Non–conservative tools for stability analysis of discrete–time homogeneous dynamics
نویسندگان
چکیده
This note considers the problem of stability analysis of discrete–time homogeneous dynamics, i.e., positively homogeneous of the first degree dynamics. An example of a homogeneous and even continuous dynamics that is globally exponentially stable and that does not admit any λ–contractive proper C–set is presented. This motivates us to propose a natural generalization of this concept, namely, (k, λ)–contractive proper C–sets. It is proven that this simple generalization yields a non– conservative Lyapunov–type tool for stability analysis of homogeneous dynamics, namely, sublinear finite–time Lyapunov functions. Moreover, practicable non–conservative stability tests are established for relevant classes of homogeneous dynamics.
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