Passive Linear Systems Research Articles

Coherent equalization of linear quantum systems

This paper introduces a H∞-like methodology of coherent filtering for equalization of passive linear quantum systems to help mitigate degrading effects of quantum communication channels. For such systems, which include a wide range of linear quantum optical devices and signals, we seek to find a near optimal equalizing filter which is itself a passive quantum system. The problem amounts to solving an optimization problem subject to constraints dictated by the requirement for the equalizer to be physically realizable. By formulating these constraints in the frequency domain, we show that the problem admits a convex H∞-like formulation. This allows us to derive a set of suboptimal coherent equalizers using J-spectral factorization. An additional semidefinite relaxation combined with the Nevanlinna–Pick interpolation is shown to lead to a tractable algorithm for the design of a near optimal coherent equalizer.

On the Dynamics of the Tavis–Cummings Model

The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.

Analysis of non-Markovian passive quantum linear systems’ response to single-photon input fields*

In this paper, we analyze the response of passive quantum linear systems in a non-Markovian environment to single photon input fields. Based on an augmented modelling method for non-Markovian quantum systems, analytic forms of output intensity and output covariance function in steady-state are derived. These results allow us to quantitatively analyze the influence of non-Markovian environment on system response under a framework of linear system theory.

A Comparative Study of Particle Swarm Optimized Control Techniques for Active Suspension System

This work presents a comparative study for performance evaluation of quarter vehicle Active Suspension System (ASS) using different control techniques. Linear and non-linear mathematical models of the systems are presented and controlled using Proportional Integral Derivative (PID), Feedback Linearization, and Fuzzy Logic Control (FLC). Particle Swarm Optimization (PSO) technique is applied to optimize the gains of the implemented controllers. A simulation process is done using MATLAB/SIMULINK and the results show that the proposed PSO-optimized PID controller has enhanced the root mean square (r.m.s) values of ride comfort, load carrying, and road holding of the linear suspension system by 26.82%, 20.95%, and 22.72% respectively compared to the linear passive suspension system. Whereas, for the nonlinear suspension system, the PSO-optimized FLC has provided better compromise of the performance criteria. The controller has improved the r.m.s values of ride comfort, load carrying, and road handling by 40.61%, 44.21%, and 27.46% respectively compared to the non-linear passive suspension system.

Introduction to Jan C. Willems’, “Dissipative Dynamical Systems, Part II: Linear Systems With Quadratic Supply Rates”

The two-part article, “Dissipative Dynamical Systems,” by Jan C. Willems, was submitted in January 1972 to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Archive for Rational Mechanics and Analysis</i> and published in the same year (vol. 45, Part I, pp. 321–351, Part II: pp. 352–393). While Part I develops the theory of dissipative systems for general input–state–output systems, Part II confines itself to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linear systems</i> . Moreover, most of Part II is about dissipativity with respect to the supply rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y{\hspace{0.06em}}^{\top}u,$</tex-math></inline-formula> that is, linear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">passive</i> systems. The main questions addressed in Part II concern the analysis of the set of storage functions of linear passive systems (with the existence of a minimal and maximal element already established in Part I) and the compatibility of storage functions with other external and internal symmetry properties of the system, such as reciprocity and reversibility. (See “The Articles of This Special Issue.”) This links the article closely to the realization theory of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">physical</i> linear systems, in particular, the network synthesis of electrical circuits, the Onsager–Casimir relation of linear thermodynamics, and the input–output analysis of linear viscoelastic systems.

A class of incrementally scattering-passive nonlinear systems

We investigate a special class of nonlinear infinite dimensional systems. These are obtained by subtracting a nonlinear maximal monotone (possibly multi-valued) operator ℳ from the semigroup generator of a scattering passive linear system. While the linear system may have unbounded linear damping (for instance, boundary damping) which is only densely defined, the nonlinear damping operator ℳ is assumed to be defined on the whole state space. We show that this new class of nonlinear infinite dimensional systems is well-posed and incrementally scattering passive. Our approach uses the theory of maximal monotone operators and the Crandall–Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax–Phillips type nonlinear semigroup that represents the whole system.

Broadband Time-Modulated Absorber beyond the Bode-Fano Limit for Short Pulses by Energy Trapping

Wideband absorption is a popular topic in microwave engineering to protect sensitive devices against broadband sources. However, the Bode-Fano criterion defines the trade-off between bandwidth and efficiency for all passive linear time-invariant systems. In this paper, we propose a broadband absorber beyond the Bode-Fano limit by creating an energy trap using time-modulated switches or diodes. This work starts with an ideal-circuit model to prove the concept, followed by two electromagnetic realizations---a frequency-selective-surface approach for general bandwidth broadening and a low-profile printed-circuit-board design. The prototype of the latter is built and measured, demonstrating a Bode-Fano integral larger than 1. This approach paves the way to many practical ultrawideband-absorber designs.

Fluid Jet Stimulation of Auditory Hair Bundles Reveal Spatial Non-uniformities and Two Viscoelastic-Like Mechanisms.

Hair cell mechanosensitivity resides in the sensory hair bundle, an apical protrusion of actin-filled stereocilia arranged in a staircase pattern. Hair bundle deflection activates mechano-electric transduction (MET) ion channels located near the tops of the shorter rows of stereocilia. The elicited macroscopic current is shaped by the hair bundle motion so that the mode of stimulation greatly influences the cell’s output. We present data quantifying the displacement of the whole outer hair cell bundle using high-speed imaging when stimulated with a fluid jet. We find a spatially non-uniform stimulation that results in splaying, where the hair bundle expands apart. Based on modeling, the splaying is predominantly due to fluid dynamics with a small contribution from hair bundle architecture. Additionally, in response to stimulation, the hair bundle exhibited a rapid motion followed by a slower motion in the same direction (creep) that is described by a double exponential process. The creep is consistent with originating from a linear passive system that can be modeled using two viscoelastic processes. These viscoelastic mechanisms are integral to describing the mechanics of the mammalian hair bundle.

Vibration Control of Quarter Car Model Using Modified PID Controller

The purpose of this research is to control a quarter car suspension system and also to reduce the fluctuated movement caused by passing thevehicle over road bump using modified PID (Proportional Integral and Derivative) controller. The proposed controller deals with dual loopfeedback signals instead of single feedback signal as in the conventional PID controller. The structure of the modified PID controller wascreated by moving the proportional and derivative actions in the feedback path while remaining the integral action in the forward path. Thus,high accuracy results were obtained. Firstly, modelling and simulation of linear passive suspension system for a quarter car system wasperformed using Matlab – Simulink software. Then the linear suspension system was activated and simulated by using an active hydraulicactuator to generate the necessary force which can be regulated and controlled by the proposed controller. The performance of whole systemhas been enhanced with a modified PID controller.

Graphene Nanoribbon Gap Waveguides for Dispersionless and Low-Loss Propagation with Deep-Subwavelength Confinement.

Surface plasmon polaritons (SPPs) have been attracting considerable attention owing to their unique capabilities of manipulating light. However, the intractable dispersion and high loss are two major obstacles for attaining high-performance plasmonic devices. Here, a graphene nanoribbon gap waveguide (GNRGW) is proposed for guiding dispersionless gap SPPs (GSPPs) with deep-subwavelength confinement and low loss. An analytical model is developed to analyze the GSPPs, in which a reflection phase shift is employed to successfully deal with the influence caused by the boundaries of the graphene nanoribbon (GNR). It is demonstrated that a pulse with a 4 μm bandwidth and a 10 nm mode width can propagate in the linear passive system without waveform distortion, which is very robust against the shape change of the GNR. The decrease in the pulse amplitude is only 10% for a propagation distance of 1 μm. Furthermore, an array consisting of several GNRGWs is employed as a multichannel optical switch. When the separation is larger than 40 nm, each channel can be controlled independently by tuning the chemical potential of the corresponding GNR. The proposed GNRGW may raise great interest in studying dispersionless and low-loss nanophotonic devices, with potential applications in the distortionless transmission of nanoscale signals, electro-optic nanocircuits, and high-density on-chip communications.

Optimization of Nonlinear Passive Suspension System to Minimize Road Damage for Heavy Goods Vehicle

Major contributors to the road damage are Heavy Goods Vehicles (HGV), resulting in high maintenance costs of roads. This high cost makes it necessary to look into the issue seriously for minimizing the road damage. An Automobile Engineer can reduce road damage through the efficient design of a suspension system. The design involves satisfying the two conflicting criteria of riding comfort and vehicle handling with the restriction on the suspension travel. This paper involves designing an automobile suspension system, to improve the performance of the vehicle without a significant change in the cost of the suspension system and minimize road damage. To achieve the aforesaid objective, the use of a nonlinear passive suspension is suitable as compared to a linear passive suspension system. For the analysis, a HGV model of vehicle suspension has been considered. The suspension system considered for investigation comprises of a cubical nonlinear spring and a linear damper. Road damage has been represented by the fourth power of the tire dynamic load. A genetic algorithm has been used to optimize the half truck model to minimize road damage. The solution has been obtained using MATLAB and SIMULINK.

Passive linear discrete-time systems: Characterization through structure

We here show that the family of finite-dimensional, discrete-time, passive, linear time-invariant systems can be characterized through the structure of a matrix-convex set, which is maximal in the sense of being closed under products of its elements Moreover, this observation unifies three setups: (i) difference inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions.It turns out that in the continuous-time case the corresponding structure is of a maximal matrix-convex cone closed under inversion.

Passive linear continuous-time systems: Characterization through structure

We here show that the family of finite-dimensional, continuous-time, passive, linear, time-invariant systems can be characterized through the structure of maximal matrix-convex cones, closed under inversion. Moreover, this observation unifies three setups: (i) differential inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the discrete-time case, the corresponding structure is of a maximal matrix-convex set, closed under multiplication among its elements.

A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck

With the increasing of the accuracy requirement of data record for on-orbit instruments, it becomes a greater challenge and brings more opportunities in design of observing spacecraft to isolate micro-vibrations of low frequency and ultra-low frequency. By imitating both multi-vertebra structure of bird’s neck and gazing stability of head, a multi-layer quasi-zero stiffness (QZS) nonlinear isolator is investigated in this paper. The mathematical model with high-order coupled nonlinear ordinary differential equations is established. Its isolation performance is analyzed by the harmonic balance method (HBM) combining with the pseudo arc length method. In comparison to the corresponding linear structure, the proposed multi-layer QZS nonlinear isolator can break the limitation of poor isolation performance in low frequency and ultra-low frequency vibration for traditional linear passive isolation systems. Also, the analysis results show that its High-Static-Low-Dynamic-Stiffness (HSLDS) property may solve the traditional contradiction between large isolation frequency band and loading capacity for reducing soft stiffness. The multi-layer QZS combined system as integration is quite capable of cumulatively expanding the effective range of dynamic displacement which is too narrow for a single QZS system. The relevant conclusions are instructive to develop preferable isolation equipment to isolate low frequency and ultra-low frequency vibration in practical engineering.

Non-linear damping for scattering-passive systems in the Maxwell class

We start from a special class of scattering passive linear infinite-dimensional systems introduced in Staffans and Weiss (SIAM J. Control and Opt., 2012). This class is called the Maxwell class of systems, because it includes the scattering formulation of Maxwell’s equations, as well as various wave and beam equations. We generalize this class by allowing a nonlinear damping term. While the system may have unbounded linear damping (for instance, boundary damping), the nonlinear damping term N is “bounded” in the sense that it defined on the whole state space (but no actual continuity assumption is made on N). We show that this new class of nonlinear infinite dimensional systems is well-posed and scattering passive. Our approach uses the theory of maximal monotone operators and the Crandall-Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax-Phillips type nonlinear semigroup that represents the whole system, with input and output signals.

Multistable Energy Shaping of Passive Linear Systems with Hybrid Mode Selector

Abstract This paper presents a novel control strategy for stable linear time–invariant systems operating with a finite number of set points. Inspired by the theory of passivity-based control, the proposed method aims at simultaneously and asymptotically stabilize all the desired working modes by means of a static nonlinear state feedback law. An asynchronous external signal is then employed to trigger a hybrid controller in order to switch between the different working modes. The proposed approach is validated by means of simulations performed on the ubiquitous mass-spring-damper system.

Plasmonic Metasurface "Bullets" and other "Moving Objects": Spatiotemporal Dispersion Cancellation for Linear Passive Subwavelength Slow Light.

A class of plasmonic metasurfaces is introduced with the ability to tailor the dispersion surface of the associated plasmon-polariton into striking novel shapes. Examples include dispersion surfaces with hyperbolic curves, with multiple van Hove singularities of various types or with points of simultaneous spatiotemporal dispersion cancellation leading to unprecedented surface flatness. The latter effect, unseen before in linear passive systems, implies slow propagation of ultrasubwavelength wave packets of any shape devoid of longitudinal or lateral broadening, limited only by absorption.

Optimisation of Linear Passive Suspension System Using MOPSO and Design of Predictive Tool with Artificial Neural Network

Optimisation of Linear Passive Suspension System Using MOPSO and Design of Predictive Tool with Artificial Neural Network

Balanced truncation of networked linear passive systems

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state–spacemodel of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.

Stability and Robust Regulation of Passive Linear Systems

We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and nonuniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbance rejection for strongly stabilizable passive systems. In the case of nonsmooth reference and disturbance signals we present conditions for nonuniform rational and logarithmic rates of convergence of the output. The results are illustrated with examples on designing controllers for linear wave and heat equations, and on studying the stability of a system of coupled partial differential equations.