Narrow Results

We consider a quantum system described by a concrete C*-algebra acting on a Hilbert space ℋ with a vector state ω induced by a cyclic vector Ω and a unitary evolution U_t such that U_tΩ = Ω, ∀t ∈ ℝ. It is proved that this vector state is a ground state if and only if it is non-faithful and completely passive. This version of a result of Pusz and Woronowicz is reviewed, emphasizing other related aspects: passivity from the point of view of moving observers and stability with respect to local perturbations of the dynamics.

This paper investigates the passivity of memristive bidirectional associate memory neural networks (MBAMNNs) with leakage and additive time-varying delays. Based on some useful inequalities and appropriate Lyapunov–Krasovskii functionals (LKFs), several delay-dependent conditions for passivity performance are obtained in linear matrix inequalities (LMIs). Moreover, the leakage delays as well as additive delays are considered separately. Finally, numerical simulations are provided to demonstrate the feasibility of the theoretical results.

A detailed controller design for indirect constant power regulation of high intensity discharge (HID) electronic ballast and the experimental implementation of an adaptive passivity-based constant power (PBC) controller has been extensively studied through simulation and the findings are reported in this paper. An indirect method to regulate the inductor current to ensure the lamp constant output power is proposed in order to overcome the difficulties in measuring the output power of the HID ballast. The controller is derived using passivity theory which guarantees global stability and asymptotic convergence of all state errors. The simulation and controller design are based on an average model using the Euler–Lagrange (EL) equations of the system. As the lamp resistance will inevitably change with ageing, an adaptive method is used to compensate for the lamp performance as the lamp ages. This equips the controller the power to adapt to load variations and there is no need to tune the design parameters values each time manually. Another interconnection and damping assignment (IDA)-PBC method is analyzed and simulation results are provided for comparison. Computer simulation and hardware implementation are carried out to verify the system model and to demonstrate the controller is robust.

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability. It is shown that the design of a suitable transition phase desired trajectory, is a crucial step. Some simulation results provide information on the robustness aspects. Finally the extension towards the case of multiple impacts, is considered.

A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the norm of perturbations from a notional laminar profile. This is achieved by decomposing the Navier–Stokes system into a feedback arrangement between the linearized system and the remaining, normally neglected, nonlinear part. The linear system is reduced using a method similar to balanced truncation, but preserving bounds on the supply rate. The method involves balancing two algebraic Riccati equations. The bounds are then used to derive bounds on the turbulent energy production. An example of the application of the procedure to flow through a long straight pipe is presented. Comparison shows that the new method approximates the supply rate at least as well as, or better than, canonical balanced truncation.

Recently, the concept of feedback passivity-based control has drawn attention to chaos control. In all existing papers, the implementations of passivity-based control laws require the system states for feedback. In this paper, a passivity-based control law which only requires the knowledge of the system output is proposed. Simulation results are provided to show the effectiveness of the proposed solution.

The recent discovery of a physical device behaving as a memristor has driven a lot of attention to memristive systems, which are likely to play a relevant role in electronics in the near future, especially at the nanometer scale. The derivation of explicit ODE models for these systems is important because it opens a way for the study of the dynamics of general memristive circuits, including e.g. stability aspects, oscillations, bifurcations or chaotic phenomena. We tackle this problem as a reduction of implicit ODE (differential-algebraic) models, and show how tree-based approaches can be adapted in order to accommodate memristors. Specifically, we prove that the derivation of a tree-based explicit ODE model is feasible for strictly passive memristive systems under broad coupling effects and without a priori current/voltage control assumptions on tree/cotree elements. Our framework applies in particular to topologically degenerate circuits and accommodates a wide class of controlled sources. We also discuss a quasilinear reduction of nonpassive problems, which do not admit an explicit ODE description in the presence of singularities; some related bifurcations are addressed in this context.

In this paper, we show that parasitic elements have a significant effect on the dynamics of memristor circuits. We first show that certain $2$-terminal elements such as memristors, memcapacitors, and meminductors can be used as nonvolatile memories, if the principle of conservation of state variables hold by open-circuiting, or short-circuiting, their terminals. We also show that a passive memristor with a strictly-increasing constitutive relation will eventually lose its stored flux when we switch off the power if there is a parasitic capacitance across the memristor. Similarly, a memcapacitor (resp., meminductor) with a positive memcapacitance (resp., meminductance) will eventually lose their stored physical states when we switch off the power, if it is connected to a parasitic resistance. We then show that the discontinuous jump that circuit engineers assumed to occur at impasse points of memristor circuits contradicts the principles of conservation of charge and flux at the time of the discontinuous jump. A parasitic element can be used to break an impasse point, resulting in the emergence of a continuous oscillation in the circuit. We also define a distance, a diameter, and a dimension, for each circuit element in order to measure the complexity order of the parasitic elements. They can be used to find higher-order parasitic elements which can break impasse points. Furthermore, we derived a memristor-based Chua’s circuit from a three-element circuit containing a memristor by connecting two parasitic memcapacitances to break the impasse points. We finally show that a higher-order parasitic element can be used for breaking the impasse points on two-dimensional and three-dimensional constrained spaces.

We study local activity and its contrary, local passivity, for linear systems and show that generically an eigenvalue of the system matrix with positive real part implies local activity. If all state variables are port variables we prove that the system is locally active if and only if the system matrix is not dissipative. Local activity was suggested by Leon Chua as an indicator for the emergence of complexity of nonlinear systems. We propose an abstract scheme which indicates how local activity could be applied to nonlinear systems and list open questions about possible consequences for complexity.

Although the passivity of integer-order systems has been extensively analyzed, the research outcomes on the passivity of fractional-order nonlinear systems (FONSs) are scarce. This paper presents some theoretical results on passivity and passivation of FONSs. Based on the definition of the passivity of FONSs, and by using the Lyapunov stability theory and the linear matrix inequality (LMI) method, some conditions are derived to assure the FONSs is passive, which enrich the existing theoretical knowledge about the passivity of FONSs. Moreover, an observer-based output passive control is established to ensure that the corresponding closed-loop system is passive by means of LMI technique and matrix singular value decomposition (SVD). Ultimately, the practicality of our yielded results is revealed by two numerical simulations.

In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, “The missing circuit element”. The memristor equations were originally supposed to represent a passive circuit element because, with active circuitry, arbitrary elements can be realized without limitations. Therefore, if the memristor equations do not guarantee that the circuit element can be realized by a passive system, the fundamental physics claims about the memristor as “missing circuit element” loses all its weight. The question of passivity/activity belongs to physics thus we incorporate thermodynamics into the study of this problem. We show that the memristor equations are physically incomplete regarding the problem of passivity/activity. As a consequence, the claim that the present memristor functions describe a passive device lead to unphysical results, such as violating the Second Law of thermodynamics, in infinitely large number of cases. The seminal memristor equations cannot introduce a new physical circuit element without making the model more physical such as providing the Fluctuation–Dissipation Theory of memristors.

The passivity conditions for stochastic neural networks with time-varying delays and random abrupt changes are considered in this paper. Sufficient conditions on passivity of stochastic neural networks with time-varying delays and random abrupt changes are developed in the linear matrix inequality (LMI) setting. The results obtained in this paper improve and extend some of the previous results.

Due to the complexity of interaction among constituents inside the whole system, it is difficult to establish accurate mathematics models to describe and analyze the complex systems exactly. There are few attempts concerning on the moving process of endocrine disruptor in human bodies, which have been the polluted material worldwide related to the reproduction, existence and development of human being. Focusing on such two challenging issues, a multi-compartment model of endocrine disruptor Benzene moving in the human body complex system is established in this paper. Furthermore, passivity of this model is described systematically. A feedback controller for this descriptor biological complex system is used under the station of strict passivity, and an example of the controller is given for a particular instantiation of the model.

In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, “The missing circuit element”. The memristor equations were originally supposed to represent a passive circuit element because, with active circuitry, arbitrary elements can be realized without limitations. Therefore, if the memristor equations do not guarantee that the circuit element can be realized by a passive system, the fundamental physics claims about the memristor as “missing circuit element” loses all its weight. The question of passivity/activity belongs to physics thus we incorporate thermodynamics into the study of this problem. We show that the memristor equations are physically incomplete regarding the problem of passivity/activity. As a consequence, the claim that the present memristor functions describe a passive device lead to unphysical results, such as violating the Second Law of thermodynamics, in infinitely large number of cases. The seminal memristor equations cannot introduce a new physical circuit element without making the model more physical such as providing the Fluctuation Dissipation Theory of memristors.