L2-Stability of nonstationary feedback systems: frequency-domain criteria

Sundareshan, Malur K. ; Thathachar, M. A. L. (1974) L2-Stability of nonstationary feedback systems: frequency-domain criteria IEEE Transactions on Automatic Control, 19 (3). pp. 217-224. ISSN 0018-9286

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Official URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumb...

Related URL: http://dx.doi.org/10.1109/TAC.1974.1100553


A frequency-domain positivity condition is derived for linear time-varying operators in L2 and is used to develop L2 stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in L2 with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

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