Abstract
For analyzing Lur'e systems consisting of linear time-invariant SISO plant and sector-bounded time-invariant nonlinear feedback the Popov criterion is traditionally used (M.A. and F.R., 1964). The multivariable extensions of Popov criterion use so called S-procedure (V.A., 1977; S. et al., 1964) to obtain (only) sufficient conditions of sign definiteness of quadratic form (QF) under multiple quadratic constraints. Such extentions are known to be conservative, because the S-procedure gives only sufficient conditions for the existence of a Lur'e-Postnikov Lyapunov function.In this paper new frequency criteria for analysis of multivariable Lur'e systems are obtained. The following problems are considered: determination of absolute stability margins, evaluation of L2-gain, tests for dissipativity or passivity, All criteria are based on non-conservative usage of Lur'e-Postnikov Lyapunov functions (L.B., 1988; L.B., 1989).The numerical approach for analyzing frequensy real-positive conditions based on solution of continuous sets of linear matrix inequalities is proposed.
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