A Framework for Prescribed-Time Integral Control Design of Feedback Nonlinear Systems

This brief investigates the global prescribed-time regulation problem for a class of uncertain feedback systems subject to matched disturbances and modeling uncertainties with unknown and time-varying system parameters. New integral controllers consisting of an integral dynamic are proposed to make all states of the uncertain systems bounded and prescribed-time convergent to zero. First, by introducing an integral dynamic and a novel state transformation, the uncertain feedback systems with disturbances are converted into a class of generalized feedback nonlinear systems. Second, by virtue of the dynamic gain technique, the problem of designing prescribed-time regulating controllers for the generalized feedback nonlinear systems is transformed into that of designing a dynamic parameter for a class of new systems. At last, following the Lyapunov stability theorem and characteristic of the dynamic parameter, the boundness of the new systems yields the prescribed-time regulation of the generalized feedback nonlinear systems, which indicates the global prescribed-time regulation of the considered systems. The effectiveness of integral controllers is verified from simulation results in a PWM-based DC-DC buck converter.