期刊
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
卷 51, 期 3, 页码 1962-1987出版社
SIAM PUBLICATIONS
DOI: 10.1137/120881993
关键词
impulsive systems; nonlinear control systems; infinite-dimensional systems; input-to-state stability; Lyapunov methods
资金
- German Research Foundation (DFG) as a part of Collaborative Research Centre, Autonomous Cooperating Logistic Processes-A Paradigm Shift and Its Limitations. [637]
We prove that impulsive systems, which possess an input-to-state stable (ISS) Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition. If an ISS Lyapunov function is the exponential one, we provide a stronger result, which guarantees uniform ISS of the whole system over sequences satisfying the generalized average dwell-time condition. Then we prove two small-gain theorems that provide a construction of an ISS Lyapunov function for an interconnection of impulsive systems if the ISS Lyapunov functions for subsystems are known. The construction of local ISS Lyapunov functions via the linearization method is provided. Relations between small-gain and dwell-time conditions as well as between different types of dwell-time conditions are also investigated. Although our results are novel already in the context of finite-dimensional systems, we prove them for systems based on differential equations in Banach spaces that makes obtained results considerably more general.
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