Control of cascade systems with time delay -- the integral cross-term approach

Presence of a time delay introduces a limitation to achievable performance and robustness of industrial control systems. This paper presents a Lyapunov based stabilization and control method for nonlinear cascade systems with time delay. The approach uses a construction of a composite Lyapunov functional for a stable cascade obtained in an intermediate step of the procedure. The functional consists of Lyapunov functions or functionals for the subsystems and a cross-term defined by an infinite integral. A strong robustness guarantee for the closed loop system is available and the stabilization can be achieved even through distributed-delay control channels