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For linear dynamic plants, we consider a new class of controllers with adjustable parameters synthesized so as to reduce the integral indicators of the influence of initial and exogenous disturbances. The controller parameters are adjusted according to a differential equation in the direction of decrease of a local objective function. The conditions are stated under which the control objective is achieved, and the losses in comparison with time-invariant linear-quadratic and -optimal controllers are given, including the case of degenerate functionals. It is shown how these controllers are used in adaptive linear-quadratic and -optimal control for indeterminate plants whose parameters belong to a given polyhedron as well as in adaptive tracking of the reference model output. [ABSTRACT FROM AUTHOR]

We suggest a new method for solving the stabilization problem under phase constraints with the use of linear matrix inequalities. We consider the cases of complete and incomplete state measurements and the presence of nonstationary parametric perturbations. In the synthesis of linear control laws, the suggested method permits one to cover all possible quadratic Lyapunov functions and indicate a set of initial values for trajectories satisfying the phase constraints. [ABSTRACT FROM AUTHOR]

The article discusses the problem of constructing H1-controls and ensuring external perturbation breaking the dynamical systems described by the linear differential equations. The control has the feedback and is generated by the controller of a linear dynamical system of a given order whose input is fed with the measured output of the plant. The synthesis of H1-controllers suggested is based on the technique of linear matrix inequalities.

This article examines the necessary solvability conditions for Multiparameter Riccati Equations in the Robust Output Feedback H-Control Problem. It considers a controlled object that contains vectors of state, perturbation, control, controlled output, and measured output. The H-control problem for this object is the problem of constructing a dynamic measured-output feedback control law suppressing perturbations to a given ratio. Under specific system conditions, this problem has a solution if and only if the matrix algebraic Riccati equations have positive semidefinite stabilizing solutions.

Investigates the frequency conditions in controller design for dynamical systems in Hilbert spaces. Systems governed by delay differential equations; Main difficulty encountered in the design of an optimal dynamic controller; Attempt to generalize the "inverse" approach in control law design to systems operator equations or inequalities; Solution of the problem on the basis of frequency conditions.

For the class of uncertain nonlinear controllable systems, the notion of a robust H∞- norm is introduced. An efficient procedure of obtaining double-ended estimates for a minimum robust H∞-norm in the class of nonlinear feedback loops is stated. An example is given of the system for which the obtained estimates coincide with one another and with a minimum robust norm. [ABSTRACT FROM AUTHOR]