Nonlinear matrix differential equations arising in the mathematical control and simulation of dynamical systems and CAD-CAM problems

2002 ◽  
Author(s):  
J. Jones
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Cad Cam ◽  
Matrix Differential Equations ◽  
Nonlinear Matrix ◽  
Matrix Differential ◽  
Mathematical Control

scholarly journals Calibrating linear continuous-time dynamical systems via perturbation analysis

Filomat ◽  
2018 ◽  
Vol 32 (5) ◽  
pp. 1909-1915
Author(s):  
Peter Weng ◽  
Frederick Phoa
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Perturbation Analysis ◽  
Continuous Time ◽  
Riccati Equations ◽  
Linear Dynamical Systems ◽  
The Matrix ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Time Linear

This work considered the continuous-time linear dynamical systems described by the matrix differential equations, and aimed at studying the perturbation analysis via solving perturbed linear dynamical systems. In specific, we solved Riccati differential equations and continuous-time algebraic Riccati equations with finite and infinite times respectively. Moreover, we stated some assumptions on the existence and uniqueness of the solutions of the perturbed Riccati equations. Similar techniques were applied to the discrete-time linear dynamical systems. Two numerical examples illustrated the efficiency and accuracy.

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