Advances in Time-Delay Systems
Silviu-Iulian Niculescu, Keqin Gu
Springer Science & Business Media, 2004. gada 21. apr. - 446 lappuses
In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora ted perfonnances for the corresponding closed-loop systems.
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abscissa algorithm approach approximation asymptotically stable Ax(t B₁ Banach space bounded chapter closed-loop system coefficient computation consider Contr control law coprime defined Definition delay differential equations delay equations delay systems denotes distributed delay dynamical systems eigenvalues eigenvectors example exists exponential finite dimensional frequency functional differential equations given Hilbert space hn+1 IEEE IEEE Trans imaginary axis implementation initial condition input interval invariant factors J. R. Partington Lemma linear systems load balancing loop Lunel Lyapunov Lyapunov function Lyapunov-Krasovskii functional Mathematical matrix method neutral systems neutral type Niculescu node nonlinear nonnegative dynamical systems obtained operator output parameters polynomial problem Proof quasipolynomial Queue r₁ robust stability roots satisfied Section semigroup space spectrally stability analysis stability exponent stabilizability stochastic delay sufficient conditions systems with delay tasks Theorem theory time-delay systems tion uncertainties unstable values Verduyn Lunel zero