Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program
IET Control Theory and Applications
Institution of Engineering and Technology (IET)
The stability of the feedback connection of a strictly proper linear time-invariant stable system with a static nonlinearity expressed by a convex quadratic program (QP) is considered. From the Karush-Kuhn-Tucker conditions for the QP, quadratic constraints that may be used with a quadratic Lyapunov function to construct a stability criterion via the S-procedure are established. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion and is much easier to implement. This approach can be extended to model predictive control and gives equivalent results to those in the literature but with a much lower dimension LMI criterion.
Copyright © 2008 Institution of Engineering and Technology (IET). This paper is a postprint of a paper submitted to and accepted for publication in IET Control Theory and Applications and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library.
Vol. 2 (7), pp. 554 - 563