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Anisotropic Norm Computation for Descriptor Systems with Nonzero-Mean Input Signals
Journal of Computer and Systems Sciences International. 2015. Vol. 54. No. 5. P. 10–23.
Andrianova O., Kurdyukov A. P., Kustov A. Y.
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 using convex optimization techniques is developed. Numerical examples illustrate methods of anisotropic norm computation.
Priority areas:
IT and mathematics
Language:
English
Springer, 2026.
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Netherlands: ScienceDirect, 2025.
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IEEE, 2024.
A.S. Popov Russian Science and Technical Society with support from V. A. Trapeznikov Institute of Control Sciences, V.A. Kotelnikov Institute of Radio Engineering and Electronics, Autex Ltd. is leading the ХХVIII International Conference «Digital Signal Processing and its Applications — DSPA-2024» ...
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Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
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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
Анизотропийная частотная теорема для линейных дискретных систем с политопическими неопределенностями
Andrianova O., Белов А. А., Гольдин Д. А., В кн.: XIII Всероссийское совещание по проблемам управления ВСПУ-2019: труды.: М.: ИПУ РАН, 2019. С. 325–329.
В данной работе решается задача робастного анизотропийного анализа линейных дискретных систем с политопическими неопределенностями. Решение поставленной задачи было получено с использованием матричных неравенств, в которых переменные зависят от параметров. Полученный результат может быть использован для построения управления по состоянию или выходу, обеспечивающего заданное качество замкнутой системы. ...
Added: October 13, 2019
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