Alexey A. Belov

Calculation of the anisotropic norm of the descriptor system

A method was proposed to calculate the anisotropic norm characterizing robustness of the linear discrete-time descriptor systems to random perturbations with uncertain statistical properties. A numerical example was presented.

Anisotropy-based bounded real lemma for linear discrete-time descriptor systems

For linear discrete-time descriptor systems bounded real lemma in terms of anisotropic norm was formulated and proved. This lemma connects boundedness of anisotropic norm by a given nonnegative parameter with existence of solution of specified generalized Riccati equation. Numerical example is given.

Computation of anisotropic norm for descriptor systems using convex optimization

For linear discrete-time descriptor systems anisotropy-based bounded real lemma in terms LMI was formulated and proved. The algorithm of anisotropic norm computation using convex optimization is given. A numerical example is considered.

Anisotropy-based suboptimal state-feedback control design using linear matrix inequalities

A computationally efficient method for the design of a suboptimal anisotropic controller for discrete descriptor systems based on convex optimization methods is proposed. Numerical examples are given.

Conditions of anisotropic norm boundedness for descriptor systems

A class of systems, described by algebraic-difference equations, is under consideration. Such systems are called descriptor (singular). For these systems the conditions of anisotropic norm boundedness are obtained. Anisotropic norm describes the root-mean-square gain of the system with respect to random Gaussian stationary disturbances, which are characterized by mean anisotropy. The conditions are formulated in the form of the theorem, detailed proof is given. Numerical example, illustrating anisotropic norm computation method for descriptor systems based of the proven theorem, is considered.

Anisotropy-based analysis for descriptor systems with norm-bounded parametric uncertainties

In this paper, linear discrete-time descriptor systems with norm-bounded parametric uncertainties are under consideration. The input signal is supposed to be a “colored” noise with bounded mean anisotropy. Sufficient conditions of anisotropic norm boundedness for such class of systems are given.

Practical Application of Descriptor Systems

With the development of computer technology, the theory of descriptor systems began to play an important role in the theory of automatic control. In this chapter, we consider some practical applications connected with the development of mathematical models of processes and control plants in descriptor form.

Basics of Discrete-Time Descriptor Systems Theory

The mathematical theory of discrete-time descriptor systems is different from the theory of normal ones. In spite of some similarities, discrete-time descriptor systems provide radically different behavior such as noncausality. This chapter deals with some important basic aspects of linear discrete-time descriptor systems.

Robust Anisotropy-Based Control

Interest in stability analysis and control for descriptor systems with parametric uncertainties has grown recently due to their frequent presence in dynamical systems. Uncertainties in such systems are often causes of instability and bad performance. It is known that control of uncertain descriptor systems is much more complicated than that of the normal ones. The aim of this chapter is to provide conditions of anisotropic norm boundedness for descriptor systems with norm-bounded parametric uncertainties and to develop methods of control design that make the closed-loop uncertain system admissible with prescribed anisotropy-based performance.

Anisotropy-Based Analysis of LDTI Descriptor Systems

In this chapter, we provide some background material on an anisotropy-based approach to the analysis of linear discrete-time systems (LDTI). Concepts of mean anisotropy of Gaussian random sequences and anisotropic norms for linear systems are introduced in [1, 2, 2] and briefly described below. This chapter deals with generalization of anisotropy-based analysis of the class of descriptor systems using generalized algebraic Riccati equations and convex optimization techniques.