Cheap Suboptimal Control of an Integral Sliding Mode for Uncertain Systems With Delays

A cheap control problem for a system with state delays and matched uncertainties is studied. First, such a cheap control problem is considered for the nominal linear system associated with the original one. A suboptimal state-feedback composite control for this problem is constructed using a singular perturbation technique. Employing this composite control in the nominal system generates the suboptimal nominal trajectory. Secondly, based on the composite control, an integral sliding mode controller is designed for the original system, providing its robust motion along the suboptimal nominal trajectory. An illustrative numerical example is presented.