Cross-Term Forwarding for Systems With Time Delay

This paper presents a Lyapunov-based control design method for nonlinear systems with time delay. The key step is construction of a composite Lyapunov functionalV for a stable cascade. This functional consists of Lyapunov functionals for the subsystems and a cross-term defined by an infinite integral. The ldquoL _g V-typerdquo control law is then employed to achieve global asymptotic stability. The design procedure can be applied recursively to stabilize complex feedforward structures. When applied to a linear cascade, it gives a formula for the control law even if some parts of the system can only be stabilized through channels with multiple non-commensurate or distributed delays.