L2 -STABILITY OF VECTOR EQUATIONS WITH NONLINEAR CAUSAL MAPPINGS

Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L² -norm of solutions are established. The obtained estimates give us explicit conditions for the L² -stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.