Robust Model Predictive Control for Takagi-Sugeno Model With Bounded Disturbances—Pólya Approach

This paper proposes a general robust model predictive control (MPC) approach for the constrained Takagi-Sugeno (T-S) fuzzy model with additive bounded disturbances. We adopt the homogeneous polynomially parameter-dependent (HPP) Lyapunov matrix with the arbitrary complexity degree and the corresponding HPP control law for the controller design. By applying the Pólya’s theorem and the extended nonquadratic boundedness property, a systematic approach to construct a set of sufficient conditions for assessing robust stability described by parameter-dependent linear matrix inequalities (LMIs) is established. The proposed approach is an improvement over the existing approaches in terms of control performance and stabilizable model range. Numerical examples are provided to show the effectiveness of the proposed robust MPC approach.