The problem of stability and stabilization for a class of circuit systems with time-varying delays via variable period sampled-data control was considered in this paper. First, the unique boundary conditions were utilized to handle the conic-type nonlinear terms. A Lyapunov-Krasovskii (L-K) functional, which can consider both time-varying delay and sampling time information, was constructed. Then, based on the free-weighting matrices and the improved reciprocally convex combination approach, sufficient conditions for system stabilization over a wider sampling interval were obtained in terms of Linear Matrix Inequalities (LMI), enabling the determination of controller gains. Finally, considering the impact of stable operation of the circuit system on the energy consumption and life cycle of the building, a time-delayed circuit system simulation verified our results, by assuming different upper bounds on time-delay and maximum sampling intervals and designing a modal-related sampled-data controller corresponding to them. The results showed the successful application of this method in the building circuit system, which provides theoretical support for the optimization of building energy consumption and the stable operation of the circuit system.