Stabilization for a class of complex interlaced systems using asymptotical gain

This paper addresses the stabilization problem of a class of interlaced systems that are not in a strict‐feedforward form and contain some severe nonlinear terms. Bounded control laws in a fractional form are explicitly constructed. The feature of stability analysis allows the closed‐loop system, when it is proven to have no finite escape time, to employ the asymptotical gain, which is obtained from an input‐to‐state stable (ISS) subsystem, to calculate the severe nonlinear terms, and the related estimate in turn guides the assignment of small controls. Together with the use of the passivity theory and the ISS‐based stability criterion, the proposed method requires no small gain analysis although the asymptotical gain is used, and differs from the state‐dependent saturation scheme since the controls do not include saturation functions. As an application, a new stabilizing control law is presented for the well‐known friction ball‐and‐beam system.