Frequency-domain stability criteria for SISO and MIMO nonlinear feedback systems with constant and variable time-delays

Abstract

New frequency-domain criteria are proposed for the L2-stability of both nonlinear single-input-single-output (SISO) and nonlinear multiple-input-multiple-output (MIMO) feedback systems, described by nonlinear integral equations. For SISO systems, the feedback block is a constant scalar gain in product with a linear combination of first-and-third-quadrant scalar nonlinearities (FATQNs) with time-delay argument functions; and, for MIMO systems, it is a constant matrix gain in product with a linear combination of vector FATQNs also with time-delay argument functions. In both the cases, the delay function in the arguments of the nonlinearities may be, in general, i) zero, ii) a constant, iii) variable-time and iv) fixed-history (only for SISO systems).