Publication

Robust Performance Analysis of Single Parameter-dependent Systems with Polynomially Parameter-dependent Lyapunov Matrices

Alireza Karimi
2014
Conference Papers

Abstract

This paper addresses the problem of H-infinity and H-2 performance analysis of continuous-time affine single parameter-dependent systems with polynomially parameter-dependent Lyapunov matrices. First, some necessary and sufficient conditions in terms of linear matrix inequalities (LMIs) are provided using (D,G) scaling approach. Then, the results are used to deal with the problem of fixed-order H-infinity and H-2 controller design via bilinear matrix inequalities (BMIs) in a nonconservative way. Simulation results demonstrate the effectiveness of the proposed approach.

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https://infoscience.epfl.ch/entities/publication/08588b67-9303-431d-bfa0-f4bb10e1c43a

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Alireza Karimi
2014
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/08588b67-9303-431d-bfa0-f4bb10e1c43a

About this result

Related concepts (13)

Trace (linear algebra)

In linear algebra, the trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A. The trace is only defined for a square matrix (n × n). It can be proven that the trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities). It can also be proven that tr(AB) = tr(BA) for any two matrices A and B. This implies that similar matrices have the same trace.

Rank (linear algebra)

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.

Matrix norm

In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions). Given a field of either real or complex numbers, let be the K-vector space of matrices with rows and columns and entries in the field . A matrix norm is a norm on . This article will always write such norms with double vertical bars (like so: ).

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