DESIGN OF FEEDBACK CONTROLS FOR DYNAMICAL SYSTEMS BY USING COMMON
LYAPUNOV FUNCTIONS
Alexander Ovseevich, Igor Ananievski
We address the problem of synthesizing a bounded feedback control of a linear dynamical system satisfying the Kalman controllability condition. An approach is developed which makes it possible to construct feedback control laws transferring the system to the origin in finite time. The approach
is based on methods of stability theory. The construction utilizes the notion of a common Lyapunov function. It is shown that the constructed control remains effective in the presence of uncontrollable perturbations of the system. As an illustration, results of numerically modelling the dynamics of a second-order system controlled by the law proposed in the paper are presented.