One-shot design of performance scaling matrices and observer-based gain-scheduled controllers depending on inexact scheduling parameters

Abstract

This paper addresses the design problem of continuous-/discrete-time observer-based Gain-Scheduled Output Feedback (GSOF) controllers for Linear Parameter-Varying (LPV) systems, in which some of the state-space matrices are multi-affine with respect to parameters, with the simultaneous design of scaling matrices for multiple uncertainty blocks under the supposition that inexact scheduling parameters are available. In the design of GSOF controllers for practical systems in induced L2∕l2-norm control framework, the following features are to be incorporated; i) structured and easily-understandable controllers are preferable to enhance the practicality, ii) the scaling matrices related to multiple uncertainty blocks which represent various design specifications are also to be designed to reduce conservatism, and iii) one-shot design is preferable to prevent numerical problems in iterative algorithm. However, in general, neither the design problems of the structured controllers nor the simultaneous design of controllers and the performance scaling matrices are formulated in terms of Linear Matrix Inequalities (LMIs). Under the supposition that the uncertainties in the provided scheduling parameters are bounded (this supposition holds true for proportional uncertainties and for absolute uncertainties as well as for the mixed ones of them), we derive a new tractable one-shot multi-affine condition for our problem via dilated/extended LMI technique under some mild assumptions for LPV systems. A numerical example well illustrates the effectiveness of our method.