Iterative Changing Supply Rates, Dynamic State Feedback, and Adaptive Stabilization of Time-Delay Systems

Global adaptive stabilization by partial state feedback is studied for time-delay cascade systems with nonlinear parameterization. The inverse-dynamics of time-delay nonlinear systems under consideration is of a lower-triangular form and assumed to satisfy certain ISS-like conditions. By taking advantage of the lower-triangular structure, we present an iterative algorithm for changing supply rates so that the time-delay zero-dynamics can be handled effectively. With the aid of the iterative technique of changing supply rates, we develop a dynamic gain-based control strategy that, together with the feedback domination design, leads to a construction of partial-state, delay-free adaptive controllers. As a result, all the states of the time-delay cascade system are regulated to the origin and the boundedness of the solution of the closed-loop system is achieved.