Stabilization of dynamic system under uncertain and random perturbations

Stabilization is considered in the sense of ensuring dissipativity (in probability) of a quasilinear dynamic system under uncertain and random disturbances, as well as random measurement errors. The problem is solved in a class of linear controls with the aid of vector Lyapunov functions by means of which the nonlinearity in the equations of motion of the system is interpreted as a weak connection between the subsystems of identifiction and control. The possibility is also examined of improving the quality of stabilization with the aid of a nonlinear control in the case that the phase vector is measured exactly.