VERSIONS OF SONTAGS INPUT TO STATE STABILITY CONDITION AND THE GLOBAL STABILIZABILITY PROBLEM

This paper deals with the global feedback stabilizability problem for interconnected nonlinear systems that are affine in the control. The corresponding feedback stabilizers are supposed to be almost smooth real mappings. The results of this paper extend those developed in recent works of the author [SIAM J. Control Optim., 29 (1991), pp. 457-473], [Systems Control Lett., 15 (1990), pp. 441-448], [SIAM J. Control Optim., 30 (1992), pp. 879-893] concerning the local stabilizability problem. The main sufficient conditions presented are of Lyapunov type, and the main idea of the paper is based on the input to state stability condition introduced by Sontag [IEEE Trans. Automat. Control, 35 (1990), pp. 473-477].