New results on linear parameter-varying time-delay systems

A class of linear parameter-varying time-delay systems where the state-space matrices depend on time-varying parameters and the time-delay is unknown but bounded is considered. Both notions of quadratic stability (using a single quadratic Lyapunov–Krasovskii function) and affine quadratic stability (using parameter-dependent Lyapunov–Krasovskii functions) are investigated. LMI-based delay-independent and delay-dependent conditions are derived for stability testing. Then, state-feedback controllers are designed which guarantee quadratic stability and an induced L 2 -norm bound. We use a parameter-independent quadratic Lyapunov–Krasovskii function for the case of dynamic output feedback control to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set. Numerical examples are presented.