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Method of Lyapunov Functions for Nonquadratic Stabilization of Controlled Systems


O.V. Druzhininа, S.N. Petrova

On the basis of the scheme of in parallel distributed compensation for stabilization of TakagiSugeno system the method of obtaining of conditions of nonquadratic stability is offered. Nonquadratic Lyapunov's function is presented in the form of a set of several Lyapunov functions. The offered stability conditions are less restrictive in comparison with known and also allow to stabilize the fuzzy systems which are not supposing the quadratic stabilization. The new stability conditions of TS-model based on using of several Lyapunov functions are obtained. It is shown that sufficient stability conditions of system can be formulated in terms of an admissibility of a set of linear matrix inequalities. The given method allows to use the structural information in base of the rules reducing restrictiveness of analysis and to increase the efficiency of calculations.
June 24, 2020
May 29, 2020

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