Integral Control for Nonlinear Systems Subject to Time-Varying Perturbations with Unknown Magnitudes

This paper focuses on the design of linear integral controllers for uncertain nonlinear systems subjected to various types of time-varying perturbations. We propose a method called the feedback domination method to address this problem. The time-varying perturbations can include constant step disturbances, exogenous time-varying disturbances with unknown magnitudes, and modeling uncertainties with unknown system parameters. The approach involves constructing a new linear integral controller with integral dynamics to drive the states of uncertain systems without nonlinear terms to the origin asymptotically Additionally, a high-gain technique is introduced to design a controller that can asymptotically drive the states of uncertain nonlinear systems to the origin. Finally, the paper introduces a new stability criterion and extends the results to a class of uncertain nonlinear systems with more general time-varying perturbations of unknown magnitudes.