Gain-Scheduling Control System Synthesis Based on Spline-Type Parameter-Dependent Quadratic Forms

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  • スプライン型のパラメータ依存二次形式を用いたゲインスケジューリング制御系の設計
  • スプラインガタ ノ パラメータ イゾン 2ジ ケイシキ オ モチイタ ゲインスケジューリング セイギョケイ ノ セッケイ

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Abstract

This paper proposes an approach to gain-scheduling control systems synthesis based on spline-type parameter-dependent quadratic forms that guarantee stability and performances of systems. We provide a procedure to derive a finite set of LMIs from a given LMI-condition on a parameter-dependent quadratic form. It is shown that (1) if there exists any solution to the derived finite set of LMIs, it produces a differentiable spline-type parameter-dependent quadratic form that meets the given LMI-condition. Moreover, we prove that (2) if there exists any differentiable quadratic form solving the given LMI, the finite set of LMIs with some division of scheduling parameter's region is always solvable. Thus unlike previous results this paper guarantees that employing computation always reduce conservatism in solving parameter-dependent LMIs. This approach is applied to parameter-dependent LMIs for analysis and synthesis of exponential stability and L2-gain performance.

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