Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls

被引：20
|
作者：
Milani, BEA [1 ]
机构：
[1] Univ Estadual Campinas, Fac Engn Eletr & Comp, BR-13081970 Campinas, SP, Brazil
来源：
AUTOMATICA | 2002年 / 38卷 / 12期
关键词：
discrete-time systems; actuator saturation; Lyapunov functions; stability regions; linear programming;
D O I：
10.1016/S0005-1098(02)00193-0
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper is concerned with piecewise-affine (PWA) functions as Lyapunov function candidates for stability analysis of time-invariant discrete-time linear systems with saturating closed-loop control inputs. Using a PWA model of saturating closed-loop system, new necessary and sufficient conditions for a PWA function be a Lyapunov function are presented. Based on linear programming formulation of these conditions, an effective algorithm is proposed for construction of such Lyapunov functions for estimation of the region of local asymptotic stability. Compared to piecewise-linear functions, like Minkowski functions, PWA functions are more adequate to capture the dynamical effects of saturation nonlinearities, giving strictly less conservative results. The complexity of the proposed approach is polynomial in state dimension and exponential in saturating control dimension, being hence appropriate for problems with large state dimension but with few saturating inputs. (C) 2002 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：2177 / 2184
页数：8
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