Conjugate Gradient Algorithm and its variants have been widely used as an excellent solution method for linear equations on vector and/or parallel supercomputers. But the effectiveness depends on the ability to parallelize the preconditioning procedure. Here, we first deal with Neumann expansion preconditioning method and extend it to polynomial preconditioning method. Both are very simple and available for a wide class of matrices. The numerical studies are made on vector/parallel supercomputer S-3800 and parallel processors KSR-1 and AP1000 to validate the vactor/parallel effect. The methods are applied to a matrix discretized by Fourier series expansion of a plasma fluid flow equation, as well as usual finite difference and finite element methods.

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Several sufficient conditions are derived for quadratic matrix polynomial systems to be overdamped based on an established characterization of the property. One of the conditions is shown to be less conservative than a previous sufficiency criterion, whereas another one to complement it. It is also pointed out that a pair of the coefficient matrices of the systems is interchangeable so long as the overdamping property is concerned. This fact may possibly double the line-up of sufficiency criteria for overdampedness, thus enriching alternatives to such testable conditions.

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化学プラントなどの製造プロセスでしばしば見られる入出力間でむだ時間の異なる多入出力システムは，異なるむだ時間を正確に予測して制御することは困難である．例えばむだ時間系に対して追従特性の良い制御系を設計できる一般化最小分散制御(GMVC)を用いても，異なるむだ時間を正確に考慮することが難しく，また目標値応答特性と外乱応答特性が同時に変化してしまうという問題点があった．そこで, 異なるむだ時間を考慮するとともに，目標値追従特性と外乱抑制性を独立して制御設計することができるGMVCに基づく多入出力２自由度制御系を提案する．

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非等方弾性体からなる板または半空間に接着された層状板におけるガイド波（定常波）について考える．伝播方向の指定されたガイド波の波数をk，位相速度をvとすれば，vとkの関係は一般に可算無限個の関数（分散曲線）v=v(k)の形で与えられる．考えている弾性体に対し，半空間でのRayleigh波あるいは接着された２つの半空間でのStoneley波が存在した場合に，弾性板あるいは層状板にはそれらの波に対応したガイド波（k→∞でRayleigh波あるいはStoneley波の速度に漸近する分散曲線v=v(k)）の存在が期待される．本講演では，上述のRayleigh波，Stoneley波の「亜音速域」での存在を仮定し，それぞれに対応するガイド波の存在を示し，分散曲線v=v(k)のk→∞での詳しい挙動を与える．手法としては，v=v(k)を決定する問題を、パラメータkを含む2階常微分方程式の固有値問題と捉え，の理論（特に因数分解）を用いて解析を行う．

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本稿では、2つの実重複スカラーブロック摂動に対する構造化特異値を計算する方法を提案する。この問題は、メインループ定理を用いることにより、1つの実パラメータに依存した係数行列からなるパラメータ依存D-Gスケーリング条件に帰着される。そこで本稿では、この条件に現れるスケーリング行列をパラメータに関するで表現し、さらに、こうして得られた条件式に一般化KYP補題を用いることで、パラメータに依存しないLMI条件を導く。

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In this paper, we unify and generalize two fast algorithms for the evaluation of polynomials and their higher-order differential coefficients.

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There are a lot of multi-inputs multi-outputs (MIMO) systems in the chemical plants of the manufacturing, and they have the multiple time delays which are different length in each their inputs and outputs pair. This paper explains two-degreeds-of-freedom (2DOF) control system based on generalized minimum variance control (GMVC) for MIMO systems. It can improve the tracking performance to the reference signals and the response property for the disturbance. And the states between the sampling period can be expressed by using the modified z transform for considering multiple time delays. Additionally Tracking Controller is designed to decoupling plant.

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化学プラントなどの製造プロセスにおいては, 入出力間でむだ時間の異なる多入出力システムがしばしば見られる. 本論文では, 各入出力間で異なるむだ時間を考慮するとともに目標値追従特性と外乱抑制性を独立して制御設計できる一般化最小分散制御に基づく多入出力２自由度制御系を提案している. さらに制御対象の骨格行列を用いた非干渉化を施すことで干渉の影響を抑えることができ, ロバスト性についても検討している.

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This paper presents a stable multivariable MRACS (Model Reference Adaptive Control System) including an estimator for unknown coefficients of polynomials which are the nondiagonal elements of the interactor matrix of the plant. It is shown that the degrees of the polynomials are bounded by the plant's degree and that there exists an identification model which retaines the left-lower triangles structure of the interactor matrix. The former relates the number of the coefficients to be estimated and the latter plays a key role on the stability proof. Thereafter, the adaptive control system is designed on the assumption of knowing degrees of diagonal elements of the interactor matrix. It is a most general extention of MRACS from the scalar system to the multivariable system in the sence that it requires the minimal restriction on the plant's transfer function and the minimal information on the plant's interactor matrix. The global stability of the total control system is proved through modification of the established method by Goodwin et al.. Some numerical examples are also presented to show the effectiveness of the proposed adaptive control in comparison with the ordinary adaptive control in which the interactor matrix should be completely known a priori.

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There are a lot of multi-inputs multi-outputs (MIMO) systems in the chemical plants of the manufacturing, and they have the multiple time delays which are different length in each their inputs and outputs pair. This paper explains two-degreeds-of-freedom (2DOF) control system based on generalized minimum variance control (GMVC) for MIMO systems. It can improve the tracking performance to the reference signals and the response property for the disturbance. And the states between the sampling period can be expressed by using the modified z transform for considering multiple time delays.

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Minimum Variance Control(MVC) is a control system of discrete time often used on the scene. But by discretization, unstable zeros may occur. And a plant becomes a non-minimum phase system, even if it is minimum phase system in continuous time. MVC can not treat a non-minimum phase system. Then, unstable zero is eliminated by introducing the delta operator which approximates discrete time to continuous time and can treat it. This technique can be extended to Multi-Inputs Multi-Outputs(MIMO) systems. This paper uses the decoupling control method called skeletal matrix, because mutual interference may have big influence in control by the MIMO system. A stable MIMO-MVC system is attained by the proposed approach which combines the delta operator and the decoupling method.

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本稿では，状態方程式の係数行列が不確かなパラメータに 多項式形式で依存する，線形時不変系のロバスト性能解析問題について 考察する． 既存の解法の多くは，系の性能を特徴づける標準的な LMI に基づいて この問題をロバスト半正定値計画問題に帰着させ， 近似的な解法を適用するというものである． これらの既存のアプローチとは異なり，本稿では 系の性能を特徴づける双対 LMI に基づくことで ロバスト性能解析問題が自然な形で未知行列を変数とする 多項式計画問題に帰着されることを示す． さらにこの計画問題に対する階層的な緩和問題を構成し， 緩和問題が非可解となればただちにロバスト性能が満たされることを示す． 最後に，緩和問題が可解となる場合に，ロバスト性能が満たされないと帰結 し得るような緩和問題の解に関するランク条件を導出する．

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There are a lot of multi-inputs multi-outputs (MIMO) systems in the chemical plants of the manufacturing, and they have the multiple time delays which are different length in each their inputs and outputs pair. This paper proposes a new technique for the MIMO system with the multiple time delays. Generalized minimum variance control was used for the control design method. The following states of time delays are held in one sampling interval by selecting sampling period. The states between the sampling period can be expressed by using the modified z transform. Thus, the discrete-time model of controlled object is obtained, and MIMO for GMVC is designed by using this model.

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This research proposes a controller design method for p-inputs/q-outputs multi-inputs multi-outputs (MIMO) systems which have a greater number of inputs variables than the number of output variables. Recently, data-driven controller design methods, that can directly derive control parameters from a set of closed-loop operating data under the conditions that cannot obtain physical models and/or accurate system parameters by system identification, has been received much attention. Although some data-driven controller design methods for MIMO systems with the same number of inputs/outputs have been proposed because there are many MIMO systems in industrial sites, there are few reports about the design methods for MIMO systems with p-inputs/q-outputs. In this research, a design method of a generalized minimum variance controller (GMVC) based on the principal component analysis (PCA) is proposed. In particular, obtained p number of inputs are reduced to q number of principal components by PCA. Moreover, a data-driven GMVC is designed for a system model construceted by the principal components and system outputs. The proposed method can derive good control parameters stably than a conventional method, and the method can reduce the number of adjustable parameters that must be set by an operator. The effectiveness of the proposed method is verified by simulation examples.

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This paper shows necessary and sufficient conditions for the solvability of the block decoupling problem by using the concept of interactor.
We first propose a method that state feedback and input transformation are directly derived from the relation of the open-loop transfer function matrix with relatively right prime factrization and the closed-loop transfer function matrix. Secondly, we introduce an unique lower left trianglar matrix, an interactor, which is defined by Wolovich and Falb, and define a lower left trianglar matrix which has similar qualities of interactor. Finally, we show our method for solving the block decoupling problem. The most advantage of our technique is that the transfer function matrices of subsystems in the block decoupled system always become the lower left trianglar matrices.

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