Finite-time fuzzy stabilisation and control for nonlinear descriptor systems with non-zero initial state

For nonlinear descriptor systems, this paper presents an approach to obtain a fuzzy controller with guaranteed finite-time stability and finite-time boundedness with non-zero initial state, which outperforms some recent work and additionally provides a precision estimation of model approximation. We prove necessary and sufficient conditions of finite-time stability and finite-time boundedness with non-zero initial state for nonlinear descriptor systems. Using Takagi-Sugeno fuzzy dynamic models and proposed sufficient conditions, we define fuzzy sets and use linear matrix inequalities to satisfy differential linear matrix inequalities. A simulation confirms efficiency and precision of the given method.