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.
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