Common Lyapunov function computation for discrete-time systems

被引：0

作者：

Hafstein, Sigurdur Freyr ^{[1
]}

机构：

[1] Univ Iceland, Fac Phys Sci, IS-107 Reykjavik, Iceland

来源：

2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC) | 2018年

关键词：

STABILITY;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.

引用

页码：3211 / 3216

页数：6

共 50 条

[41] Model order reduction for discrete-time linear systems with the discrete-time polynomials [J].

Yao-Lin Jiang ;

Jun-Man Yang ;

Kang-Li Xu .

Japan Journal of Industrial and Applied Mathematics, 2019, 36 :1005-1020

[42] Computation of Neural Networks Lyapunov Functions for Discrete and Continuous Time Systems with Domain of Attraction Maximization [J].

Bocquillon, Benjamin ;

Feyel, Philippe ;

Sandou, Guillaume ;

Rodriguez-Ayerbe, Pedro .

PROCEEDINGS OF THE 12TH INTERNATIONAL JOINT CONFERENCE ON COMPUTATIONAL INTELLIGENCE (IJCCI), 2020, :471-478

[43] Local Control Lyapunov Functions for Constrained Linear Discrete-Time Systems: The Minkowski Algebra Approach [J].

Rakovic, Sasa V. ;

Baric, Miroslav .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (11) :2686-2692

[44] Local assignability of Lyapunov exponents of linear discrete-time system [J].

Banshchikova, I. N. .

IZVESTIYA INSTITUTA MATEMATIKI I INFORMATIKI-UDMURTSKOGO GOSUDARSTVENNOGO UNIVERSITETA, 2021, 57 :3-76

[45] Control of discrete-time nonlinear systems via finite-step control Lyapunov functions [J].

Noroozi, Navid ;

Geiselhart, Roman ;

Gruene, Lars ;

Wirth, Fabian R. .

SYSTEMS & CONTROL LETTERS, 2020, 138

[46] Lyapunov Functions, Stability and Input-to-State Stability Subtleties for Discrete-Time Discontinuous Systems [J].

Lazar, Mircea ;

Heemels, W. P. Maurice H. ;

Teel, Andy R. .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (10) :2421-2425

[47] Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems [J].

Sun, C. ;

Fang, B. ;

Huang, W. .

IET CONTROL THEORY AND APPLICATIONS, 2011, 5 (03) :535-537

[48] Stability and linearization: discrete-time systems [J].

Sandberg, IW .

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, 2002, 30 (05) :511-517

[49] Discrete-time negative imaginary systems [J].

Ferrante, Augusto ;

Lanzon, Alexander ;

Ntogramatzidis, Lorenzo .

AUTOMATICA, 2017, 79 :1-10

[50] On the stabilization of linear discrete-time systems [J].

Ferreira, C ;

Silva, FC .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 390 :7-18

← 1 2 3 4 5 →