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

G. Li; W.P. Heath; B. Lennox

doi:10.1109/CDC.2006.376768

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

G. Li
, W.P. Heath
, B. Lennox

University of Manchester

Research output: Contribution to conference › Paper › peer-review

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

Original language	Unknown
Pages	4247-4252
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2006.376768
Publication status	Published - 7 May 2007
Externally published	Yes
Event	Proceedings of the 45th IEEE Conference on Decision and Control - San Diego, United States Duration: 13 Dec 2006 → 15 Dec 2006

Conference

Conference	Proceedings of the 45th IEEE Conference on Decision and Control
Country/Territory	United States
City	San Diego
Period	13/12/06 → 15/12/06

Access to Document

10.1109/CDC.2006.376768

Cite this

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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",

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