Polynomial fuzzy observer design: A sum of squares approach

This paper presents a sum of squares (SOS, for brevity) approach to polynomial fuzzy observer design for polynomial fuzzy systems. First, we briefly summarize previous results with respect to a polynomial fuzzy system and controller that are more general representation of the well-known Takagi-Sugeno (T-S) fuzzy system and controller, respectively. Secondly, we propose a polynomial fuzzy observer to estimate states of the polynomial fuzzy system and derive an SOS condition to design a polynomial fuzzy controller and observer. A key feature of the SOS design condition is that it realizes the so-called separation principle, that is, that a polynomial fuzzy controller and a polynomial fuzzy observer can be separately designed without lack of guaranteeing the stability of the overall control system. The design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy controller and observer designs). In addition, the design condition in the proposed approach can be represented in terms of SOS and is symbolically and numerically solved via the recent developed SOSTOOLS and a semidefinite program (SDP) solver, respectively. To illustrate the validity of the design approach, a design example is provided. The example shows the utility of our SOS approach to the polynomial fuzzy observer-based control.