Asymptotic Expansions and a New Numerical Algorithm of the Algebraic Riccati Equation for Multiparameter Singularly Perturbed Systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Asymptotic Expansions and a New Numerical Algorithm of the Algebraic Riccati Equation for Multiparameter Singularly Perturbed Systems

Authors:	Hiroaki MukaidaniTetsu Shimomura Koichi Mizukami

Institution:	^a Faculty of Information Sciences, Hiroshima City University, 3-4-1 Ozuka-Higashi, Asaminami-ku, Hiroshima, 731-3194, Japan ^b Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima, 739-8524, Japan ^c Faculty of Engineering, Hiroshima Kokusai Gakuin University, 6-20-1, Nakano Aki-ku, Hiroshima, 739-0321, Japanf1mukaida@im.hiroshima-cu.ac.jpf1

Abstract:	In this paper we study a continuous-time multiparameter algebraic Riccati equation (MARE) with an indefinite sign quadratic term. The existence of a unique and bounded solution of the MARE is newly established. We show that the Kleinman algorithm can be used to solve the sign indefinite MARE. The proof of the convergence and the existence of the unique solution of the Kleinman algorithm is done by using the Newton-Kantorovich theorem. Furthermore, we present new algorithms for solving the generalized multiparameter algebraic Lyapunov equation (GMALE) by means of the fixed-point algorithm.

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