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On the solvability of linear matrix equations

Mlj Malo Hautus
- Vol. 8207
TLDR
In this paper, the authors generalized linear matrix equations to nonsquare equations, nonpolynomial type equations, in particular equations given by an integr~l, and finally to equations over an arbitrary commutative ring with unit element.
Abstract
Linear matrix equations were studied by Sylvester, Stephanos, Datuashvili and Roth. In this paper, solvability tz::Onditions given by. these authors are generalized in various directions: to nonsquare equations, nonpolynomial type equations, in particular equations given by an integr~l, and finally to equations over an arbitrary commutative ring with unit element.

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Citations
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Book

Control of Linear Systems with Regulation and Input Constraints

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On regulation under sampling

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On the regulator problem for a class of LTI systems with delays.

TL;DR: This paper deals with the problem of tracking a reference signal while maintaining the stability of the closed loop system for linear time invariant systems with delays in the states and proposes a solution for both the state and error feedback regulation.
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Smoothing Tie-Line Power Fluctuations for Industrial Microgrids by Demand Side Control: An Output Regulation Approach

TL;DR: It is demonstrated that the demand side control based on output regulation is able to achieve not only zero steady error in rejecting the time-varying wind power disturbance but also guarantee the satisfactory dynamic performance of modulated loads for the grid-connected IMG.
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Nonlinear Robust Control of a Batch Fermentation Reactor

TL;DR: In this article, a nonlinear robust regulator is applied to track a singular optimal reference signal derived for a batch beverage fermentation, based on a model of the process that includes the energy balance and the mass balances of the biomass, ethanol and the sugars involved in the fermentation.
References
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Book

The Theory of Matrices

TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book

Theory of matrices

Journal ArticleDOI

Explicit Solutions of Linear Matrix Equations

Peter Lancaster
- 01 Oct 1970 -