Constraints on control input and output of polynomial fuzzy systems via a sum of squares approach

This paper presents the constraint of input and output design of a nonlinear system via sum of square (SOS). This proposed SOS-based controller is able to limit the closed-loop system to satisfy the input and output constraints. Those SOS constraint conditions are more general than the existing linear matrix inequality (LMI) constraint conditions. The constraint conditions are represented in terms of sum of squares of the polynomial fuzzy systems and can be numerically solved via the recent developed SOSTOOLS. To illustrate the validity of the constraint design approach with stability condition, a design example is provided. Computer simulations show that the SOS-based approaches are more effective than the LMI-based approaches.