Delay independent static output feedback variable structure control for affine nonlinear systems

In this paper, a stabilisation problem for a class of nonlinear control systems with uncertainties involving time-varying delay, is considered. It does not require that the nominal system is linearisable or partial linearisable. The bounds on both matched and mismatched uncertainties are nonlinear and time delayed. A static output feedback variable structure control is synthesized to stabilise the system uniformly asymptotically. A control strategy to enforce exponential stability is also derived. The Lyapunov-Razuminkhin approach is used to deal with the time delay, and the bounds on the uncertainties are used in the control design to enhance the robustness. The designed control does not depend on the time delay and thus it is not required that the time delay is known. Finally, the obtained results are tested on a simple mechanical system through simulation.