Static output feedback control for LPV systems under affine uncertainty structure

Abstract

This paper addresses the static output feedback (SOF) control design problem of Linear Parameter Varying (LPV) affine systems. We aim all along the work to establish robust stability and stabilizability conditions, formulated in terms of Linear Matrix Inequalities (LMIs). The conditions are parameterized by a real α that allows to bring to feasibility some unfeasible problems. Also the separation between the Lyapunov matrix and the state matrix are done by use of some useful lemmas. This reduces the conservatism engendered and achieves the relaxation of the problem by the addition of slack variables.We prove by numerical examples the contribution of the newly proposed approach for both the analysis and the synthesis of the LPV system.

Generalized robust gain-scheduled PID controller design for affine LPV systems with polytopic uncertainty

“…Along this line, convexity in the scheduling and uncertain parameters can be ensured also by restricting the closed-loop LPV structure, system or controller to avoid cross term effects of the scheduling parameters. Authors in [30], within the framework of static outputfeedback controller design, ensured convexity under AQS conditions for affine LPV systems by making the static output-feedback controller parameters independent on the scheduled parameters. In [31], the author has restricted the system interconnection with the control input u(t) to be parameter-independent, and hence he annihilated multiplication of the scheduling parameters.…”

Robust discrete-time gain-scheduled guaranteed cost PSD controller design

“…Furthermore, different relaxation techniques have been deployed to reduce the conservativeness caused by the multi-convexity requirement [11], [12], [13], [14]. Multi-convexity has been differently solved, usually by restricting the closed-loop LPV structure, system or controller to avoid cross term effects of the scheduling parameters [15], [16], [17], [18].…”