On use of general Lyapunov function in investigation of stability problem for Takagi–Sugeno systems

We study a stability of the zero solution for a nonlinear system of ODE by use of Takagi–Sugeno (TS) representation. It is known that the most constructive sufficient conditions on stability and stabilization for TS systems have been established using a general quadratic Lyapunov function (GQFL). These conditions may be expressed in the form of linear matrix inequalities (LMI). However, such results are often too conservative. On the base of modified Lyapunov method we propose some weakened asymptotic stability conditions that reduce requirements for CQLF. The results are applicable to a wider class of systems. We give illustrative examples.