ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

被引：35
作者：
Gruene, Lars [1 ]
Kellett, Christopher M. [2 ]
机构：
[1] Univ Bayreuth, Inst Math, D-95440 Bayreuth, Germany
[2] Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2014年 / 59卷 / 11期
关键词：
Discrete-time systems; input-to-state stability (ISS); Lyapunov methods; TO-STATE STABILITY; CHANGING SUPPLY FUNCTIONS; MODEL-PREDICTIVE CONTROL; DIFFERENCE INCLUSIONS; STABLE SYSTEMS; INPUT; STABILIZATION; ROBUSTNESS;
D O I：
10.1109/TAC.2014.2321667
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Input-to-State Stability (ISS) and the ISS-Lyapunov function are useful tools for the analysis and design of nonlinear systems. Motivated by the fact that many feedback control laws, such as model predictive or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov functions were originally introduced in a so-called implication-form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipative-form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication-form ISS-Lyapunov function and provide a complete characterization of ISS-Lyapunov functions for discrete-time systems with discontinuous dynamics.
引用
收藏
页码：3098 / 3103
页数：6
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