A new approach is proposed for solving the problem of suppressing nonrandom bounded exogenous disturbances in linear control systems using dynamic output feedback. The approach is based on reducing the problem to a matrix optimization problem with the feedback matrix and the observer matrix as the variables. A gradient method for finding dynamic output feedback is written out and justified. A number of examples are considered.

We propose an approach to the normalization of the excitation of the identification loop regressor constructed based on the dynamic extension and mixing procedure. With a constant estimation loop gain, applying this approach allows one to have the same upper bound on the parametric identification error for scalar regressors with various degrees of excitation, a feature that is a significant advantage for practice. The approach developed is compared with the well-known regressor amplitude normalization method, and it is shown that the classical normalization method does not have the above-mentioned property. As a validation of our theoretical conclusions, the results of comparative mathematical modeling are presented for the classical gradient estimation loop, loops with amplitude regressor normalization, and loops with the proposed regressor excitation normalization.

A simple, universal approach to solving the sparse filtering problem - problem using a reduced number of outputs - with arbitrary bounded exogenous disturbances by employing an observer is presented. The approach is based on the invariant ellipsoid method and the technique of linear matrix inequalities. An application of this concept has made it possible to reduce the original problem to a semidefinite programming problem that is easy to solve numerically. The approach is distinguished by its simplicity and ease of implementation and covers both continuous- and discrete-time statements of the problem. The efficiency of the procedure proposed is demonstrated by a test example.

A scheme for controlling oscillations is proposed, in which, within the framework of a coupled system, the van der Pol cycle mode is imposed on a conservative system that admits a family of periodic motions. The acting control is found, the cycle is constructed, the attraction domain of the cycle is determined, and a control law and an algorithm for the asymptotic exit of the coupled system to the cycle mode are given.

A twin-rotor electromechanical system whose output variables make angular motions in the vertical and horizontal planes is explored as a control plant. The mathematical model of the mechanical subsystem, which is essentially nonlinear, includes cross-coupling between propellers, dry-friction torques, and unspecified parameters; it is also subject to uncontrolled external perturbations. A mathematical model of the electric subsystem (considered dynamics of dc-drives) is approximated by linear differential equations. Directly measured are output variables, drive armature currents, and control inputs. The block-based approach was used to develop a decomposition procedure for the synthesis of a dynamic feedback that enables output variables to track specified signals with a given accuracy. To suppress unmatched perturbations, everywhere bounded nonlinear S-shaped local couplings are formed that are ensured by discontinuous controls with constant amplitudes; this enables the design constraints on state and control variables to be taken into account at the stage of synthesis. Measurements of angular positions have been used to develop a procedure for the adjustment of a reduced dynamic observer of angular velocities with S-shaped corrective actions, which does not require the model of the plant to be defined or a dynamic model of external perturbations to be introduced. The effectiveness of the approach developed has been confirmed by simulations in the MATLAB-Simulink environment.