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.
In this paper, linear discrete-time time-invariant (LDTI) normal and descrip- tor systems with norm-bounded parametric uncertainties are under consid- eration. 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 numerical example is given.
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 and minimizes its a-anisotropic norm (mean anisotropy level a is known).
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 guar- antees 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 disk. The proposed control design procedure is based on solving convex optimization problem with strict constraints. The numerical effectiveness is illustrated by numerical example.
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 closed- loop system and boundedness of its anisotropic norm, is designed.
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 uncertain descriptor systems is proposed. Numerical example is included to illustrate the effectiveness of the present result.
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 the effectiveness of the present result.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.