Manual Progress in Differential-Algebraic Equations: Deskriptor 2013

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It will serve as an ideal resource for applied mathematicians and engineers, in particular those from mechanics and electromagnetics, who work with coupled differential equations. Springer Professional.

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Back to the search result list. For the stability analysis of linear time-invariant descriptor systems two different generalizations of the classical Lyapunov matrix equation are considered. The first generalization includes the singular matrix related to the time-derivatives of the descriptor variables in an obviously symmetric form; the second one shows at a first sight no symmetry which additionally has to be asked for explicitly. Both approaches will be compared with each other showing different solvability conditions and different solutions in general.


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But for the problem of analyzing asymptotic stability the solution behaviors of the two generalized Lyapunov matrix equations coincide. In spite of the different procedures both approaches lead to the same Lyapunov function for the analysis of asymptotic stability of linear time-invariant descriptor systems.


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  • Progress in Differential-Algebraic Equations: Deskriptor 2013.

The two approaches will be illustrated by the stability analysis of mechanical descriptor systems, i. Although the application of the approaches usually is very costly, they represent suitable tools for the stability analysis of linear time-invariant descriptor systems. We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the asymptotic stability of the zero dynamics and stabilizability. To this end, the concepts of autonomous zero dynamics, transmission zeros, right-invertibility, stabilizability in the behavioral sense and detectability in the behavioral sense are introduced and algebraic characterizations are derived.

It is then proved, for the class of right-invertible systems with autonomous zero dynamics, that asymptotic stability of the zero dynamics is equivalent to three conditions: stabilizability in the behavioral sense, detectability in the behavioral sense, and the condition that all transmission zeros of the system are in the open left complex half-plane.

Online Progress In Differential Algebraic Equations Deskriptor

Furthermore, for the same class, it is shown that we can achieve, by a compatible control in the behavioral sense, that the Lyapunov exponent of the interconnected system equals the Lyapunov exponent of the zero dynamics. This contribution not only provides a new necessary and sufficient condition for causal observability of nonlinear descriptor systems but also a method to design the causal observer. The approach is based on the transformation of the descriptor system into a state-space form, the so called coupled state-space system.

This description exists for all regular descriptor systems no matter if they are proper or not. If the new condition is satisfied, the coupled state-space system can be modified and can be used to design a state-space observer. Issue Issue Issue Larisa A.


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Vlasenko V. Karazin Kharkov National University, Ukraine.

Anatoliy G. Valeriy V. Arkadiy A. Chikriy V.

ISBN 13: 9783662449257

KEY WORDS: descriptor system , differential algebraic equation , quadratic performance functional , impulse intensities , moments of impulse application , optimal impulse control , adjoint state , two-point boundary value problem , radio technical filter , transient state. Zaitsev, Nelya V. Gradoboyeva, Grigoriy D. Samoilenko, Yuriy P. Begell Digital Portal. Krasovskiy N. App Download Follow Us. Macbooks All In Ones 2 in 1 Laptops. Home Theaters Headphones. Towels Sink Urinals.

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