PROPORTIONAL LOCAL ASSIGNABILITY OF LYAPUNOV SPECTRUM OF LINEAR DISCRETE TIME-VARYING SYSTEMS

被引：17
|
作者：
Babiarz, Artur [1 ]
Banshchikova, Irina [2 ]
Czornik, Adam [1 ]
Makarov, Evgenii [3 ]
Niezabitowski, Michal [1 ,4 ]
Popova, Svetlana [2 ,5 ]
机构：
[1] Silesian Tech Univ, Fac Automat Control Elect & Comp Sci, Inst Automat Control, Akad 16, PL-44100 Gliwice, Poland
[2] Udmurt State Univ, Dept Differential Equat, Univ Skaya 1, Izhevsk 426034, Russia
[3] Natl Acad Sci Belarus, Inst Math, Surganova 11, Minsk 220072, BELARUS
[4] Univ Silesia, Fac Math Phys & Chem, Inst Math, Bankowa 14, PL-40007 Katowice, Poland
[5] Russian Acad Sci, Inst Math & Mech, Ural Branch, S Kovalevskaja St 16, Ekaterinburg 620219, Russia
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2019年 / 57卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
pole assignment problem; proportional local assignability; Lyapunov spectrum; linear discrete time-varying systems; EXPONENTS; CONTROLLABILITY;
D O I：
10.1137/17M1141734
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 consider a local version of the pole assignment problem for linear discrete time-varying systems. Our aim is to obtain sufficient conditions to place the Lyapunov spectrum of the closed-loop system in an arbitrary position within some neighborhood of the Lyapunov spectrum of the free system using an appropriate time-varying linear feedback. Moreover, we assume that the norm of the matrix of linear feedback should be bounded from above by the distance between these two spectra with some constant multiplier. We prove that diagonalizability, Lyapunov regularity, and stability of the Lyapunov spectrum each separately are the required sufficient conditions provided that the open-loop system is uniformly completely controllable.
引用
收藏
页码：1355 / 1377
页数：23
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