Abstract
In this article, the computation of μ-values known as Structured Singular Values SSV for the companion matrices is presented. The comparison of lower bounds with the well-known MATLAB routine mussv is investigated. The Structured Singular Values provides important tools to analyze the stability and instability analysis of closed loop time invariant systems in the linear control theory as well as in structured eigenvalue perturbation theory.
Highlights
The μ-values [1] is an important mathematical tool in control theory, it allows to discuss the problem arising in the stability analysis and synthesis of control systems
To quantify the stability of a closed-loop linear time-invariant system subject to the structured perturbations, the structures addressed by the SSV are very general and allow covering all types of parametric uncertainties that can be incorporated into the control system by using real and complex Linear Fractional Transformations LFT's
An upper bound of the SSV provides sufficient conditions to guarantee robust stability analysis of feedback systems, while a lower bound provides sufficient conditions for instability analysis of the feedback systems
Summary
The μ-values [1] is an important mathematical tool in control theory, it allows to discuss the problem arising in the stability analysis and synthesis of control systems. The numerical algorithms, which are being used in practice, provide both upper and lower bounds of SSV. The comparison of numerical results to approximate the lower bounds of the SSV associated with pure complex uncertainties is presented. It explain how the computation of the SSV can be addressed by an inner-outer algorithm, where the outer algorithm determines the perturbation level and the inner algorithm determines a (local) extremizer of the structured spectral value set.
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