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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 3, 1991, pp. 345–355
DOI: 10.4171/ZAA/455

Published online: 1991-09-30

Stability of Nonlinear Systems with Periodically Nonstationary Linear Part

V.A. Yakubovich

Multidimensional nonlinear systems with periodically nonstationary linear part are considered. It is supposed that nonlinear blocks satisfy some integral quadratic constraint. The necessary and sufficient condition of absolute stability with respect to output for such systems are established in terms of certain properties of solutions of a linear Hamiltonian system with periodic coefficients. In the case of constant coefficients this condition transforms into a well-known frequency criterion of absolute stability.

Keywords: Nonlinear system, quadratic integral constraint, absolute stability, frequency criteria, Hamiltonian system, nonoscilativity, quadratic functional, positive definiteness

Yakubovich V.A.: Stability of Nonlinear Systems with Periodically Nonstationary Linear Part. Z. Anal. Anwend. 10 (1991), 345-355. doi: 10.4171/ZAA/455