Output feedback stabilisation for uncertain nonlinear time-delay systems subject to input constraints

Robust stabilization of a class of imperfectly known systems with time-varying time-delays via output feedback is investigated. The systems addressed are composed of a nonlinear nominal system influenced by nonlinear perturbations which may be time-, state, delayed state, and/or input-dependent. The output of the system is modelled by a nonlinear function, which may depend on the delayed states, and inputs, together with a feed-through term. Using bounding information on the perturbations, in terms of specified growth conditions, classes of unconstrained and constrained output feedback controllers are designed in order to guarantee a prescribed stability property for the closed-loop systems, provided appropriate stability criteria hold. Two stability criterion are given: one in terms of a Linear Matrix Inequality (LMI), the other is algebraic in nature, obtained using a Geršgorin theorem.