  The objective of the paper is to put canonical Lyapunov function(CLF),
canonizing diffeomorphism (CD) and canonical form of dynamical systems (CFDS),
which have led to the generalization of the Lyapunov second method, in
perspective of their high efficiency for Mathematical Modelling and Control
Design. We show how the symbiosis of the ideas of Henri Poincare and Nikolay
Chetaev leads us to CD, CFDS and CLF. Our approach successfully translates into
mathematical modelling and control design for special two-angles synchronized
longitudinal maneuvering of a thrust-vectored aircraft. The essentially
nonlinear five-dimensional mathematical model of the longitudinal flight
dynamics of a thrust-vectored aircraft in a wing-body coordinate system with
two controls, namely the angular deflections of a movable horizontal stabilizer
and a turbojet engine nozzle, is investigated. The wide-sense robust and stable
in the large tracking control law is designed. Its core is the hierarchical
cascade of two controlling attractor-mediators and two controlling terminal
attractors embedded in the extended phase space of the mathematical model of
the aircraft longitudinal motion. The detailed demonstration of the elaborated
technique of designing wide-sense robust tracking control for the nonlinear
multidimensional mathematical model constitutes the quintessence of the paper.
