Abstract
In this chapter we consider systems with time-periodic nonlinearities. We begin by formulating a special version of the frequency condition, which involves sequences and Fourier series instead of more abstract measures used in Chap. 3. It is proved that for SISO nonlinearities, slope-restricted in the state variable, a result similar to the multiplier form of Chap. 3 can be obtained. The result is then extended to gradient MIMO nonlinearities and to so-called quasimonotone nonlinearities. Some of these results are applied to derived stability conditions for forced oscillations. Then, a class of linear periodic MIMO systems is considered, which is then extended to a certain parametric class of nonlinearities.
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© 2013 Springer-Verlag London
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Altshuller, D. (2013). Time-Periodic Systems. In: Frequency Domain Criteria for Absolute Stability. Lecture Notes in Control and Information Sciences, vol 432. Springer, London. https://doi.org/10.1007/978-1-4471-4234-8_4
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DOI: https://doi.org/10.1007/978-1-4471-4234-8_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4233-1
Online ISBN: 978-1-4471-4234-8
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