This paper presents an analytical study of a DC motor under interval uncertainties and introduces a novel method based on interval analysis for optimizing its control. The key benefit of using an interval-based uncertainty model is its independence from any specific probability distribution, allowing the system to be examined using only known upper and lower bounds. The proposed interval analysis is applied within the framework of linear quadratic regulator (LQR) control to realistically simulate and optimize the DC motor’s behavior. To achieve this, Pontryagin’s principle is employed to derive the necessary conditions for the interval LQR problem, which are then transformed into a system of ordinary differential equations (ODEs) through algebraic techniques. By solving this nonlinear interval ODE system, the confidence interval for the feedback controller is determined, ensuring that the actual solution lies within this interval. The Chebyshev inclusion method is used to address the uncertain ODE system.