The stability analysis of systems with nonlinear feedback expressed by a quadratic program

Author

Li, Guang ; Heath, William P. ; Lennox, Barry

Author_Institution

Control Syst. Centre, Manchester Univ.

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

4247

Lastpage

4252

Abstract

We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP). We establish quadratic constraints from the Karush-Kuhn-Tucker (KKT) conditions that may be used to construct a piecewise quadratic Lyapunov function via the S-procedure. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion. Our approach can be extended to model predictive control (MPC), and gives equivalent results to those in the literature but with a much lower dimension LMI criterion

Keywords

Lyapunov methods; closed loop systems; feedback; linear matrix inequalities; linear systems; nonlinear control systems; predictive control; quadratic programming; stability; Karush-Kuhn-Tucker conditions; Lyapunov function; closed loop system; linear matrix inequality; linear time invariant plant; model predictive control; nonlinear feedback; quadratic program; stability analysis; Control systems; Linear feedback control systems; Linear matrix inequalities; Lyapunov method; Nonlinear control systems; Quadratic programming; Stability analysis; Stability criteria; Temperature control; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.376768

Filename

4177607