Open Access
Stability of Invariant Maximal Semidefinite Subspaces. II. Applications: Self-Adjoint Rational Matrix Functions,
TLDR
In this article, the stability of self-adjoint rational matrix functions and matrix polynomials, as well as hermitian solutions of symmetric matrix algebraic Riccati equations, is studied.Abstract:
The stability of various factorizations of self-adjoint rational matrix functions and matrix polynomials, as well as of hermitian solutions of symmetric matrix algebraic Riccati equations, is studied. In the first part of this paper results on stability of certain classes of invariant subspaces of a matrix which is self-adjoint in an indefinite inner product were obtained. These results serve as the main tools in the investigation.read more
Citations
More filters
Book ChapterDOI
Stability of Invariant Lagrangian Subspaces II
André C. M. Ran,Leiba Rodman +1 more
TL;DR: In this article, the authors considered various stability properties of real invariant lagrangian subspaces for real matrices which are either symmetric or skew-symmetric in a real quadratic form.
Book ChapterDOI
Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review
Peter Lancaster,Leiba Rodman +1 more
TL;DR: In this article, the Riccati Equation for an unknown n × n matrix X of the form of a quadratic matrix equation X = XDX + XA + A*X - C = 0, where A, D, C are hermitian complex matrices with C and D hermitians.
Linear quadratic problems with indefinite cost for discrete time systems
A. C. M. Ran,Harry L. Trentelman +1 more
TL;DR: In this paper, a geometric characterization of the set of all hermitian solutions of the discrete-time algebraic Riccati equation is given, and necessary and sufficient conditions for the existence of optimal control are given.
Journal ArticleDOI
Stable Invariant Lagrangian Subspaces: Factorization of Symmetric Rational Matrix Functions and Other Applications
André C. M. Ran,Leiba Rodman +1 more
TL;DR: In this paper, several applications of earlier results by the authors concerning various notions of stability of invariant lagrangian subspaces are studied, such as stability of symmetric minimal factorizations of real symmetric rational matrix functions, stability of factorization of matrix polynomials, and stably well-posed matricial boundary value problems with symmetries.
Journal ArticleDOI
Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices
TL;DR: In this article, the Lagrangian invariant subspaces for real and complex matrices are analyzed for perturbation analysis and the index of stability and conditional stability is derived.
References
More filters
Journal Article
Optimal Filtering
TL;DR: This book helps to fill the void in the market and does that in a superb manner by covering the standard topics such as Kalman filtering, innovations processes, smoothing, and adaptive and nonlinear estimation.
Book
Linear Optimal Control Systems
Huibert Kwakernaak,Raphael Sivan +1 more
TL;DR: In this article, the authors provide an excellent introduction to feedback control system design, including a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.
Book
Indefinite Inner Product Spaces
TL;DR: In this paper, the authors present a survey of the inner product spaces of linear operators without topology, including Cayley Transform and Cayley Principal Vectors of Cayley Transforms.
Related Papers (5)
Stability of invariant maximal semidefinite subspaces. II. applications: Self-adjoint rational matrix functions, Algebraic Riccati equations
André C. M. Ran,Leiba Rodman +1 more