Kotov T. Robust stabilization and weighted damping of bounded disturbances in descriptor control systems

This dissertation is devoted to the development of constructive methods of generalized (weighted) H∞-optimization for the class of linear descriptor (differential-algebraic) control systems in the presence of limited perturbations in the equations of object dynamics, as well as controlled and controlled control. At the same time, generalized quality criteria of such systems are used, which characterize the weighted level of quenching of external and initial perturbations (DV Balandin, MM Kogan, OG Mazko, Z. Feng). The main results that determine the scientific novelty of the dissertation: • the structure of the general solution of the initial problem for regular descriptor systems with the agreed initial conditions is investigated; • a method for finding the vectors of the worst external and initial perturbations in descriptor systems with respect to weighted quality criteria is proposed; • the problem of synthesis of descriptor systems with a dynamic controller is reduced to a similar problem with a static controller in an extended phase space; • necessary and sufficient conditions for the existence of stabilizing static and dynamic regulators for the observed output, in which the closed system belongs to the class of permissible descriptor systems and its weighted level of quenching of external and initial perturbations is less than the specified value; • the combined method of linear and quadratic matrix inequalities in the problem of weighted H∞-control for descriptor systems with polyhedral uncertainty of matrix coefficients is generalized; • the method of constructing an ellipsoidal family of matrices of generalized H∞-regulators according to the observed output is developed; • developed research methods, which are reduced to the solution of systems of linear and quadratic matrix inequalities, are used in the problems of robust stabilization and generalized H∞-optimization of specific descriptor control models.