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 inte...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）. The stability criteria are derived from certain recently introduced algebraic inequalities concerning the scalar and vector nonlinearities, and involve the causal＋anticausal O＇Shea-Zames-Falb multiplier function （scalar for SISO systems and matrix for MIMO systems）. Its time-domain gl-norm is constrained by the coefficients and characteristic parameters （CPs） of the nonlinearities and, in the case of the time-varying delay, by its rate of variation also. The stability criteria, which are independent of Lyapunov-Krasovskii or Lyapunov-Razumikhin functions and do not seem to be derivable by invoking linear matrix inequalities, seem to be the first of their kind. Two numerical examples for each of SISO and MIMO systems illustrate the criteria.展开更多
文摘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）. The stability criteria are derived from certain recently introduced algebraic inequalities concerning the scalar and vector nonlinearities, and involve the causal＋anticausal O＇Shea-Zames-Falb multiplier function （scalar for SISO systems and matrix for MIMO systems）. Its time-domain gl-norm is constrained by the coefficients and characteristic parameters （CPs） of the nonlinearities and, in the case of the time-varying delay, by its rate of variation also. The stability criteria, which are independent of Lyapunov-Krasovskii or Lyapunov-Razumikhin functions and do not seem to be derivable by invoking linear matrix inequalities, seem to be the first of their kind. Two numerical examples for each of SISO and MIMO systems illustrate the criteria.
