Upper and lower bounds for the solution of the general matrix Riccati differential equation on a time scale
type: Item
instance of: scholarly article
title: Upper and lower bounds for the solution of the general matrix Riccati differential equation on a time scale
zbMATH Open document ID: 1013.34023
DOI: 10.1016/S0377-0427(01)00441-1
author: Johnny Henderson
author: John M. Davis
author: K. Rajendra Prasad
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The authors study the general matrix Riccati differential equations (GMRDE) on a time scale of the form \[ R^{\Delta}(t) = A(t) + B(t)R(t) + R(\Gamma (t)) B^{*} - R(\Gamma(t))C(t)R(t), \tag{1} \] where \(A(t)\) and \(C(t)\) are symmetric \(n\times n\)-matrices while \(B(t), V(t), T(t)\) and \(R(t)\) are \(n\times n\)-matrices, and the star denotes the transpose of the matrix. Some properties of time scale and operations on time scale are defined. Applying the quazilinearization technique to the general matrix Riccati differential equation on \(T\), the authors obtain the linear equation \[ U^{\Delta}(t)=[B(t)-T(t)C(t)U(t)+U(\gamma(t))][B^{*}(t)-C(t)T(t)]+ A(t)+ T(t)C(t)T(t) \tag{2} \] with \(U(0)=E\). The solution to the linearized equation in terms of fundamental matrices and an upper bound for the solution to equation (1) on \(T\) are obtained. In the next section, a lower bound for the solution to equation (1) is found. Finally, the authors study the monotonicity of successive approximations.
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34B45
zbMATH DE Number: 1758474
zbMATH Keywords: matrix Riccati equation
zbMATH Keywords: time scale
zbMATH Keywords: quazilinearization
zbMATH Keywords: monotonicity
Wikidata QID: Q115339011
MaRDI profile type: Publication
cites work: Continued Fraction Representations of Maximal and Minimal Solutions of a Discrete Matrix Riccati Equation
cites work: Q4716258
cites work: Q3198160
cites work: Methods of nonlinear analysis. Vol. 1
cites work: Quasi-linearization and the matrix Riccati equation
cites work: Approximate solutions with a priori error bounds for continuous coefficient matrix Riccati equations.
cites work: Q2723195
cites work: A matrix cross ratio theorem for the Riccati equation
cites work: Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations
cites work: Non-blow-up conditions for Riccati-type matrix differential and difference equations
cites work: Coupled matrix Riccati equations in minimal cost variance control problems
cites work: Analysis on measure chains - a unified approach to continuous and discrete calculus
cites work: Existence of algebraic matrix Riccati equations arising in transport theory
cites work: Iterative solution for a certain class of algebraic matrix riccati equations arising in transport theory
cites work: Q4716262
cites work: Q4845420
cites work: A note on matrix Riccati functional differential equations
cites work: Upper and lower bounds for the solution of the general matrix Riccati differential equation
cites work: On the use of the quasilinearization method in the growth of a pathogenic bacteria
cites work: Families of Solutions of Matrix Riccati Differential Equations
cites work: Q4397695
full work available at URL: s0377-0427(01)00441-1
OpenAlex ID: W2051050751
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description: scientific article; zbMATH DE number 1758474