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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, we study the stabilization of a linearized viscous Saint-Venant system by constrained Dirichlet boundary control in infinite time horizon. We proved the well posedness of the considered stabilization problem. Also, using an augmented state method, we were able to determine the optimal control (the constrained control) as a feedback control law. Moreover, thanks to the feedback control law, we proved the exponential stability of the solution to the linearized viscous Saint-Venant system, (defined by an unbounded operator). Some numerical experiments are given to illustrate the efficiency of the constrained Dirichlet boundary control. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using the Picard iteration method. Different from the previous works, our paper presents a new theory using the Hadamard fractional integral. We have proved the convergence of the solution of the averaged HIDSFOS to that of the standard HIDSFOS in the sense of the mean square and also in probability. Some examples are given at the end of this paper to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]