arXiv subjects

Danilo Braghini

Publications and source records attributed to Danilo Braghini.

6 recordsLinked to original sources

arXiv2026

Comparing Spatially Periodic Feedback and Space-Time Modulation for Unidirectional Wave Propagation in a 1D Mass-Spring-Damper System

Unidirectional wave propagation has emerged as a key concept in the dynamics of non-reciprocal mechanical and acoustic metamaterials. This work investigates two fundamentally distinct strategies for achieving directional wave propagation in a periodic one-dimensional mass-spring-damper lumped system: space-time modulation and spatially periodic feedback. In the first approach, the stiffness is modulated periodically in both space and time. The resulting space-time periodic system is analyzed using a Plane Wave Expansion (PWE) formulation based on the Bloch-Floquet theory to obtain the dispersion relation. The traveling modulation produces asymmetric dispersion diagrams and directional band gaps, within which elastic waves propagate preferentially in a single direction due to broken time-reversal symmetry. In the second approach, non-reciprocity is introduced through a spatially periodic feedback action. The force can depend on the displacement and/or its derivatives, such as velocity or acceleration, and is applied to the masses along the system. The lumped system with a finite number of unit cells is modeled using classical mechanics principles, yielding a state-space model of the system. The active mechanism can generate directional amplification or attenuation via the non-Hermitian skin effect (NHSE), characterized by boundary-localized modes identified by a topological invariant, the winding number. The stability of the space-time periodic system is assessed through the Lyapunov-Floquet theory. In the periodic feedback case, stability is investigated using the eigenvalues of the state matrix. These results provide design guidelines for directional wave propagation in elastic waveguides.

physics.app-ph↗

arXiv2026

Static Output Feedback Stabilization of Linear Systems with Multiple Delays

This work proposes a new procedure for the stabilization of time-delay systems using Static Output Feedback (SOF) control. A previous convex optimization approach to SOF for Ordinary Differential Equations (ODEs) is extended to time-delay systems through the use of a proposed state-space representation. This approach is based on solving two convex optimization problems, which are extensions of Linear Matrix Inequalities (LMIs) to infinite-dimensional systems. The first problem is stabilization under state feedback control; the second problem takes advantage of the Projection Lemma, which is extended here from matrices to Partial Integral (PI) operators. Finally, the results are compared with other SOF solutions for systems with delay found in the literature, showing a significant reduction in conservatism.

math.OC↗

arXiv2025

PIETOOLS 2025: User Manual

The PIETOOLS 2025 User Manual describes all the features of version 2025 of the MATLAB toolbox PIETOOLS for the analysis and control of Partial Integral Equations (PIEs). The manual is aimed to guide, with examples, first-time users to four fundamental features of PIETOOLS: converting coupled ODE-PDEs, DDEs, DDFs, etc., to PIE representation; analysis of stability and input-output properties of PIEs; design of optimal observers and controllers for PIEs; simulation of open- and closed-loop PIE systems. The use of PIETOOLS is not limited to the features described above. However, the manual focuses on these features to provide a holistic understanding of the workflow of PIETOOLS, which will serve as a foundation to develop more complicated programs, for example, the design of boundary feedback controllers, robust observers, robust controllers, etc..

math.OC↗

arXiv2022

PIETOOLS 2022: User Manual

PIETOOLS 2022 manual is a document that describes all the features of the MATLAB toolbox for the analysis and control of Partial Integral Equations (PIEs). The manual is aimed to guide, with examples, the first time users to three fundamental features of PIETOOLS: converting coupled ODE-PDEs, DDEs, DDFs, etc., to PIE representation; analysis of stability and input-output properties of PIEs; design of optimal observers and controllers for PIEs. The use of PIETOOLS is not limited to the features described above. However, the manual focuses on these features to provide a holistic understanding of the workflow of PIETOOLS, which will serve as a foundation to develop more complicated programs, for example, the design of boundary feedback controllers, robust observers, robust controllers, etc.

math.OC↗

arXiv2022

Non-Hermitian acoustic waveguides with periodic electroacoustic feedback

In this work, we investigate non-Hermitian acoustic waveguides designed with periodically applied feedback efforts using electrodynamic actuators. One-dimensional spectral (infinite-dimensional) and finite element (finite-dimensional) models for plane acoustic waves in ducts are used. It is shown that dispersion diagrams of this family of metamaterials exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or amplification along opposite directions for all pass bands. The effects of different feedback laws are investigated. Furthermore, the non-Hermitian skin effect manifesting as topological modes localized at the boundaries of finite domains is investigated and successfully predicted by the topology of the reciprocal space. This work extends previous numerical results obtained for a piezoelectric rod system and contributes to recent efforts in designing active metamaterials with novel properties associated with the physics of non-Hermitian systems, which may find fruitful technological applications related to noise control, wave localization, filtering and multiplexing.

physics.app-ph↗

arXiv2021

Non-Hermitian elastic waveguides with piezoelectric feedback actuation: non-reciprocal bands and skin modes

In this work, we investigate non-Hermitian elastic waveguides with periodically applied proportional feedback efforts, implemented through piezoelectric sensors and actuators. Using onedimensional spectral models for longitudinal motion, it is shown that dispersion diagrams of this family of structures exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or amplification along opposite directions for all pass bands. The effects of positive and negative proportional feedback, as well as local and non-local actuation are investigated. Overall, switching the sign of the feedback effort inverts the amplification direction, while increasing the degree of non-locality produces splitting of the pass bands into multiple bands with interchanging non-reciprocal behavior. Furthermore, skin modes localized at the boundaries of finite domains are investigated and successfully predicted by the winding number of the complex dispersion bands. These results contribute to recent efforts in designing metamaterials with novel properties associated with the physics of non-Hermitian systems, which may find fruitful technological applications relying on vibration and noise control, wave localization, filtering and multiplexing.

cond-mat.mtrl-sci↗