Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results

XIE Guang-ming; WANG Long; YE Qing-kai

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(9): 919-928

XIE Guang-ming, WANG Long, YE Qing-kai. Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results[J]. Applied Mathematics and Mechanics, 2003, 24(9): 919-928.

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Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results

Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P.R.China

Received Date: 2002-01-29
Rev Recd Date: 2003-03-25
Publish Date: 2003-09-15

Abstract

Abstract

The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. First, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitoins and lemmas are necessary research tools for controllability analysis.
- hybrid dynamic system,
- switched linear system,
- time-delay,
- controllability,
- gener-alized cyclic invariant subspace,
- switching sequence,
- switching path

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References(24)

References

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