Realization and Discretization of Asymptotically Stable Homogeneous Systems

被引：48
|
作者：
Efimov, Denis [1 ,2 ,3 ]
Polyakov, Andrey [1 ,2 ,3 ]
Levant, Arie [1 ,2 ,4 ]
Perruquetti, Wilfrid [1 ,2 ]
机构：
[1] INRIA, Non A Team, Parc Sci Haute Borne, F-59650 Villeneuve Dascq, France
[2] Ecole Cent Lille, CRIStAL UMR CNRS 9189, F-59651 Villeneuve Dascq, France
[3] Univ ITMO, Dept Control Syst & Informat, St Petersburg 197101, Russia
[4] Tel Aviv Univ, Sch Math Sci, IL-6997801 Tel Aviv, Israel
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2017年 / 62卷 / 11期
关键词：
Computer simulation; Lyapunov methods; System implementation; FIXED-TIME STABILIZATION; FINITE-TIME; LYAPUNOV FUNCTION; STABILITY; DESIGN;
D O I：
10.1109/TAC.2017.2699284
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that the explicit Euler method has certain drawbacks for the global approximation of homogeneous systems with nonzero degrees, whereas the implicit Euler scheme ensures convergence of the approximating solutions to zero. Properties of absolute and relative errors of the respective discretizations are investigated.
引用
收藏
页码：5962 / 5969
页数：8
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