Finite-time control for LPV systems with parameter-varying time delays and exogenous disturbances

In this paper, we consider the stability analysis and control synthesis of finite-time boundedness problems for linear parameter-varying (LPV) systems subject to parameter-varying time delays and external disturbances. First, the concepts of uniform finite-time stability and uniform finite-time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter-varying time delays finite-time bounded, are presented by using parameter-dependent Lyapunov–Krasovskii functionals and free-weight matrix technologies. Moreover, on the basis of the results on the uniform finite-time boundedness, the parameter-dependent state feedback controllers are designed to finite-time stabilize LPV systems. Both analysis and synthesis conditions are delay-dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior-point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach.