Abstract
This article presents a stability analysis of linear time invariant systems arising in system theory. The computation of upper bounds of structured singular values confer the stability analysis, robustness and performance of feedback systems in system theory. The computation of the bounds of structured singular values of Toeplitz and symmetric Toeplitz matrices for linear time invariant systems is presented by means of low rank ordinary differential equations (ODE’s) based methodology. The proposed methodology is based upon the inner-outer algorithm. The inner algorithm constructs and solves a gradient system of ODE’s while the outer algorithm adjusts the perturbation level with fast Newton’s iteration. The comparison of bounds of structured singular values approximated by low rank ODE’s based methodology results tighter bounds when compared with well-known MATLAB routine mussv, available in MATLAB control toolbox.
Highlights
The stability analysis of non-linear systems is an important problem in systems theory
In order to solve the optimization problem presented in Definition 8, we use an iterative method based on low-rank ordinary differential equations [8]
The lower bound of structured singular value is 1, which is much tighter than the one approximated by mussv
Summary
The stability analysis of non-linear systems is an important problem in systems theory. The structured singular value (SSV) is a versatile tool in systems theory that allows us to address the central problem in the analysis of control systems. The SSV tool can be used to determine the stability and instability of linear time invariant feedback control systems in the presence of structured and unstructured perturbations. SSV provides the tools necessary to examine the performance of input–output systems in linear control These tools are helpful to study stability analysis of structured eigenvalue perturbation theory and that of uncertain linear control systems. We present the pseudo-spectrum of Toeplitz matrices
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