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This paper provides a parametrization of optimal anisotropic controllers for linear discrete time invariant systems. The controllers to be designed are limited by causal dynamic output-feedback control laws. The obtained solution depends on several adjustable parameters that determine the specific type of controller, and is of the form of a system of the Riccati equations relating to a -optimal controller for a system formed by a series connection of the original system and the worst-case generating filter corresponding to the maximum value of the mean anisotropy of the external disturbance. [ABSTRACT FROM AUTHOR]

The design problem of an adaptive state observer for linear time-varying systems is considered. Some parameters of a time-varying plant are assumed to be unknown numbers multiplied by known functions of time. The approach proposed below is based on identification methods of adaptation. In other words, the main idea is to transform a mathematical model in the form of a linear time-varying differential equation to a static linear regression model containing unknown parameters. In this case, both the unknown parameters of the plant and its initial conditions are the unknown parameters of the regression model under consideration. Further, standard gradient methods or other parametric identification approaches are used to estimate the unknown parameters of the regression model and to construct the observer. The results of computer simulations illustrate the effectiveness of the new state observer design method. [ABSTRACT FROM AUTHOR]

Usually in the context of the anisotropy-based robust performance analysis stochastic systems with zero initial condition are investigated. In this paper we extend this analysis and consider a linear discrete time invariant system under random disturbances and with the nonzero initial condition. In accordance with the basic postulates of the anisotropy-based control theory the disturbance attenuation capabilities of system are quantified by the anisotropic generalized gain which is defined as the largest root mean square gain of the system with respect to a random input and the nonzero initial condition, anisotropy of which is bounded by a given nonnegative parameter a. [ABSTRACT FROM AUTHOR]

Consideration was given to a model of recursive conveyor process which is an extension of the classical conveyor. A method for efficient calculation of the process time characteristics in a linear time was described. On the basis of the calculated characteristics, the scheduling of recursive conveyor processes comes to calculation of analytical expressions. The proposed model can be used in the APS-systems and MES-systems of control of production, as well as for scheduling in some traditional fields of application of the scheduling theory. [ABSTRACT FROM AUTHOR]

We consider the problem of asymptotic analysis of the zeros of a sampled system of a linear time-invariant continuous system as the sampling period decreases. We show that for a continuous prototype system with delay the limits of a part of the model's zeros are roots of certain polynomials whose coefficients are determined by the relative order of the prototype system and delay. In the special case of zero delay these polynomials coincide with Euler polynomials. Zeros of these generalized Euler polynomials are localized: we show that they are all simple and negative, and that they move monotonically between the zeros of classical Euler polynomials as the fractional part of the delay divided by the sampling period grows. Our results lead to sufficient and 'almost necessary' conditions for the stable invertible of the discrete model for all sufficiently small values of the sampling period. [ABSTRACT FROM AUTHOR]

This paper considers some synthesis issues for SISO LTI systems. It is shown that direct application of universal methods (such as the two-Riccati approach or the LMI technique) appears impossible in degenerate situations without noisy measurements. [ABSTRACT FROM AUTHOR]

An analytical solution of the B.V. Bulgakov problem of maximum of the norm of finite state of the stationary linear system with one control (perturbation) function taking values over an interval was proposed. The switching function of the worst relay perturbation was shown to depend on time and coordinates and be the product of the phase system vector, its transition matrix transposed to it, and the transposed column of the coefficients at perturbation. [ABSTRACT FROM AUTHOR]

We consider the simultaneous stabilization problem for linear time-invariant stationary objects of arbitrary order. For such objects, we formulate numerically verifiable necessary and sufficient simultaneous stabilization conditions and show a constructive algorithm for the construction of a stabilizing controller with minimal restrictions on the structure and parameters of the stabilized objects. We give a general scheme of studying simultaneous stabilizability of a family of objects and analyze in detail a numerical algorithm for finding a stabilizing controller with applied interval analysis. To solve the problem, we use an approach based on the study of affine transformations of controller parameter spaces into the spaces of coefficients of denominators of closed-loop objects. [ABSTRACT FROM AUTHOR]

Bifurcation conditions are found for the periodic solutions in systems of differential equations with the perturbation (small disturbance) in the case of existence of joined Floke solutions in a linearized nonperturbed system. For this case a multidimensional analog of the Malkin bifurcation function is built up. [ABSTRACT FROM AUTHOR]

We consider an ε-optimal model reduction problem for a linear discrete time-invariant system, where the anisotropic norm of reduction error transfer function is used as a performance criterion. For solving the main problem, we state and solve an auxiliary problem of H ε-optimal reduction of a weighted linear discrete time system. A sufficient optimality condition defining a solution to the anisotropic ε-optimal model reduction problem has the form of a system of cross-coupled nonlinear matrix algebraic equations including a Riccati equation, four Lyapunov equations, and five special-type nonlinear equations. The proposed approach to solving the problem ensures stability of the reduced model without any additional technical assumptions. The reduced-order model approximates the steady-state behavior of the full-order system. [ABSTRACT FROM AUTHOR]

It is a survey of recent extensions and new applications for the classical D-decomposition technique. We investigate the structure of the parameter space decomposition into root invariant regions for single-input single-output systems linear depending on the parameters. The D-decomposition for uncertain polynomials is considered as well as the problem of describing all stabilizing controllers of the certain structure (for instance, PID-controllers) that satisfy given H ∞-criterion. It is shown that the D-decomposition technique can be naturally linked with M-Δ framework (a general scheme for analysis of uncertain systems) and it is applicable for describing feasible sets for linear matrix inequalities. The problem of robust synthesis for linear systems can be also treated via D-decomposition technique. [ABSTRACT FROM AUTHOR]

The problem of modal sampled-data control for continuous-time linear time-invariant plant with delay is considered. The characteristic matrix of the system is constructed. An algorithm is given for generating the set of causal discrete-time controllers that place eigenvalues of the characteristic matrix at specified points of the complex plane. [ABSTRACT FROM AUTHOR]

Singular $$\mathcal{H}$$ 2-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular $$\mathcal{H}$$ 2-problems. A parameterization of the set of optimal controllers is given. [ABSTRACT FROM AUTHOR]

Control systems described by linear difference equations are studied, assuming that control actions are bounded both in magnitude (geometrically) and norm (integrally). The states in the phase space to which a system can be transferred from the origin and the states from which a system can be transferred to the origin are studied. Examples are given. [ABSTRACT FROM AUTHOR]