State‐feedback control of LPV sampled‐data systems

Abstract

In this paper, we address the analysis and the state‐feedback synthesis problems for linear parameter‐varying (LPV) sampled‐data control systems. We assume that the state‐space data of the plant and the sampling interval depend on parameters that are measurable in real‐time and vary in a compact set with bounded variation rates. We explore criteria such as the stability, the energy‐to‐energy gain (induced L2 norm) and the energy‐to‐peak gain (induced L2 ‐to‐ L∞ norm) of such sampled‐data LPV systems using parameter‐dependent Lyapunov functions. Based on these analysis results, the sampled‐data state‐feedback control synthesis problems are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities that can be solved via efficient interior‐point algorithms.