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Статья
2017

On the use of a general quadratic Lyapunov function for studying the stability of Takagi–Sugeno systems


N. O. SedovaN. O. Sedova, Zh. E. EgrashkinaZh. E. Egrashkina
Русская математика
https://doi.org/10.3103/S1066369X17050097
Abstract / Full Text

We study the stability of the zero solution to a nonlinear system of ordinary differential equations on the base of its Takagi–Sugeno (TS) representation. As is known, the most constructive stability and stabilization conditions for TS systems stated as linear matrix inequalities are established with the help of a general quadratic Lyapunov function (GQLF). However, such conditions are often too rigid. Using a modification of the Lyapunov direct method, we propose asymptotic stability conditions with weaker requirements to GQLF. They allow an application to a wider class of systems. We also give some illustrative examples.

Author information
  • Ulyanovsk State University, ul. L. Tolstogo 42, Ulyanovsk, 432017, RussiaN. O. Sedova & Zh. E. Egrashkina
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