A Lyapunov Characterization of Prescribed Performance Control Systems

This article contributes a Lyapunov formulation for prescribed performance controller designs. In particular, we first show that the closed-loop system of a typical class of prescribed performance control systems can be transformed into an interconnection of input-to-state practically stable (ISpS) subsystems characterized by ISpS-Lyapunov functions. Then, we take advantage of the gain-interconnections between the subsystems and construct a Lyapunov function for the closed-loop system. The proposed approach is validated through prescribed performance control for both single-input single-output (SISO) and multi-input multi-output (MIMO) plants, as well as systems not necessarily in the lower-triangular form and systems with dynamic uncertainty.