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In this study, the Lyapunov technique is used to analyze the observer-based control problem for polynomial fuzzy fractional order (PFFO) models. The case of polynomial matrices with unmeasurable states is considered to increase the applicability of the PFFO models in the design problem. In this regard, we offer two design procedures. First, the design conditions are presented in a one-step procedure. In this design, the non-convex conditions are transformed in a set of sum of squares (SOS) by introducing a new symbolic variable except the state vector β and its estimated β ^ . The obtained SOS conditions are presented involve three independent symbolic variables which increase both computing complexity and conservatism. To get around this shortcoming, a second design method is developed. By using the suggested method, SOS conditions requiring just two separate symbolic variables may be obtained. The architecture is shown in two stages; however, the observer and controller gains are computed in a single stage in order to further minimize conservatism. In order to demonstrate the utility of the suggested theoretical analysis, a simulated example is then provided. [ABSTRACT FROM AUTHOR]

In this paper, a robust fault estimation for polynomial systems with time delay via a polynomial adaptive observer is presented and described. In fact, in contrast to previous research works on actuator faults, the learning rate utilized to govern the convergence speed of states and faults errors is not predetermined but is derived using the sum of squares optimization problem. Furthermore, the H ∞ optimization approach was created to reduce the impact of disturbances on state estimation error and fault estimation error. Finally, an illustrative practical example is given to validate the effectiveness of the suggested methodology. [ABSTRACT FROM AUTHOR]