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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analysis applications approach approximation assignment assume asymptotically stable Banach space bounded chapter characteristic closed closed-loop system complete computation consider constant continuous control law corresponding defined Definition delay equations delay systems denotes dependent described determined difference differential equations discussed distributed effect eigenvalues error estimate example exists factors feedback Figure finite flow frequency function give given Hence imaginary implementation independent initial input integral interval Introduction invariant leads Lemma linear systems load balancing Lyapunov Mathematical matrix method neutral node nonnegative Note observer obtained operator parameters performance periodic polynomial positive present problem Proof properties Queue Remark respect robust stability roots satisfied shown solution space spectrally stability stochastic sufficient tasks Theorem theory time-delay systems tion transfer uncertainties unstable values zero