Noncausal multipliers for nonlinear system stability

Abstract

Using the Popov approach, new absolute stability conditions in multiplier form are derived for a single-loop system with a time-invariant stable linear element G in the forward path and a nonlinear time-varying gain k(f)@(-) in the feedback path. The classes of nonlinearities considered are the monotonic, odd Linear time invariant stable monotonic, and power law. The stability multiplier contains causal and noncausal terms; for absolute stability, the latter give rise to a lower bound (which is believed to be new) on dk/df and the former, as in earlier investigations, to an upper bound on dk/df. Asymptotic stability conditions for a linear system are realized as a limiting k(t)$(r) Nonlinear rnernoryless