Dynamic Output Feedback Control of 2-D Linear Parameter-Varying Systems

Abstract

This chapter is devoted to studying the robust $\mathcal {H}_{\infty }$ dynamic output feedback (DOF) controller design problem for 2-D LPV systems. For a 2-D discrete system in a form of the well-known FMLSS model with linear time-varying parameters, sufficient conditions are first established for the existence of the desired $\mathcal {H}_{\infty }$ DOF controller in terms of PLMIs. Then, by decoupling technique and linearizing variable transform method, the desired DOF controller can be obtained by solving a convex optimization problem with the application of efficient interior-point optimization algorithm. A gridding technique is applied to convert the infinite-dimensional optimization problem into a finite-dimension one.