J.E. Egrashkina - Post-graduate Students, Ulyanovsk State University. E-mail: kartoxena@gmail.com N.O. Sedova - Dr.Sc. (Phys.-Math.), Professor, Ulyanovsk State University. E-mail: nata-sedova@yandex.ru

The paper presents some stability and stabilization results for nonlinear ODE. These results are based on the LPV representation of the equation which provides the basis for constructing continuous Takagi-Sugeno (TS) systems. An important feature of the employment of TS systems is the opportunity to establish stability and to design a stabilizing control via LMI that are obtained by the Lyapunov direct method. So the control for nonlinear system can be designed by routine procedures. The paper presents an overview of the known results on stability and stabilization for TS systems and discusses advantages and drawbacks of different approaches, as well as some directions of further investigations.

 

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