Controller Design Under Fuzzy Pole-Placement Specifications: An Interval Arithmetic Approach

This paper discusses fuzzy specifications for robust controller design, as a way to define different specification levels for different plants in a family and allow the control of performance degradation. Controller synthesis will be understood as mapping a fuzzy plant onto a desired fuzzy set of closed-loop specifications. In this context, a fuzzy plant is considered as a possibility distribution on a given plant space. In particular, pole placement in linear plants with fuzzy parametric uncertainty is discussed, although the basic idea is general and could be applied to other settings. In the case under consideration, the controller coefficients are the solution of a fuzzy linear system of equations with a particular semantics. Modal interval arithmetic is used to solve the system for each <formula formulatype="inline"><tex>$\alpha$</tex> </formula>-cut. The intersection of the solutions, if not empty, constitutes the solution to the robust control problem.