Input-Output-to-State Stability Tools for Hybrid Systems and Their Interconnections

被引:27
作者
Sanfelice, Ricardo G. [1 ]
机构
[1] Univ Arizona, Dept Aerosp & Mech Engn, Tucson, AZ 85721 USA
基金
美国国家科学基金会;
关键词
Hybrid control; hybrid systems; input-output stability; Lyapunov functions; small gain theorem; SMALL-GAIN THEOREM; ISS SYSTEMS; DETECTABILITY; PRINCIPLES;
D O I
10.1109/TAC.2013.2292455
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 present results for the analysis of input/output properties of a general class of hybrid systems given by a flow set, a flow map, a jump set, a jump map, and an output map. For this class of systems, the notion of input-output-to-state stability is introduced in the first part of the technical note. Under mild assumptions on the functions and sets defining a hybrid system, sufficient conditions for this notion in terms of Lyapunov functions are derived. Equivalences between Lyapunov functions for input-output-to-state stability for asymptotic and exponential decay rates are established. The sufficient conditions and equivalences are linked to the existence of norm observers for hybrid systems. These results are used in the second part of the technical note to study interconnections of hybrid systems. An interconnection result in terms of a Lyapunov-based small gain theorem is also presented. Examples illustrate the results.
引用
收藏
页码:1360 / 1366
页数:7
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