Stability analysis of nonlinear quadratic systems via polyhedral Lyapunov functions

作     者：Amato, Francesco Calabrese, Francesco Cosentino, Carlo Merola, Alessio 

作者机构：Magna Graecia Univ Catanzaro Sch Comp Sci & Biomed Engn I-88100 Catanzaro Italy MIT SENSEable City Lab Cambridge MA 02139 USA 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：2011年第47卷第3期

页      面：614-617页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

主　　题：Nonlinear systems Quadratic systems Lyapunov stability Domain of attraction Polyhedral functions LMIs optimization 

摘      要：Quadratic systems play an important role in the modeling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). For such systems it is mandatory not only to determine whether the origin of the state space is locally asymptotically stable, but also to ensure that the operative range is included into the convergence region of the equilibrium. Based on this observation, this paper considers the following problem: given the zero equilibrium point of a nonlinear quadratic system, assumed to be locally asymptotically stable, and a certain polytope in the state space containing the origin, determine whether this polytope belongs to the domain of attraction of the equilibrium. The proposed approach is based on polyhedral Lyapunov functions, rather than on the classical quadratic Lyapunov functions. An example shows that our methodology may return less conservative results than those obtainable with previous approaches. (c) 2010 Elsevier Ltd. All rights reserved.