arXiv subjects

Mahyar Mahinzaeim

Publications and source records attributed to Mahyar Mahinzaeim.

6 recordsLinked to original sources

arXiv2026

Exponential stability of abstract boundary-coupled positive systems

In this paper, we study the well-posedness and exponential stability of a class of abstract boundary-coupled positive systems. Within a general semigroup framework, we establish well-posedness in terms of existence, uniqueness, and regularity of solutions. More concretely, we derive some simple and readily verifiable tests on the boundary coupling operators for the verification of the well-posedness of the coupled system and, at the same time, provide spectral criteria that guarantee exponential stability of the solutions. The analysis is based on two complementary approaches: the feedback-theoretic method and perturbation techniques for resolvent positive operators on Banach lattices (i.e., Banach spaces equipped with a compatible order structure). This unified framework allows for a systematic treatment of a broad class of boundary couplings in abstract dynamical systems. Several examples are presented to illustrate the applicability of the theoretical results.

math.OC↗

arXiv2026

An approach to the LQG/LTR design problem with specifications for finite-dimensional SISO control systems

This is an expository paper which discusses an approach to the linear quadratic Gaussian/loop transfer recovery (LQG/LTR) design problem for finite-dimensional single-variable (single-input/single-output, SISO) control systems. The approach is based on the utilisation of weighting augmentation for incorporating design specifications into the framework of the LTR technique for LQG compensator design. The LQG compensator is to simultaneously meet given analytical low- and high-frequency design specifications expressed in terms of desirable sensitivity and controller noise sensitivity functions. The paper is aimed at non-specialists and, in particular, practitioners in finite-dimensional LQG theory interested in the design of feedback compensators for closed-loop performance and robustness shaping of SISO control systems in realistic situations. The proposed approach is illustrated by a detailed design example: the torque control of a geared DC motor with an elastically mounted output shaft.

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arXiv2024

The Riesz basisness of the eigenfunctions and eigenvectors connected to the stability problem of a fluid-conveying tube with boundary control

In the present paper we study the stability problem for a stretched tube conveying fluid with boundary control. The abstract spectral problem concerns operator pencils of the forms \begin{equation*} \mathcal{M}\left(λ\right)=λ^2G+λD+C\quad\text{and}\quad\mathcal{P}\left(λ\right)=λI-T \end{equation*} taking values in different Hilbert product spaces. Thorough analysis is made of the location and asymptotics of eigenvalues in the complex plane and Riesz basisness of the corresponding eigenfunctions and eigenvectors. Well-posedness of the closed-loop system represented by the initial-value problem for the abstract equation \begin{equation*} \dot{x}\left(t\right)=Tx\left(t\right) \end{equation*} is established in the framework of semigroups as well as expansions of the solutions in terms of eigenvectors and stability of the closed-loop system operator $T$. For the parameters of the problem we give regions, larger than those in the literature, in which a stretched tube with flow, simply supported at one end, with a boundary controller applied at the other end, can be made exponentially stable.

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arXiv2024

The analysis of vertex feedback stabilisability of a star-shaped network of fluid-conveying pipes

It is an outstanding problem whether a pipe-flow system on a star-shaped network is stabilisable by a feedback control on the common vertex. In the present paper we deal with this problem. In particular, we study the equation governing the small vibrations of a stretched elastic pipe conveying fluid in a star-shaped network and examine the question of vertex feedback stabilisability of such a system via control moments. Finding an answer to the question is not straightforward, for the system operator associated with the corresponding closed-loop system is unbounded and nonselfadjoint. An approach to the study of the stabilisation problem for the closed-loop system is presented based on the spectral approach previously introduced by the authors for star graphs of stretched elastic beams. When the tension in the pipes is greater than the square of the fluid-flow velocity, we establish a positive result that in fact gives the strong property of uniform exponential stability of the closed-loop system.

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arXiv2024

Spectral analysis of a viscoelastic tube conveying fluid with generalised boundary conditions

We study the spectral problem associated with the equation governing the small transverse motions of a viscoelastic tube of finite length conveying an ideal fluid. The boundary conditions considered are of general form, accounting for a combination of elasticity and viscous damping acting on both the slopes and the displacements of the ends of the tube. These include many standard boundary conditions as special cases such as the clamped, free, hinged, and guided conditions. We derive explicit asymptotic formulae for the eigenvalues for the case of generalised boundary conditions and specialise these results to the clamped case and the case in which damping acts on the slopes but not on the displacements. In particular, the dependence of the eigenvalues on the parameters of the problem is investigated and it is found that all eigenvalues are located in certain sectorial sets in the complex plane.

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arXiv2023

On the exponential stability of Beck's Problem on a star-shaped graph

We deal with the as yet unresolved exponential stability problem for Beck's Problem on a metric star graph with three identical edges. The edges are stretched Euler--Bernoulli beams which are simply supported with respect to the outer vertices. At the inner vertex we have viscoelastic damping acting on the slopes of the edges. We carry out a complete spectral analysis of the system operator associated with the abstract spectral problem in Hilbert space. Within this framework it is shown that the eigenvectors have the property of forming a Riesz (i.e.\ an unconditional) basis, which makes it possible to directly deduce the exponential stability of the corresponding $C_0$-semigroup using spectral information for the system operator alone. A physically interesting conclusion is that the particular choice of vertex conditions ensures the exponential stability even when the elasticity acting on the slopes of the edges is absent.

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