Control Lyapunov function method for robust stabilization of multistable affine nonlinear systems

被引：2

作者：

Barroso, Nelson F. F. ^{[1
,2
]}

Ushirobira, Rosane ^{[1
]}

Efimov, Denis ^{[1
]}

机构：

[1] Univ Lille, Inria, CNRS, UMR 0189 CRIStAL, F-59000 Lille, France

[2] Univ Lille, Inria, CNRS, UMR 0189 CRIStAL, 40,Av Halley,Villeneuve Ascq, F-59650 Lille, France

来源：

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL | 2023年 / 33卷 / 11期

关键词：

control Lyapunov functions; (integral) input-to-state stability; multistability; TO-STATE STABILITY; UNIVERSAL CONSTRUCTION; INPUT; FEEDBACK; ISS;

D O I：

10.1002/rnc.6700

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we study the problem of robust stabilization of affine nonlinear multistable systems in the presence of exogenous disturbances. The results are based on the theory of input-to-state stability (ISS) and integral input-to-state stability (iISS) for systems with multiple invariant sets. The notions of ISS and iISS control Lyapunov functions (CLFs) and the small control property are extended within the multistability framework. Such properties are also complemented by the concept of a weak iISS CLF and corresponding small control property. It is verified that the universal control formula can be applied to yield the ISS (iISS) property for the closed-loop system. The efficiency of the extended CLF framework in the multistable sense is illustrated for a Duffing system and in application to a noise-induced transition in a semiconductor-gas-discharge gap system.

引用

页码：6354 / 6370

页数：17

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