Local analysis of continuous-time Takagi–Sugeno fuzzy system with disturbances bounded by magnitude or energy: A Lagrange multiplier method

This paper is concerned with the problem of computing the bounds of disturbances for continuous-time Takagi–Sugeno fuzzy model. Two kinds of disturbances are investigated by applying the non-parallel distributed compensation (non-PDC) law, non-quadratic Lyapunov function and Lagrange multiplier method. One is bounded by magnitude, the other is bounded by energy. If the exogenous disturbances are bounded by magnitude, the maximal value of the magnitude under which the closed-loop system can be controlled is obtained by solving an optimization problem. On the other hand, if the disturbances are bounded by energy, except for the maximal bound, some conditions are derived to get two local regions (a smaller and a bigger) such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set (where the original system can be represented as T–S model exactly). In the end, the effectiveness of the proposed results is demonstrated by two examples.