Discrete-time Gain-Scheduled Output-Feedback controllers exploiting inexact scheduling parameters via Parameter-Dependent Lyapunov Functions

This paper addresses the design problem of Gain-Scheduled Output-Feedback (GSOF) controllers for discretetime Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). In our problem setting, it is supposed that scheduling parameters are provided with some uncertainties. In this practical problem setting, we give a sufficient condition for designing GSOF controllers exploiting the uncertain scheduling parameters which minimize the induced l₂-norm in terms of Parameter-Dependent Bilinear Matrix Inequalities (PDBMIs). Two algorithms for solving the PDBMIs, i.e. line search and iterative algorithms, are shown. Under the ideal situation, i.e. exact values of scheduling parameters are available, our method then recovers the conventional design method via PDLFs.