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Controllability of nonlinear systems with multiple delays

In the present paper local constrained controllability problems for nonlinear system with constant delays in the control are formulated and discussed. Using some mapping theorems taken from functional analysis and linear approximation methods sufficient conditions for relative and absolute local constrained controllability in a given time interval are derived and proved. The present paper extends controllability conditions with unconstrained controls given in the literature to cover the case of nonlinear systems with delays in control and with constrained controls. Special case of semilinear systems without delays is also considered.