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- W4299532567 abstract "The root locus is an important tool for analysing the stability and time constants of linear finite-dimensional systems as a parameter, often the gain, is varied. However, many systems are modelled by partial differential equations or delay equations. These systems evolve on an infinite-dimensional space and their transfer functions are not rational. In this paper a rigorous definition of the root locus for infinite-dimensional systems is given and it is shown that the root locus is well-defined for a large class of infinite-dimensional systems. As for finite-dimensional systems, any limit point of a branch of the root locus is a zero. However, the asymptotic behaviour can be quite different from that for finite-dimensional systems. This point is illustrated with a number of examples. It is shown that the familiar pole-zero interlacing property for collocated systems with a Hermitian state matrix extends to infinite-dimensional systems with self-adjoint generator. This interlacing property is also shown to hold for collocated systems with a skew-adjoint generator." @default.
- W4299532567 created "2022-10-02" @default.
- W4299532567 creator A5049638450 @default.
- W4299532567 creator A5082176398 @default.
- W4299532567 date "2014-09-24" @default.
- W4299532567 modified "2023-09-23" @default.
- W4299532567 title "Root locii for systems defined on Hilbert spaces" @default.
- W4299532567 doi "https://doi.org/10.48550/arxiv.1409.7081" @default.
- W4299532567 hasPublicationYear "2014" @default.
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