This paper addresses the robust stabilization problem of first-order uncertain systems. To treat the robust stabilization problem, an interval-based stabilization method using stability conditions of the non-commensurate elementary fractional transfer function of the second kind is developed. Some analytic expressions are determined to compute the set of all stabilizing controller parameters and plot the stability boundary. A robust performance control is also developed to fulfil some desired time-domain performances as the iso-overshoot property. The fractional controller can be used combined with the Smith predictor to control a first-order system with time delay and achieve desired specifications. Numerical examples are presented to illustrate the obtained results.
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