The global asymptotic stability and stabilization in nonlinear cascade systems with delay (Q1006986)

The paper deals with nonlinear delay systems of a special type --- so called cascade systems. For such systems, certain sufficient conditions for the local and global uniform asymptotic stability, as well as the stabilizability of the equilibrium, are established. Proofs of the statements are conducted by a standard scheme with the use of Lyapunov-type functionals. It is proved that the use of auxiliary constant-sign functionals and functions with constant-sign derivatives essentially simplifies the statement of sufficient conditions for the asymptotic stability of a cascade. An illustrating example is given.