Kusii S. Robust stabilization and optimization of control systems with limited perturbations

In this thesis, criteria for the existence of output feedback static and dynamic regulators providing asymptotic stability of linear control systems with a safe spectral stability margin are obtained. It is shown that the methods of constructing the stabilizing regulators that follow from the criteria can be used for some class of nonlinear control systems. An iterative algorithm for constructing static output feedback stabilizing regulator redused to solving linear matrix inequalities is developed for discrete control systems. Using the Lyapunov quadratic function method, criterions for the existence of stabilizing regulators that provides specified evaluation of the weighted damping level of external and initial perturbations are formulated for classes of linear systems with controlled and observed outputs. Constructive algorithms for robust stabilization and generalized H-optimization of the classes of systems are developed and numerically implemented for specific mechanical objects by using dynamic regulators with zero initial vector.