|Title||L2 -STABILITY OF VECTOR EQUATIONS WITH NONLINEAR CAUSAL MAPPINGS|
|Publication Type||Journal Article|
|Year of Publication||2008|
|Journal||Dynamic Systems and Applications|
|AMS Subject Classification||34K20, 34K99, 93D05, 93D25|
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.