1979
DOI: 10.1007/bf01397001
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A computational solution for a Matrix Riccati differential equation

Abstract: Summary. This paper is concerned with the solution of the finite time Riccati equation. The solution to the Riccati equation is given in terms of the partition of the transition matrix. Matrix differential equations for the partition of the transition matrix are derived and are solved using computational methods. Examples illustrating the method are presented and the computational algorithms are given.

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Cited by 23 publications
(11 citation statements)
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“…By using this approach, the solution of MRDE is obtained by partitioning the transition matrix of the associated Hamiltonian system [11]. Another class of methods is based on transforming MRDE into a linear matrix differential equation and then solving MRDE analytically or computationally [12,13,14]. However, the method in [15] is restricted for cases when certain coefficients of MRDE are non-singular.…”
Section: Introductionmentioning
confidence: 98%
“…By using this approach, the solution of MRDE is obtained by partitioning the transition matrix of the associated Hamiltonian system [11]. Another class of methods is based on transforming MRDE into a linear matrix differential equation and then solving MRDE analytically or computationally [12,13,14]. However, the method in [15] is restricted for cases when certain coefficients of MRDE are non-singular.…”
Section: Introductionmentioning
confidence: 98%
“…These equations are solved analytically or computationally . In , an analytic procedure of solving the D R E of the linear quadratic control problem for homing systems is presented, a solution K ( t ) of the D R E is obtained by using K ( t ) = P ( t )/ f ( t ), where f ( t ) and P ( t ) are solutions of certain first‐order ordinary linear differential equations. However, the technique given in is restricted to single input.…”
Section: Introductionmentioning
confidence: 99%
“…By using this approach, the solution of MRDE is obtained by partitioning the transition matrix of the associated Hamiltonian system [35]. Another class of method is based on transforming MRDE into a linear matrix differential equation and then solving MRDE analytically or computationally [20,31,32]. However, the method in [30] is restricted for cases when certain coefficients of MRDE are nonsingular.…”
Section: Introductionmentioning
confidence: 99%