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.
KeywordsQuadratic Form Sector Condition Frequency Condition Linear Block Multiplier Form
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