Control and Observation of the Matrix Riccati Differential Equation

2009 ◽  
pp. 169-184
Author(s):  
G. Dirr ◽  
U. Helmke ◽  
J. Jordan
Keyword(s):  
Differential Equation ◽  
Riccati Differential Equation ◽  
The Matrix

scholarly journals A special property of the matrix Riccati equation

1974 ◽  
Vol 10 (2) ◽  
pp. 245-253 ◽  
Author(s):  
A.N. Stokes
Keyword(s):  
Differential Equation ◽  
Riccati Equation ◽  
Symmetric Matrix ◽  
Special Property ◽  
Positive Definiteness ◽  
Symmetric Matrices ◽  
Unusual Property ◽  
Riccati Differential Equation ◽  
The Matrix ◽  
Independent Variable

In the domain of real symmetric matrices ordered by the positive definiteness criterion, the symmetric matrix Riccati differential equation has the unusual property of preserving the ordering of its solutions as the independent variable changes, Here is is shown that, subject to a continuity restriction, the Riccati equation is unique among comparable equations in possessing this property.

scholarly journals On the exact solution of the matrix Riccati differential equation*

2011 ◽  
Vol 44 (1) ◽  
pp. 14556-14561 ◽  
Author(s):  
L. Ntogramatzidis ◽  
A. Ferrante
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Riccati Differential Equation ◽  
The Matrix

scholarly journals A canonical form and solution for the matrix Riccati differential equation

1985 ◽  
Vol 26 (3) ◽  
pp. 355-361 ◽  
Author(s):  
R. B. Leipnik
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Canonical Form ◽  
The Self ◽  
State Equations ◽  
Riccati Differential Equation ◽  
Adjoint Matrix ◽  
Transient Problem ◽  
The Matrix ◽  
Constant Coefficients

AbstractA canonical form of the self-adjoint Matrix Riccati Differential Equation with constant coefficients is obtained in terms of extremal solutions of the self-adjoint Matrix Riccati Algebraic (steady-state) Equations. This form is exploited in order to obtain a convenient explicit solution of the transient problem. Estimates of the convergence rate to the steady state are derived.

scholarly journals Accessibility of the matrix Riccati differential equation

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 4130031-4130032
Author(s):  
G. Dirr ◽  
U. Helmke
Keyword(s):  
Differential Equation ◽  
Riccati Differential Equation ◽  
The Matrix

scholarly journals Optimization Algorithm of Matrix Riccati Differential Equation and Application

2011 ◽  
Vol 2-3 ◽  
pp. 801-806
Author(s):  
Xiang Lin Hou ◽  
De Sheng Huang ◽  
Cong Chen
Keyword(s):  
Differential Equation ◽  
Matrix Element ◽  
Optimization Method ◽  
Control Parameters ◽  
Riccati Differential Equation ◽  
Dynamic Design ◽  
Design Variables ◽  
The Matrix ◽  
New Thinking ◽  
Riccati Matrix

To the matrix Riccati differential equation, based on dynamic design Variables Optimization Method, making unknown element of Riccati matrix as design variables, square sum of defined summation matrix element as objective function, a kind of new optimization Method about element of Riccati matrix orders is built. Universal program is formed. Practical examples are computed. Effectiveness is shown through result. The method is a new thinking for computing high order matrix Riccati Differential equation and obtaining control parameters.

scholarly journals Asymptotic distribution of singularities of solutions of Matrix-Riccati differential equations

1992 ◽  
Vol 34 (1) ◽  
pp. 112-131
Author(s):  
Gerhard Jank
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Finite Number ◽  
Periodic Solutions ◽  
Critical Points ◽  
Riccati Differential Equation ◽  
Riccati Differential Equations ◽  
The Matrix ◽  
Matrix Riccati Differential Equations

AbstractIn the present paper, we make use of the method of asymptotic integration to get estimates on those regions in the complex plane where singularities and critical points of solutions of the Matrix-Riccati differential equation with polynomial co-efficients may appear. The result is that most of these points lie around a finite number of permanent critical directions. These permanent directions are defined by the coefficients of the differential equation. The number of singularities outside certain domains around the permanent critical directions, in a circle of radius r, is of growth O(log r). Applications of the results to periodic solutions and to the determination of critical points are given.

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