In this paper we present an algorithmic technique for determining a feedback compensator which will stabilize the interval dynamic system specifically the robust regulator design for interval plants. The approach taken here is to allow the system parameters to live within prescribed intervals then design a dynamic feedback compensator which guarantees closed-loop system stable. The main contribution of this paper is the idea of introducting a "simplified Kharitonov`s results" for low order polynomials to search for suitable compensator parameters in the compensator parammeter space to make the uncertain system robust. We also design the robust regulator which will $D_{phi}$ -stabilize (have the closed-loop poles in the left sector only) the dynamic interval system while having good performance. the numerical examples are given to show the substantially improved robustness which results from our approach.