An iterative method and maximal solution of Coupled algebraic Riccati equations

Document Type : Research Paper

Author

Department of Mathematics, Jahrom University, P.O. Box: 74135-111, Iran.

10.22059/jac.2022.88374

Abstract

Coupled Riccati equation has widely been applied to various engineering areas such as jump linear quadratic problem, particle transport theory, and Wiener–Hopf decomposition of Markov chains. In this paper, we consider an iterative method for computing the Hermitian solution of the Coupled Algebraic Riccati Equations (CARE) which is usually encountered in control theory. We show some properties of this iterative method. Furthermore, it will also be demonstrated that the maximal solution can be obtained numerically via a certain linear or quadratic inequalities optimization problem. Numerical examples are presented and the results are compared.

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