for LPV systems with parameter-varying time delays. In the light of the above, this paper investigates the stability and stabilization of polytopic LPV systems with parameter-varying time delays. An innovative representation for the rate of variation of the parameter is Mathematical Problems in Engineering stated Based on this representation and parameterdependent Lyapunov functionals, delay-dependent sufficient conditions for the stability and stabilization are derived in terms of LMIs. two examples are given to illustrate the effectiveness of the methods presented in this paper.
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