Transformation of a linear time-varying system into a linear time-invariant system
- 1 April 1978
- journal article
- research article
- Published by Taylor & Francis in International Journal of Control
- Vol. 27 (4) , 589-602
- https://doi.org/10.1080/00207177808922395
Abstract
It is shown that any linear time-varying system can be transformed into a time-invariant one provided that its state transition matrix φ(t. t0) is known. In this paper two fairly large classes of linear time-varying systems that can be explicitly transformed into time-invariant ones without using full information on φ(t. t0) are identified. They are the algebraically invariable systems and the γ-algebraically invariable systems. These classes include the well known Floquet systems and the Euler systems as special cases. It is also shown that any commutative system is γ-algebraieally invariable. Explicit methods of finding the desired algebraic transformation and the tγtransformation are also given. Several examples are presented and their stability is discussed.Keywords
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