Document Zbl 1384.93051

Design of imaginary spectrum of LTI systems with delays to manipulate stability regions. (English) Zbl 1384.93051

Insperger, Tamás (ed.) et al., Time delay systems. Theory, numerics, applications, and experiments. Selected papers based on the presentations at the 12th IFAC workshop, Ann Arbor, MI, USA, June 28–30, 2015. Cham: Springer (ISBN 978-3-319-53425-1/hbk; 978-3-319-53426-8/ebook). Advances in Delays and Dynamics 7, 127-140 (2017).

Summary: This chapter is on the design problem of Linear Time-Invariant (LTI) Systems with delays. Our recent studies on the use of algebraic techniques, namely resultant and iterated discriminants operations, in connection with the well-known Rekasius transformation implemented on the system characteristic equation already revealed that it is indeed possible to compute the exact range of the imaginary spectrum of such systems. This know-how, which is the key toward understanding the stabilty/instability decomposition of the system, is utilized here to craft the imaginary spectrum of LTI systems with multiple delays, specifically with the aim to manipulate stability regions in a systematic manner in the delay parameter space.
For the entire collection see [Zbl 1380.34003].

Cited in 1 Document

MSC:

93B60	Eigenvalue problems
93C05	Linear systems in control theory
34K06	Linear functional-differential equations
34K20	Stability theory of functional-differential equations
93B17	Transformations
93D99	Stability of control systems

Keywords:

linear time-invariant (LTI) systems; Rekasius transformation; imaginary spectrum; stabilty/instability decomposition

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