Control of deterministically uncertain systems by a differential inequality approach

The authors consider nonlinear uncertain control systems described by ordinary differential inclusions, which model the deterministic uncertainty acting on the dynamics, Asymptotic tracking or linearization is obtained through a differential inequality approach via variable structure control methods. Discontinuous control laws may lead to state equations not possessing classical solutions; however, Filippov solutions do not work in general. Suitable immersions of the original control system lead to either ordinary or partial differential inequalities of the Hamilton-Jacobi type in the continuous state feedback control law, thereby avoiding discontinuous dynamics