Box invariance in biologically-inspired dynamical systems

被引：65

作者：

Abate, Alessandro ^{[1
]}

Tiwari, Ashish ^{[2
]}

Sastry, Shankar ^{[3
]}

机构：

[1] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

[2] SRI Int, Comp Sci Lab, Menlo Pk, CA 94025 USA

[3] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

来源：

AUTOMATICA | 2009年 / 45卷 / 07期

关键词：

Positive invariance; Invariant sets; Biological systems; Nonquadratic Lyapunov functions; Switched and Hybrid systems; STABILITY;

D O I：

10.1016/j.automatica.2009.02.028

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A dynamical system is box invariant if there exists a box-shaped positively invariant region. We show that box invariance can be checked in cubic time for linear and affine systems, and that it remains decidable for classes of nonlinear systems of interest (with polynomial structure). We present results on the robustness of box invariance for linear systems using spectral properties of Metzler matrices. We also present sufficient conditions for establishing box invariance of switched and hybrid systems. In general, we argue that box invariance is a characteristic of many biologically-inspired dynamical models. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1601 / 1610

页数：10

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