Mohammedali, Khalid Hammood
(2019)
Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation.
PhD thesis, Universiti Sains Malaysia.
Abstract
where ,A B and C are nn matrices such that , TBB TCC and ( ) . nn X t R This
nonlinear Riccati matrix differential equation may also be viewed as a quadratic ordinary
differential equation. The above equation may be generalized for delay differential
equations with retarded arguments, in which the delay term occurs as a constant time
delay in ()Xt but not in ()Xt (the derivative will disappear and the equation will become
algebraic Riccati matrix equation after the initial condition is used). In this thesis we study
the variational iteration method and use it to solve nonlinear Riccati matrix differential
equation and nonlinear Riccati matrix delay differential equations. The solution approach
requires, initially, the derivation of the variational iteration method for solving such types
of equations and then proof of its convergence to the exact solution in two cases with and
without delay. The Adomian decomposition method is then applied for solving nonlinear
Riccati matrix differential equation in two cases with and without delay.
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