Stabilization of Linear Dynamic Objects According to the Measured-Error State Under Constraints on the Phase and Control Variables

We consider the problem of estimating the region of admissible initial states of a linear dynamic system for which the linear controller obtained in the problem of synthesizing the control under constraints on the phase and control variables without taking into account the error in measuring the state and also provides stabilization in the case of control in the form of a linear feedback on the state measured with a limited relative error. The approach to the solution is based on the application of the method of quadratic Lyapunov functions and the apparatus of linear matrix inequalities. Sufficient conditions are formulated for finding the boundaries of this area. Stabilization problems are considered as examples of an inverted pendulum and body movement in an electromagnetic suspension. The results of the numerical simulation are presented.