Static Output-Feedback Tracking Control For Positive Polynomial Fuzzy Systems

Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this paper, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transforming the non-convexity conditions when both positive and stability conditions exist into convexity conditions that can be solved by the convex programming techniques. This paper focuses on the static output-feedback tracking control issue of positive polynomial fuzzy-model-based (PPFMB) systems. The purpose of the tracking control is to design an appropriate static output feedback polynomial fuzzy controller which can drive the system states of the nonlinear plant to follow those of a stable reference model subject to an $H_\infty$ performance. The concept of imperfectly matched premises is employed to enhance the design and implementation flexibility. To circumvent the problem of non-convex stability conditions, an approach is employed to transform the non-convex stability conditions into convex ones by introducing a novel Scalar Implantation Transformation (SIT) technique. Besides, the partition approximation of membership functions with local information of membership functions is used to promote stability analysis and synthesis of controllers. The positive and relaxed stability conditions for static outputfeedback tracking control with $H_\infty$ performance being taken into account are obtained in terms of sum-of-squares (SOS). Finally, a simulation example is presented to verify the effectiveness of the proposed tracking control approach.