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RECURSIVE APPROACH OF H∞ OPTIMAL FILTERING FOR MULTIPARAMETER SINGULARLY PERTURBED SYSTEMS
Hiroaki Mukaidani* Tetsu Shimomura** Hua Xu***
* Faculty of Information Sciences, Hiroshima City University,
3–4–1, Ozukahigashi Asaminami–ku Hiroshima, 731–3194 Japan.
e–mail:mukaida@im.hiroshima-cu.ac.jp
** Graduate School of Education, Hiroshima University, 1–1–1,
Kagamiyama Higashi–Hiroshima, 739–8524 Japan.
*** Graduate School of Business Sciences, The University of
Tsukuba, 3–29–1, Otsuka Bunkyou–ku Tokyo, 112–0012 Japan.
In this paper, we study the H_infinity optimal filtering for multiparameter singularly perturbed system (MSPS). In order to obtain the solution, we must solve the multiparameter algebraic Riccati equations (MARE) with indefinite sign quadratic term. First, the existence of a unique and bounded solution of such MARE is newly proven. The main results in this paper are to propose a new recursive algorithm for solving the MARE and to find sufficient conditions regarding the convergence of our proposed algorithm. Using the recursive algorithm, we show that the solution of the MARE converges to a positive semi-definite stabilizing solution with rate of the linear convergence.
Keywords: Multiparameter singularly perturbed system (MSPS), Multiparameter algebraic Riccati equations (MARE), H∞ optimal filtering, Recursive algorithm
Session slot T-Th-A13: Large Scale Systems I/Area code 5a : Large Scale Systems
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