Journal ArticleDOI
On the discrete Riccati equation
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TLDR
In this article, the trace of the solution to the discrete algebraic matrix Riccati equation has been shown to have a bound on the number of elements in the trace, which is the smallest bound known.Abstract:
Several bounds have been reported recently for the trace of the solution to the discrete algebraic matrix Riccati equation. This note adds an alternative one to them.read more
Citations
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Journal ArticleDOI
Kalman filtering and Riccati equations for descriptor systems
TL;DR: In this article, the authors derived a 3-block form for the optimal filter and a corresponding 3block Riccati equation for a general class of time-varying descriptor models which need not represent a well-posed system in that the dynamics may be either over or under constrained.
Journal ArticleDOI
Iterative matrix bounds and computational solutions to the discrete algebraic Riccati equation
TL;DR: Bilateral matrix bounds for the solution of the discrete algebraic Riccati equation (DARE) are presented and Computational algorithms to solve the DARE follow.
Journal ArticleDOI
Lower summation bounds for the discrete Riccati and Lyapunov equations
N. Komaroff,B. Shahian +1 more
TL;DR: Lower eigenvalue summation (including trace) bounds for the discrete algebraic Riccati and Lyapunov matrix equations are presented in this article, which are tighter than, or supplement, existing results.
Journal ArticleDOI
Upper matrix bound of the solution for the discrete Riccati equation
TL;DR: A new upper matrix bound of the solution for the discrete algebraic matrix Riccati equation is developed and is used to derive bounds on the eigenvalues, trace, and determinant of the same solution.
Journal ArticleDOI
Upper bounds for the solution of the discrete Riccati equation
TL;DR: In this paper, upper bounds for individual eigenvalues and summations of eigen values including the trace of the solution of the discrete algebraic Riccati equation are presented, some of which are new, and some supplement bounds in the literature.
References
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Journal ArticleDOI
The design of suboptimal linear time-varying systems
D. Kleinman,Michael Athans +1 more
TL;DR: In this article, the authors deal with the determination of suboptimal feedback laws for the control of linear time-varying systems with quadratic performance criteria, where easily implementable time functions are used to generate the required time varying gains; free constant parameters in the control law description are chosen so as to minimize an averaged control cost.
Journal ArticleDOI
Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformations
Journal ArticleDOI
A brief summary of the bounds on the solution of the algebraic matrix equations in control theory
T. Mori,I. A. Deresei +1 more
TL;DR: This paper collects the bounds that have been presented up to now and summarizes them in an unified form to prove particularly convenient for those wishing to get a ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds.
Journal ArticleDOI
On bounds of the Riccati and Lyapunov matrix equations
TL;DR: In this article, the traces of the solutions of the algebraic Riccati and Lyapunov matrix equations are established in the continuous and discrete domain, respectively, and lower bounds for the sum of the eigenvalue of the matrix solutions are given.
Journal ArticleDOI
Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equations and the continuous Lyapunov equation
TL;DR: In this paper, the eigenvalues and sums and products of the Eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapinov matrix equation were studied.
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