Determination of the Tolerable Sector of Series Nonlinearities in Uncertain Time-Delay Systems Under Dynamical Output Feedback

Several sufficient conditions which guarantee robust stability of uncertain time-delay systems under dynamical output feedback with a class of series nonlinearities are derived in the time domain. Each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness. Properties of the matrix measure and the comparison theorem are employed to give robustness conditions which assure asymptotic stability rather than ultimate boundedness of trajectories. Moreover, for each uncertain time-delay system, a class of series nonlinearities lying in the sector [α, β] are found such that the overall feedback system with these nonlinearities is still asymptotically stable. An algorithm based on these robust stabilization criteria is presented to determine the tolerable range of series nonlinearities from the inverse viewpoint. It is shown that the plant uncertainties and nonlinearities may destabilize the system. Hence the nominal feedback system without series nonlinearities should be sufficiently stable to ensure robust stability.