Compensation of state-dependent state delay for nonlinear systems

We extend the technique for compensating state-dependent delays from systems with delayed inputs to systems with delayed states. We focus on predictor-feedback design for nonlinear systems in the strict-feedback form, having a state-dependent state delay on the virtual input. The two key challenges are the definition of the predictor state and the fact that the predictor design does not follow immediately from the delay-free design. We resolve these challenges and we establish asymptotic stability of the resulting infinite-dimensional nonlinear system for general nonnegative-valued delay functions of the state. Due to an inherent limitation on the delay rate, and since the delay rate depends on the state, we obtain only regional stability results. However, for forward-complete systems, we provide an estimate of the region of attraction in the state space of the infinite-dimensional system. We finally provide two examples, including an example of stabilization of a cooling system.