摂動項を含むH_∞タイプリカッチ方程式のための再帰的アルゴリズム [in Japanese] The Recursive Algorithm for H_∞ Type Riccati Equation with Small Parameter. [in Japanese]
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This paper considers new recursive algorithm to find the positive semidefinite stabilizing solution of H∞ type Riccati equation with small parameter where the solution P depend on the ε. In order to obtain the stabilizing solution of the H∞ type Riccati equation, we must solve the generalized algebraic Riccati equation. Using the recursive algorithm, we show that the solution of the generalized algebraic Riccati equation converges to a positive semidefinite stabilizing solution with the rate of convergence of O(εk).We also show that for singularly perturbed systems, if the H∞ norm of the transfer matrix function is less than the H∞ norms for the fast system and for the reduced slow system, then the H∞ type Riccati equation has a positive semidefinite stabilizing solution.
- The Transactions of the Institute of Electrical Engineers of Japan. C
The Transactions of the Institute of Electrical Engineers of Japan. C 117(10), 1464-1471, 1997-10