http://hdl.handle.net/1983/1598 Wed, 15 May 2013 19:32:41 GMT 2013-05-15T19:32:41Z http://hdl.handle.net/1983/1609 The stability analysis of systems with nonlinear feedback expressed by a quadratic program Li, G; Heath, William P; Lennox, Barry 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 Fri, 01 Dec 2006 00:00:00 GMT http://hdl.handle.net/1983/1609 2006-12-01T00:00:00Z http://hdl.handle.net/1983/1608 An improved stability criterion for a class of Lur'e systems Li, G; Heath, William P; Lennox, Barry We consider the stability of the feedback connection of a linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program. By generalizing the class of candidate Lyapunov functions we improve on existing results in the literature. A Lyapunov function is constructed via the S-procedure from quadratic constraints established using the Karush-Kuhn-Tucker (KKT) conditions. The stability criterion can be expressed as a linear matrix inequality (LMI) condition. We discuss some simple examples that demonstrate the improved results. Sat, 01 Dec 2007 00:00:00 GMT http://hdl.handle.net/1983/1608 2007-12-01T00:00:00Z http://hdl.handle.net/1983/1607 Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program Li, G; Heath, William P; Lennox, Barry 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. Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/1983/1607 2008-01-01T00:00:00Z http://hdl.handle.net/1983/1606 A disturbance rejection anti-windup framework and its application to a substructured system Li, G; Herrmann, G; Stoten, DP; Tu, J-Y; Turner, MC In this paper, we consider the disturbance rejection problem of stable systems with input saturation based on the anti-windup (AW) framework developed by Weston and Postlethwaite (W&P). The performance is improved by explicitly incorporating a transfer function representing the effect of the disturbance on the nonlinear loop during the AW compensator synthesis. The suggested AW-design approach improves disturbance rejection performance over the design framework usually suggested for the coprime-factorization based W&P-approach. For this, an extra degree of freedom is exploited for the coprime factorization which usually results in an implicitly computed multivariable algebraic loop for the AW-implementation. Suitable suggestions are made to overcome the algrabraic loop through explicit computations. The approach is applied to the control of a dynamic substructured system (DSS) subject to a measurable excitation/disturbance signal and actuator limits. The benefit of this approach is demonstrated for a quasi-motorcycle DSS simulation. Mon, 01 Dec 2008 00:00:00 GMT http://hdl.handle.net/1983/1606 2008-12-01T00:00:00Z