LINEARIZATIONS FOR RATIONAL MATRIX FUNCTIONS AND ROSENBROCK SYSTEM POLYNOMIALS

被引:33
作者
Alam, Rafikul [1 ]
Behera, Namita [1 ]
机构
[1] IIT Guwahati, Dept Math, Gauhati 781039, India
关键词
LTI system; zeros; poles; rational matrix function; eigenvalue; spectrum; eigenvector; minimal realization; matrix polynomial; matrix pencil; linearization; Fiedler pencil; GENERALIZED SCHUR DECOMPOSITION; ARBITRARY PENCIL-A; ROBUST SOFTWARE; ERROR-BOUNDS; LAMBDA-B;
D O I
10.1137/15M1008622
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Our aim in this paper is twofold: First, for solving rational eigenproblems we introduce linearizations of rational matrix functions and propose a framework for their constructions via minimal realizations. We also introduce Fiedler-like pencils for rational matrix functions and show that the Fiedler-like pencils are linearizations of the rational matrix functions. Second, for computing zeros of a linear time-invariant system Sigma in state-space form, we introduce a trimmed structured linearization, which we refer to as a Rosenbrock linearization, of the Rosenbrock system polynomial S(lambda) associated with Sigma. Also we introduce Fiedler-like pencils for S(lambda), describe an algorithm for their constructions, and show that the Fiedler-like pencils are Rosenbrock linearizations of the system polynomial S(lambda).
引用
收藏
页码:354 / 380
页数:27
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