Stabilization for Singular Fractional-Order Systems via Static Output Feedback

The stabilization problem of singular fractional-order systems with fractional commensurate order <inline-formula> <tex-math notation="LaTeX">$0 < \alpha < 2$ </tex-math></inline-formula> via static output feedback is studied in this paper. For the <inline-formula> <tex-math notation="LaTeX">$0 < \alpha < 1$ </tex-math></inline-formula> case, two methods for the static output feedback control design are provided. In the first method, the controller is designed without decomposing the system matrix, and less variables are within the second method. Furthermore, a method that is similar to the second method of the <inline-formula> <tex-math notation="LaTeX">$0 < \alpha < 1$ </tex-math></inline-formula> case is provided for the <inline-formula> <tex-math notation="LaTeX">$1\leq \alpha < 2$ </tex-math></inline-formula> case. The controller parameters are computed by solving matrix inequalities, and efficient iterative algorithms are built to solve the resultant matrix inequalities. Numerical examples are provided to show the effectiveness of the proposed results.

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