Existence of a Periodic Solution for a Coupled System of Differential Equations

Matrix differential equations are playing key roles in solving problems in many fields of study such as control theory. Control system theory is a branch of engineering that handles how to manipulate a dynamical system’s inputs to change the behavior or outcome of the system to something that is desired. Control systems have been around at least as far back as the float-regulated water clock developed by the Greeks in the third century BC; however, control theory as a branch of mathematics wasn’t explored until much later in the mid-19th century. Since that time, the theory has been used almost entirely by professional engineers and mathematicians. Coupled Riccati differential equations play distinguished role in the control theory [2] (such as optimal control problem, stochastic control problem and other control theory problems like the linear systems and dynamic games). Here, we consider a coupled Riccati differential equation and use an appropriate Green’s function to reduce it a Fredholm integral equation. Finally, we prove the existence of a periodic solution. © 2022 American Institute of Physics Inc.. All rights reserved.

Ragusa M.A. 1, 2 , Razani A.3
Сборник материалов конференции
  • 1 University of Catania, Department of Mathematics and Computer Sciences, Catania, Italy
  • 2 RUDN University, Moscow, Russian Federation
  • 3 Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran
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