Abstract
In this article we consider numerical approximation of structured singular values ($\mu-$values). The lower bounds for $\mu-$values are approximated by using ordinary differential equations based technique. The structured singular values provide a vital tool to investigate stability of feedback systems. We also compute the lower bounds of $\mu-$values for certain matrices that correspond to symmetries in control systems.
Highlights
The Structured Singular Values known as μ-values is a well-known mathematical tool in control, introduced in 1981 by J
The structured singular values denoted by μ for a given matrix M ∈ Cn,n or M ∈ Rn,n and a set of block diagonal matrices ΘB is defined as μΘB (M ) :=
In the following table 7, we give comparison of numerical approximation to both lower and upper bounds of structured singular values approximated by the well-known MATLAB routine mussv and algorithm [12] for the matrix A8
Summary
The Structured Singular Values known as μ-values is a well-known mathematical tool in control, introduced in 1981 by J. The structured singular values denoted by μ for a given matrix M ∈ Cn,n or M ∈ Rn,n and a set of block diagonal matrices ΘB is defined as μΘB (M ) :=. In above definition 2.1, det(·) represent the determinant of a matrix (I − M ∆) while minimum is over an admissible perturbation ∆ In this particular case we will denote the set of pure complex uncertainties by ΘB. For a given n-dimensional complex matrix M ∈ Cn×n and a perturbation level the structured spectral value set is the collection of all eigenvalues of matrix ( M ∆) defined as ΛΘB (M ) 0. While for the case of outer algorithm, we make use of an iterative method to first vary the perturbation level 1 This gives the knowledge of the computation of derivative of a local extremizer say ∆( 1) with respect to some fixed parameter 1. Where μΘB (M ) is the upper bound of μ-value approximated by mussv
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Analysis and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
