SYNTHESIS OF STABILIZATION SYSTEMS OF PROGRAM MOTION FOR NONLINEAR OBJECTS OF CONTROL

Nonlocal necessary and sufficient conditions for existence of stabiliz ing pairs are obtained for nonlinear control systems. The stabilizatio n pair includes an admissible stabilizing control and a Lyapunov funct ion that assures asymptotic stability of the zero solution of the corr esponding closed system in deviations, or, what is the same, a given p rogram motion. The problem of stabilizing program motion with incomple te information on the state vector, when certain coordinates of the ob ject of control cannot be measured, and the problem of stabilization i n the presence of constraints on the phase coordinates, and stabilizat ion with respect to part of the variables are considered. All of our r esults are extended to discrete systems. A constructive method for con struction of stabilizing pairs, using a transition to a finite system of inequalities with subsequent calculation by computer is developed. The results can be used for designing CAD subsystems of nonlinear cont rol systems.