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May 15, 2026
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Anisotropy-based Analysis for Descriptor Systems with Norm-Bounded Parametric Uncertainties

P. 1–4.
Belov A., Olga G. Andrianova

In this paper, linear discrete-time descriptor systems
with norm-bounded parametric uncertainties are under consider-
ation. 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.

Language: English
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Keywords: descriptor systemsanisotropy-based control theory

In book

PROCEEDINGS OF 2016 INTERNATIONAL CONFERENCE “STABILITY AND OSCILLATIONS OF NONLINEAR CONTROL SYSTEMS” (PYATNITSKIY’S CONFERENCE)
IEEE, 2016.
Similar publications
Non-iterative Solution to Robust Anisotropy-based Analysis and Control Problems for Uncertain Descriptor Systems
Andrianova O., Белов А. А., , in: 2019 23rd International Conference on System Theory, Control and Computing (ICSTCC).: IEEE, 2019. P. 455–460.
The problem of robust admissibilization with guaranteed random disturbance attenuation level for discrete-time time-invariant (LDTI) descriptor systems with norm-bounded uncertainties is considered. The input disturbance is supposed to be a stationary Gaussian sequence with bounded mean anisotropy level. The solutions to analysis and robust statefeedback control problems are formulated in terms of matrix inequalities. The obtained conditions are convex over ...
Added: December 5, 2019
Robust state-feedback H_\infty control for discrete-time descriptor systems with norm-bounded parametric uncertainties
Belov A., Andrianova O., International Journal of Systems Science 2019 Vol. 50 No. 6 P. 1303–1312
This paper deals with a state feedback H ∞ control problem for linear time-invariant discrete-time descriptor systems with norm-bounded parametric uncertainties. To this end, bounded real lemma (BRL) is extended on the class of uncertain descriptor systems. The control design procedure based on the conditions of BRL for uncertain descriptor systems is proposed. Numerical examples are included to illustrate ...
Added: May 2, 2019
Robust Anisotropy-Based Control for Uncertain Descriptor Systems with Transient Response Constraints
Andrianova O., Belov A., IFAC-PapersOnLine 2018 Vol. 51 No. 32 P. 515–520
In this paper, a problem of robust anisotropy-based control with regional pole assignment for descriptor systems with norm-bounded parametric uncertainties is concerned. The goal is to find a state-feedback control law, which guarantees desirable disturbance attenuation level from stochastic input with unknown covariance to controllable output of the closed-loop system, and ensures, that all finite ...
Added: December 16, 2018
Suboptimal Anisotropy-based Control for Linear Discrete-time Systems with Norm-bounded Uncertainties
Andrianova O., Belov A., , in: 2018 14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference) (STAB).: IEEE, 2018. P. 1–4.
In this paper, suboptimal anisotropy-based control for linear discrete-time systems with norm-bounded parametric uncertainties is designed. State-feedback and static outputfeedback control laws, that guarantee a known level of rejection of random input disturbances, are constructed. A numerical example is given. ...
Added: July 16, 2018
On Optimal Anisotropy-Based Control Problem for Discrete-Time Descriptor Systems
Belov A., Andrianova O., , in: 2018 26th Mediterranean Conference on Control and Automation (MED).: [б.и.], 2018. P. 661–666.
This paper is dedicated to optimal state-feedback control problem for discrete-time descriptor systems in presence of “colored” noise with known mean anisotropy level. Here “colored” noise stands for a stationary Gaussian sequence, generated by a linear shaping filter from the Gaussian white noise sequence. The control goal is to find a state feedback control law which makes the closed-loop system admissible ...
Added: July 16, 2018
Robust performance analysis of linear discrete-time systems in presence of colored noise
Andrianova O., Belov A., European Journal of Control 2018 No. 42 P. 38–48
In this paper, linear discrete-time time-invariant (LDTI) normal and descriptor systems with norm-bounded parametric uncertainties are under consideration. The input signal is supposed to be a “colored” noise with bounded known mean anisotropy level (spectral color). The conditions of anisotropic norm boundedness for such class of systems are derived. The algorithm is based on convex optimization technique. A ...
Added: June 10, 2018
Suboptimal Anisotropy-based Control Design for Discrete-Time Systems with Nonzero-Mean Input Disturbances
Belov A., Andrianova O., , in: PROCEEDINGS OF 2016 INTERNATIONAL CONFERENCE “STABILITY AND OSCILLATIONS OF NONLINEAR CONTROL SYSTEMS” (PYATNITSKIY’S CONFERENCE).: IEEE, 2016. P. 1–4.
In this paper, linear discrete-time systems with Gaussian input disturbances are considered. Input sequences are characterized by nonzero mean and bounded mean anisotropy. Suboptimal control law, which guarantees stability of the closedloop system and boundedness of its anisotropic norm, is designed. ...
Added: February 6, 2018
On Anisotropy-Based Control Problem with Regional Pole Assignment for Descriptor Systems
Belov A. A., Andrianova O., , in: Proceedings of the 2017 21st International Conference on Process Control, PC 2017.: IEEE, 2017. P. 12–17.
In this paper, anisotropy-based control problem with regional pole assignment for descriptor systems is investigated. The purpose is to find a state-feedback control law, which guarantees desirable disturbance attenuation level from stochastic input with unknown covariance to controllable output of the closed-loop system, and ensures, that all finite eigenvalues of the closed-loop system belong to the given region inside the unit ...
Added: February 6, 2018
A New Anisotropy-Based Control Design Approach for Descriptor Systems Using Convex Optimization Techniques
Belov A. A., Andrianova O., IFAC-PapersOnLine 2015 Vol. 48 No. 11 P. 372–377
The paper presents a solution of anisotropy-based suboptimal controller design problem for descriptor systems. The goal is to design a state feedback and full information control for the system such that the closed-loop system is admissible, and its anisotropic norm (mean anisotropy level is set) is bounded by a given positive real value. A numerical ...
Added: October 20, 2017
On LMI Approach to Robust State-Feedback H∞Control for Discrete-Time Descriptor Systems with Uncertainties in All Matrices
Belov A. A., Andrianova O., IFAC-PapersOnLine 2017 Vol. 50 No. 1 P. 15483–15487
This paper deals with a state feedback H∞ control problem for linear discrete-time time-invariant (LDTI) uncertain descriptor systems. Considered systems contain norm-bounded parametric uncertainties in all matrices. Bounded real lemma (BRL) for descriptor systems with all known matrices is extended on the class of uncertain systems. The control design procedure based on the conditions of BRL for ...
Added: October 20, 2017
On some anisotropy-based analysis problems for linear discrete-time descriptor systems with nonzero-mean input signals
Andrianova O., Наука и образование: научное издание МГТУ им. Н.Э. Баумана 2014 P. 160–174
The paper presents a novel concept of anisotropy-based analysis for linear discrete-time descriptor systems with nonzero-mean input signals. Descriptor systems are a general case of normal systems. They contain both differential (difference) equations and algebraic equations. In this paper, the algorithm for mean anisotropy computation of the Gaussian stationary random sequence with nonzero mean (we ...
Added: October 20, 2017
Anisotropy-Based Suboptimal State-Feedback Control Design Using Linear Matrix Inequalities
Belov A. A., Andrianova O., Automation and Remote Control 2016 Vol. 77 No. 10 P. 1741–1755
A computationally efficient method for the design of a suboptimal anisotropic con- troller for discrete descriptor systems based on convex optimization methods is proposed. Nu- merical examples are given. ...
Added: October 20, 2017
Anisotropic Norm Computation for Descriptor Systems with Nonzero-Mean Input Signals
Andrianova O., Kurdyukov A. P., Kustov A. Y., Journal of Computer and Systems Sciences International 2015 Vol. 54 No. 5 P. 10–23
Linear stationary discrete-time descriptor systems with input sequences of random Gaussian nonzero-mean vectors with bounded mean anisotropy are under consideration. Conditions of anisotropic norm boundedness for such systems are given in terms of generalized discrete-time algebraic Riccati equations (GDARE) and linear matrix inequalities (LMI). On basis of these results, the algorithm of anisotropic norm computation ...
Added: October 20, 2017
Robust anisotropy-based control of linear discrete-time descriptor systems with norm-bounded uncertainties
Belov A. A., Andrianova O., IFAC-PapersOnLine 2017 Vol. 50 No. 1 P. 15471–15476
The paper deals with linear discrete-time time-invariant (LDTI) descriptor systems with norm-bounded parametric uncertainties. 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. The control design procedure, based on these conditions, is proposed. Numerical example is given. ...
Added: October 19, 2017
Conditions of anisotropic norm boundedness for descriptor systems
Andrianova O., Belov A. A., Kurdyukov A. P., Journal of Computer and Systems Sciences International 2015 Vol. 54 No. 1 P. 27–38
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 ...
Added: October 19, 2017
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