Solving the State Equation of a System by Walsh Function
Tang Guoxi
Abstract
Tang Guoxi
Abstract
In this paper, We deal with the solution of the state equation of a system by the Walsh function, that is, we shall find the solution of a matrix differential equation by the Walsh function, and introduce a solution of the higher-order matrix differential equation. First, after a certain transform, we turn the higher- order matrix differential equation into a state equation. Then we find the solution of the state equation by the Walsh function. Finally after a certain transform, we obtain a solution of the higher-order matrix differential equation.
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In this paper, We deal with the solution of the state equation of a system by the Walsh function, that is, we shall find the solution of a matrix differential equation by the Walsh function, and introduce a solution of the higher-order matrix differential equation. First, after a certain transform, we turn the higher- order matrix differential equation into a state equation. Then we find the solution of the state equation by the Walsh function. Finally after a certain transform, we obtain a solution of the higher-order matrix differential equation.
Key concepts: Universal differential equation, First-order partial differential equation, Mathematics, Matrix differential equation, Exact differential equation, Differential equation, Riccati equation, Matrix difference equation