Advances in Time-Delay Systems by Sjoerd M. Verduyn Lunel (auth.), Silviu-Iulian Niculescu,

By Sjoerd M. Verduyn Lunel (auth.), Silviu-Iulian Niculescu, Keqin Gu (eds.)

In the mathematical description of a actual or organic procedure, it's a universal perform \0 think that the longer term habit of Ihe method thought of relies basically at the current slate, and for that reason might be defined by way of a finite sct of standard diffe­ rential equations. this can be passable for a wide classification of functional platforms. even though. the lifestyles of lime-delay parts, reminiscent of fabric or infonnation shipping, of­ tcn renders such description unsatisfactory in accounting for vital behaviors of many functional platforms. certainly. due principally to the present loss of powerful metho­ dology for research and keep an eye on layout for such platforms, the lime-delay components arc usually both ignored or poorly approximated, which often leads to research and simulation of inadequate accuracy, which in turns results in terrible functionality of the structures designed. certainly, it's been established within the zone of computerized keep watch over quite small hold up could lead to instability or considerably deteriora­ ted perfonnances for the corresponding closed-loop systems.

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In the sequel, the uncertain quasipolynomial (6) wi ll be tenned interval, diamond. and spherical quasi polynomials if all its coeffi cient polynomials Uk(S, (tk) are interval, diamond, and spherical polynomials, respectively. 3 Frequency·Sweeping Conditions We shall present several necessary and sufficient frequency-sweeping conditions for the uncertain quasipolynomial (6) when its coefficients are characterized by lp balls. In this case, the polynom ial fam ilies ak(s, O"k) ass ume the form ...

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