Design and Stability Analysis of Third‐Order Twisting Control Systems With Application to DC–DC Converters

ABSTRACT For the switching‐mode systems, the stability is closely related to the symbolic sequence of system states. Utilizing a symbolic sequence transformation technique, this paper designs a third‐order twisting algorithm (TA) and studies its finite‐time stability. A stability condition of second‐order TA is established, and an analytic expression of convergence time for second‐order TA is deduced. By analyzing the importance mechanism of Platform Phase in the symbolic sequence, a stabilized third‐order TA is developed, and a new strategy on parameter selection is given to achieve the finite‐time stability of third‐order TA. The derived convergence times starting from different initial states reveal the quantitative influence of control parameters on dynamic performances of TA, providing guidance for the design of settling time‐customized TA. The application of TA in DC–DC converters is presented, and the comparative experiments demonstrate the superior performances of the proposed method in terms of response time, control accuracy, and disturbances rejection.