H∞ and L2 - to - L∞ gain control of linear parameter-varying systems with parameter-varying delays

Abstract

The analysis and state-feedback synthesis problems for linear parameter-varying systems with parameter-varying time delays are addressed. It is assumed that the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore the stability, L2 gain performance and L2 - to- L∞ gain performance for these systems using parameter-dependent Lyapunov functionals. In addition, the design of parameter-dependent state-feedback controllers that guarantee stability and desired induced norm performance are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities that can be solved via efficient interior-point algorithms.