Journal ArticleDOI
Eigenvector scaling in a solution of the matrix Riccati equation
TLDR
An eigenvector matrix is used in deriving an explicit expression for the solution of the matrix Riccati equation and the eigenvectors are not normalized in the usual sense of the word but must be scaled in one of two particular ways.Abstract:
An eigenvector matrix is used in deriving an explicit expression for the solution of the matrix Riccati equation. A misleading situation arises from the derivation of this expression as originally published [1], which it is the purpose of this correspondence to clarify. For the expression to be valid the eigenvectors are not normalized in the usual sense of the word but must be scaled in one of two particular ways.read more
Citations
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Book ChapterDOI
Invariant Subspace Methods for the Numerical Solution of Riccati Equations
TL;DR: An overview is given of progress over the past ten to fifteen years towards reliable and efficient numerical solution of various types of Riccati equations.
Journal ArticleDOI
Survey paper: A survey of some recent results in linear multivariable feedback theory
TL;DR: In this paper, a review of multivariable feedback system design techniques from the frequency-response viewpoint is given, including a comparison of the advantages and disadvantages of each type of design method, including Non-Interacting Control, Modal Control, Optimal Control, Commutative Control, The Inverse Nyquist Array and The Characteristic Locus.
Journal ArticleDOI
A general transfer function approach to linear stationary filtering and steady-state optimal control problems
TL;DR: An application of the transfer-function approach in determining the class of all systems that share the same optimal solution is introduced, and the superiority of its computational method for systems having a small number of inputs and outputs is demonstrated.
Journal ArticleDOI
The optimal root loci of linear multivariable systems
TL;DR: In this paper, a root-locus approach was used to study all orders of behavior of the closed-loop poles of the optimal system and to relate the asymptotic behaviour of the poles to that of the original system.
Journal ArticleDOI
Some topics in algebraic systems theory: a survey†
TL;DR: In this paper, a concise review is given of some recent developments in matrix algebra to linear control systems, including stability criteria for system characteristic polynomials, realization and polynomial matrices, matrix Riccati equations and optimal control.
References
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Journal ArticleDOI
Matrix Quadratic Solutions
TL;DR: Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients was applied in this article, where the solution was derived by using a linear combination of matrix quadratics and constant coefficients.
Journal ArticleDOI
A negative exponential solution for the matrix Riccati equation
TL;DR: A new form is presented for the transient solution of the matrix Riccati equation associated with the linear optimal regulator and filter problems for time-invariant plants in a form such that the transient terms decay exponentially with time, leaving the steady-state terms.
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