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Common Lyapunov functions for families of commuting nonlinear systems. (English) Zbl 1129.34321
Summary: We present constructions of a local and global common Lyapunov function for a finite family of pairwise commuting globally asymptotically stable nonlinear systems. The constructions are based on an iterative procedure, which at each step invokes a converse Lyapunov theorem for one of the individual systems. Our results extend a previously available one which relies on exponential stability of the vector fields.

MSC:
34D20 Stability of solutions to ordinary differential equations
93D30 Lyapunov and storage functions
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