Toward a Rational Matrix Approximation of the Parameter-Dependent Riccati Equation Solution

Abstract This paper considers the problem of solving parameter-dependent Riccati equations. In this paper, a tractable iterative scheme involving mainly additions and multiplications is developed for finding solutions to arbitrary accuracy. It is first presented in the parameter-independent case and then extended to the parametric case. It hinges upon two results: (i) a palindromic quadratic polynomial matrix characterization of the matrix sign and square root functions. (ii) a particular representation of parameter-dependent matrices with negative and positive power series with respect to parameters. Several numerical examples are given throughout the paper to prove the validity of the proposed results.

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