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Versions of Sontag’s ”input to state stability condition” and the global stabilizability problem. (English) Zbl 0788.93076

Summary: 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 Optimization 30, No. 4, 879-893 (1992; Zbl 0751.93071), Syst. Control Lett. 15, No. 5, 441-448 (1990; Zbl 0729.93060)] 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 E. D. Sontag [IEEE Trans. Autom. Control 35, No. 4, 473-476 (1990; Zbl 0704.93056)].

MSC:

93D15 Stabilization of systems by feedback
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