Robust H∞ input-output finite time boundedness of delayed nonlinear systems: Analysis and controller design

This paper addresses the robust H∞ input-output finite-time boundedness (IO-FTB) problem for a class of continuous delayed nonlinear systems with external disturbances. Both analysis and controller design issues are concerned. For the system under discussion, the nonlinearity is described by a dynamical bound rather than its exact dynamics, which covers all nonlinear systems that are locally Lipschitz. Throughout this paper, first, the concept of IO-FTB is originally established for time-delayed nonlinear systems, which relaxes the need for zero initial conditions. Second, under the direction of this newly proposed concept, system performance analyses are presented for IO-FTB and robust H∞ IO-FTB issues, respectively. Then a state feedback controller is designed which guarantees the H∞ disturbance attenuation performance for all unknown nonlinearities lying in a known hypersphere and all admissible norm-bounded disturbances. Finally, a numerical example is provided to validate the developed controller.