Piecewise affine model-based H∞ static output feedback control of constrained non-linear processes

Abstract

This study develops two efficient static output feedback (SOF) control approaches for a class of constrained non-linear processes represented by uncertain piecewise affine models. The parameter uncertainties in the piecewise affine models are assumed to be time varying and norm bounded. With the aid of the congruence transformation, degenerate ellipsoids-based S-procedure, and some bounding inequalities, the piecewise SOF controller can be easily obtained by solving a convex semi-definite programming problem subject to some linear matrix inequalities. The resulting closed-loop system stability can be guaranteed as well as the H ∞ control performance, and the stabilising design is less conservative owing to the piecewise quadratic Lyapunov functions. The performance of the proposed control approaches are demonstrated by simulation results on a non-linear benchmark plant.