Gain-scheduled open-loop system design for LPV systems using polynomially parameter-dependent Lyapunov functions

Abstract

This paper addresses the design problem of full-order Gain-Scheduled (GS) open-loop systems, such as GS filters and GS inverse systems, which are independent of unmeasurable parameters for Linear Parameter-Varying (LPV) systems in which the state-space matrices are polynomially parameter dependent. Using structured polynomially Parameter-Dependent Lyapunov Functions (PDLFs), in which some conservatism is admitted, we propose design methods for our addressed problems via parametrically affine Linear Matrix Inequality (LMI) conditions that are easily solved via semi-definite programming. For parametrically affine LPV systems including polytopic systems, our design methods theoretically encompass existing methods which use structured quadratically PDLFs. Our proposed methods include robust open-loop system design as a special case. Several numerical examples are introduced to demonstrate the effectiveness of our methods.