Energy functions for dissipativity-based balancing of discrete-time nonlinear systems

被引:5
作者
Lopezlena, Ricardo [1 ]
Scherpen, Jacquelien M. A. [1 ]
机构
[1] Delft Univ Technol, Delft Ctr Syst & Control, NL-2628 CD Delft, Netherlands
关键词
nonlinear systems; dissipative systems; discrete-time systems; controllability; observability;
D O I
10.1007/s00498-006-0007-z
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Most of the energy functions used in nonlinear balancing theory can be expressed as storage functions in the framework of dissipativity theory. By defining a framework of discrete-time dissipative systems, this paper presents existence conditions for their discrete-time energy functions along with algorithms to find them based on dynamic optimization problems. Furthermore, the important case of the nonlinear discrete-time versions of the controllability and observability functions, its properties and algorithms to find them are presented. These algorithms are illustrated with linear and nonlinear examples.
引用
收藏
页码:345 / 368
页数:24
相关论文
共 50 条
[41]   Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems [J].
Hanba, Shigeru .
AUTOMATICA, 2017, 76 :49-52
[42]   Equivalent types of ISS Lyapunov functions for discontinuous discrete-time systems* [J].
Geiselhart, Roman ;
Noroozi, Navid .
AUTOMATICA, 2017, 84 :227-231
[43]   Stabilization to ISS for Discrete-time Impulsive Hybrid Systems with Mixed K-Dissipativity [J].
Liu Bin ;
Liu Tengfei ;
Hill, David J. .
2011 30TH CHINESE CONTROL CONFERENCE (CCC), 2011, :1753-1758
[44]   On the genericity of the observability of controlled discrete-time systems [J].
Ammar, S ;
Vivalda, JC .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2005, 11 (02) :161-179
[45]   Steady-State Analysis and Regulation of Discrete-Time Nonlinear Systems [J].
Pavlov, Alexey ;
van de Wouw, Nathan .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2012, 57 (07) :1793-1798
[46]   Map Invariance and the State Reconstruction Problem for Nonlinear Discrete-time Systems [J].
Kazantzis, Nikolas .
EUROPEAN JOURNAL OF CONTROL, 2009, 15 (02) :105-119
[47]   Optimal control for nonlinear discrete-time systems: A successive approximation approach [J].
Tang, GY ;
Wang, HH .
2004 8TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION, ROBOTICS AND VISION, VOLS 1-3, 2004, :344-349
[48]   Irreducibility and reduction of discrete-time nonlinear control systems:: An alternative approach [J].
Kotta, Ü ;
Pawluszewicz, E ;
Nömm, S .
SYSTEM STRUCTURE AND CONTROL 2001, VOLS 1 AND 2, 2001, :357-362
[49]   Sensitivity approach to optimal control for affine nonlinear discrete-time systems [J].
Tang, GY ;
Xie, N ;
Liu, P .
ASIAN JOURNAL OF CONTROL, 2005, 7 (04) :448-454
[50]   Dissipativity-Based Sampled-Data Control for Fuzzy Switched Markovian Jump Systems [J].
Xia, Jianwei ;
Chen, Guoliang ;
Park, Ju H. ;
Shen, Hao ;
Zhuang, Guangming .
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2021, 29 (06) :1325-1339