Dynamic parallel distributed compensation for Takagi-Sugeno fuzzy systems: An LMI approach
This study is devoted to a unified design of dynamic feedback controllers for nonlinear systems described by Takagi-Sugeno rule-based models. These models assume the form of local linear dependencies with the dynamic part governed by the expression \[ \text{if parameters }p_i(t)\dots\text{then }dx/dt= A_ix(t)+ B_iu(t) \] and the output relationship described by the rules \[ \text{if parameters }p_i(t)\dots\text{then }y(t)= C_ix(t), \] \(i= 1,2,\dots, n\) with \(x(t)\), \(u(t)\) and \(y(t)\) denoting the state, input and output variables, respectively. The underlying control is proposed in the form of a dynamic parallel distributed compensation viewed as a nonlinear dynamic feedback control. In the proposed design, both stabilization and multi-objective control synthesis are covered. It is shown that this design can be formulated as a linear matrix inequality (LMI) problem. A numerical example (control of an inverted pendulum) is included.
scientific article; zbMATH DE number 1478245