期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 54, 期 10, 页码 2389-2404出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2009.2028980
关键词
Integral input-to-state stability (iISS); Lyapunov function; necessary condition; nonlinear interconnected systems; small gain condition
资金
- Japan Society for the Promotion of Science [19560446]
- U.S. National Science Foundation [ECS-0093176, DMS-0504462]
This paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input-to-state stable(iISS) systems with external inputs. The treatment of USS and input-to-state stable (ISS) systems is unified. Both necessary conditions and sufficient conditions are investigated using a Lyapunov formulation. In the presence of model uncertainty, this paper proves that, for the stability of the interconnected system, at least one subsystem is necessarily ISS which is a stronger stability property in the set of iISS. The necessity of a small-gain-type property is also demonstrated. This paper proposes a common form of smooth Lyapunov functions which can establish the USS and the ISS of the interconnection comprising iISS and ISS subsystems whenever the small-gain-type condition is satisfied. The result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature. Global asymptotic stability is discussed as a special case.
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