Saturated Delayed Controls for Feedforward Nonlinear Systems

The saturated delayed feedback is presented to globally stabilize a class of feedforward nonlinear systems whose nominal dynamics is the cascade of multiple oscillators and multiple integrators. Key strategies are stated as follows. 1) To compensate the arbitrarily large input delay and to carry out the recursive analysis, we transform the concerned system into a normal form. 2) In the convergence analysis for multiple oscillators that are relatively difficult to treat, we combine the saturated delayed terms, define the composite Lyapunov functions and use the Cauchy formula. 3) For ease of the analysis on nonlinear terms, we employ saturation levels to restrict them. As applications, the usual feedforward nonlinear systems (with multiple integrators as the nominal dynamics) and the null-controllable linear systems are dealt with in some new manners; and a saturated delayed controller is presented for the well-known TORA system.