RECURSIVE APPROACH OF H_∞ OPTIMAL FILTERING FOR MULTIPARAMETER SINGULARLY PERTURBED SYSTEMS

摘要

In this paper, we study the H_∞ 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 the rate of convergence of O(||μ||~(i+1)).