Constructive control Lyapunov functions for affine nonlinear systems with zero dynamics;

Symmetries of zero dynamics of nonlinear systems;

When there are common Lyapunov functions found in both the linear parts and zero dynamics of the nominal systems,the robust stability of the systems available to arbitrary switching can be obtained by way of constructing a common Lyapunov function relying on uncertain parameters.

Since the transfer functions between the control fin deflection and overload ot Tail-controlled Skid-to-Turn missiles are of nonminimum phase,zero dynamics is unstable.

The excitation system controller was designed to stabilize terminal voltage via zero dynamic theory,while steam-valving controller was designed to enhance angle stability via variable structure control.