system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

a bounded complementary sensitivity function ensures topology independent stability of homogeneous dynamical networks this paper investigates the topology independent stability of homogeneous dynamical networks composed of interconnected equal systems precisely dynamical systems with identical nominal transfer function f s are associated with the nodes of a directed graph whose arcs account for their dynamic interactions described by a common nominal transfer function g s it is shown that topology independent stability is guaranteed for all possible interconnections with interaction degree defined as the maximum number of arcs leaving a node equal at most to n if the infty norm of the complementary sensitivity function nf s g s 1 nf s g s 1 is less than 1 this bound is nonconservative in that there exist graphs with interaction degree n that are unstable for an infty norm greater than 1 when nodes and arcs transferences are affected by uncertainties with norm bound k 0 topology independent stability is robustly ensured if the infty norm is less than 1 1 2nk for symmetric systems stability is guaranteed for all topologies with interaction degree at most n if the nyquist plot of nf s g s does not intersect the real axis to the left of 1 2 the proposed results are applied to fluid networks and platoon formation

modular groups of quantum fields in thermal states for a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half sided translations the modular flows corresponding to the algebras of the forward light cone and a space like wedge admit a simple geometric description in two dimensional models that factorize in light cone coordinates at large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone for each domain there is also a one parameter group with a positive generator for which the thermal state is a ground state formally this may be regarded as a certain converse of the unruh effect

on the existence of equilibrium states in local quantum field theory it is shown that any local quantum field theory admits thermodynamical equilibrium states kms states for all positive temperatures provided it satisfies a nuclearity condition proposed by wichmann and one of the authors which restricts the admissible number of local degrees of freedom

modular intersections of von neumann algebras in quantum field theory we show that modular intersections of von neumann algebras occur naturally in quantum field theory an example are local observable algebras associated with wedge regions which have a lightray in common see also bo 2 wi 3 conversely starting from a set of four algebras lying in a specified modular position relative to each other we construct a net of local observables of a 2 1 dimensional quantum field theory

modular hamiltonians on the null plane and the markov property of the vacuum state we compute the modular hamiltonians of regions having the future horizon lying on a null plane for a cft this is equivalent to regions with a boundary of arbitrary shape lying on the null cone these hamiltonians have a local expression on the horizon formed by integrals of the stress tensor we prove this result in two different ways and show that the modular hamiltonians of these regions form an infinite dimensional lie algebra the corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities but act non locally outside the null plane we regain this result in greater generality using more abstract tools on the algebraic quantum field theory finally we show that modular hamiltonians on the null surface satisfy a markov property that leads to the saturation of the strong sub additive inequality for the entropies and to the strong super additivity of the relative entropy

conformal quantum field theory and half sided modular inclusions of von neumann algebras letn be von neumann algebras on a hilbert space a comon cyclic and separarting vector assume to be cyclic and separating also forn denote byj jn the modular conjugations to and n the associated modular operators if open image in new window and open image in new window these data define in a canonical way a conformal quantum field theory in a cricle conversely the chiral part of a conformal quantum field theory in two dimensions always yields such data in a natural way

brief paper diagonal stability of a class of cyclic systems and its connection with the secant criterion we consider a class of systems with a cyclic interconnection structure that arises among other examples in dynamic models for certain biochemical reactions we first show that a secant criterion for local stability derived earlier in the literature is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices we then revisit a recent generalization of this criterion to output strictly passive systems and recover the same stability condition using our diagonal stability result as a tool for constructing a lyapunov function using this procedure for lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties

scale and mobius covariance in two dimensional haag kastler net given a two dimensional haag kastler net which is poincare dilation covariant with additional properties we prove that it can be extended to a mobius covariant net additional properties are either a certain condition on modular covariance or a variant of strong additivity the proof relies neither on the existence of stress energy tensor nor any assumption on scaling dimensions we exhibit some examples of poincare dilation covariant net which cannot be extended to a mobius covariant net and discuss the obstructions

comparison between finite volume and finite element methods for an elliptic system arising in electrochemical engineering abstract a 2d mathematical model of a solid oxide fuel cell is presented the physics of the cell and the simplifying assumptions are first presented then the governing equations and boundary conditions are laid out the resulting system is a coupled system of elliptic equations with interface source terms and jumps the aim of this paper is to compare the discretization by the finite volume method with the discretization by finite element methods

duality bounds in robustness analysis abstract multipliers are used in stability theory to reduce conservatism and exploit structural information about system components for an important class of stability problems which gives a resulting infinite dimensional multiplier optimization a corresponding dual problem is stated the dual gives valuable information about the original problem in particular error bounds for its finite dimensional approximations 1997 elsevier science ltd

distributed robust control of linear multi agent systems with parameter uncertainties this article considers the distributed robust control problems of uncertain linear multi agent systems with undirected communication topologies it is assumed that the agents have identical nominal dynamics while subject to different norm bounded parameter uncertainties leading to weakly heterogeneous multi agent systems distributed controllers are designed for both continuous and discrete time multi agent systems based on the relative states of neighbouring agents and a subset of absolute states of the agents it is shown for both the continuous and discrete time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the h control problems of a set of decoupled linear systems having the same dimensions as a single agent a two step algorithm is presented to construct the distributed controller for the continuous time case which does not involve any conservatism and meanwhile decouples the feedback gain design from the commun

stability analysis of systems with generalized frequency variables a class of large scale multi agent systems with decentralized information structures can be represented by a linear system with a generalized frequency variable in this paper we investigate fundamental properties of such systems stability and d stability exploiting the dynamical structure specifically we first show that such system is stable if and only if the eigenvalues of the connectivity matrix lie in a region of the complex plane specified by the generalized frequency variable the stability region is characterized in terms of polynomial inequalities leading to an algebraic stability condition we also show that the stability test can be reduced to a linear matrix inequality lmi feasibility problem involving generalized lyapunov inequalities and that the lmi result can be extended for robust stability analysis of systems subject to uncertainties in the interconnection matrix we then extend the result to d stability analysis to meet practical requirements and provide a unified treatment of d stability conditions for ease of implementation finally numerical examples illustrate utility of the stability conditions for the analysis of biological oscillators and for the design of cooperative stabilizers

an algebraic characterization of vacuum states in minkowski space an algebraic characterization of vacuum states on nets ofc algebras over minkowski space is given and space time translations are reconstructed with the help of the modular structures associated with such states the result suggests that a condition of geometrical modular action might hold in quantum field theories on a wider class of spacetime manifolds

a scalable robust stability criterion for systems with heterogeneous lti components a scalable robust stability criterion for interconnected systems with heterogeneous linear time invariant components is presented in this paper the criterion involves only the properties of individual components and the spectrum of the interconnection matrix which can be verified with relatively low computational effort and more importantly maintains scalability of the analysis our main result shows that if the components are single input single output siso then the criterion has an appealing graphical interpretation which resembles the classical nyquist criterion

a finite volume scheme for a noncoercive elliptic equation with measure data we show here the convergence of the finite volume approximate solutions of a convection diffusion equation to a weak solution without the usual coercitivity assumption on the elliptic operator and with weak regularity assumptions on the data numerical experiments are performed to obtain some rates of convergence in two and three space dimensions

a mortar finite volume method for a fractured model in porous media abstract in this paper we consider a mortar finite volume method for a fractured model of flow in porous media in this model the permeability coefficients are variable between the fracture and the surrounding porous media a finite volume method based on raviart thomas elements combined with the mortar technique of domain decomposition is presented in which sub domains are triangulated independently and the meshes do not match at interfaces the great advantage of the method is avoiding solving the saddle point problem since the numerical scheme is just related to the pressure p and the velocity u can be expressed by p we also prove error estimates of order h on the discrete h 1 norm between the exact solution p and the mortar finite volume solution p and the l 2 2 norm between u and u finally numerical experiments have been performed to show the consistency of the convergence rates with the theoretical analysis

synchronization of networks of heterogeneous agents with common nominal behavior this paper deals with the problem of synchronization in networks of heterogeneous agents with common nominal behavior the agents are modeled as possibly nonlinear perturbed versions of a common siso nominal lti operator and they are interconnected via a sparse memoryless interconnection operator coherent with the communication graph underlying the network the network is said to synchronize if the outputs of the agents tend to align along given directions the most important case being consensus or agreement the paper provides a general result based on iqcs that ensures synchronization of the network with robustness w r t uncertainties in the interconnection and in each agent s dynamics scalability issues are discussed in the scenario where the interconnection operator is a constant normal matrix yielding the generalization of the very popular linear consensus algorithm the wide range of applicability of the proposed criterion is shown by providing synchronization conditions in some important examples whenever possible graphical criteria are proposed for checking the required conditions

natural energy bounds in quantum thermodynamics given a stationary state for a noncommutative flow we study a boundedness condition depending on a parameter 0 which is weaker than the kms equilibrium condition at inverse temperature this condition is equivalent to a holomorphic property closely related to the one recently considered by ruelle and d antoni zsido and shared by a natural class of non equilibrium steady states our holomorphic property is stronger than ruelle s one and thus selects a restricted class of non equilibrium steady states we also introduce the complete boundedness condition and show this notion to be equivalent to the pusz woronowicz complete passivity property hence to the kms condition

modular theory and the reconstruction of four dimensional quantum field theories in this letter we construct a representation of the 3 1 dimensional poincare group by modular groups of von neumann algebras lying in a specified modular position with respect to each other combining this new result with an old one of bisognano wichmann j math phys 16 985 1975 we obtain a net of local observables of a 3 1 dimensional quantum field theory out of a finite set of algebras

a popov criterion for networked systems abstract we consider robustness analysis of heterogeneous and homogeneous networked systems based on integral quadratic constraints iqcs first we show how the analysis decomposes into lower dimensional problems if the interconnection structure is exploited this generally leads to a significant reduction of the computational complexity secondly by considering a set of iqcs that characterizes the eigenvalues of the interconnection matrices of symmetrically networked systems we derive a popov like criterion for such systems in particular when the nodes of the networked system are single input single output linear time invariant operators the criterion can be illustrated using a generalized popov plot in such cases the popov criterion is also a necessary condition in the sense that if the criterion is violated then a destabilizing network with the specified eigenvalue distribution can be constructed

consensus of heterogeneous lti agents a robust stability criterion is derived for a class of higher order consensus algorithms in distinction to the standard consensus problem where the dynamics of all individual agents are the same and of low dimension the criterion for reaching consensus now depends on the full spectrum of the communication graph and not only the largest nonzero eigenvalue the new consensus criterion is posed as a nyquist like criterion that provides a clear separation between the individual dynamics and the spectrum of the graph our results are illustrated on a formation control problem for a target encircling task

classification of subsystems for graded local nets with trivial superselection structure we classify haag dual poincare covariant subsystems open image in new window of a graded local net open image in new window on 4d minkowski spacetime which satisfies standard assumptions and has trivial superselection structure the result applies to the canonical field net open image in new window of a net open image in new window of local observables satisfying natural assumptions as a consequence provided that it has no nontrivial internal symmetries such an observable net open image in new window is generated by the abstract versions of the local energy momentum tensor density and the observable local gauge currents which appear in the algebraic formulation of the quantum noether theorem moreover for a net open image in new window of local observables as above we also classify the poincare covariant local extensions open image in new window which preserve the dynamics

particle physics and quantum field theory at the turn of the century old principles with new concepts the present state of quantum field theory qft is analyzed from a new viewpoint whose mathematical basis is the modular theory of von neumann algebras its physical consequences suggest new ways of dealing with interactions symmetries hawking unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory interactions are incorporated by using the fact that the s matrix is a relative modular invariant of the interacting relative to the incoming net of wedge algebras this new point of view allows many interesting comparisions with the standard quantization approach to qft and is shown to be firmly rooted in the history of qft its radical change of paradigm aspect becomes particularly visible in the quantum measurement problem

on the relation between modular theory and geometry in this paper we comment on part of a recent paper by schroer and wiesbrock therein they calculate some new modular structure for the u 1 current algebra weyl algebra we point out that their findings are true in a more general setting the split property allows an extension to doubly localized algebras

half sided modular inclusions of von neumann algebras letn m be von neumann algebras on a hilbert spaceh a common cyclic and separating vector denote m n resp jm jn the associated modular operators and conjugations assume m it n it n fort 0 we call such an inclusion half sided modular then we prove the existence of a oneparameter unitary groupu a onh a r with generator frac 1 2 pi ln delta cal n ln delta m mathbin lower 3ex hbox buildrel over smash scriptstyle vphantom x 0 and relations 1 itu a it it nit u a nit u e 2 ta for alla t r 2 jmjn u 2 3 nit u 1 it u 1 for allt r 4 n u 1 u 1

nuclear maps and modular structures i general properties abstract we establish a correspondence between the split property of inclusions a b of von neumann algebras and nuclearity properties of the natural embeddings p l a lp b p 1 2 given by the modular theory

robust stability analysis of sparsely interconnected uncertain systems in this paper we consider robust stability analysis of large scale sparsely interconnected uncertain systems by modeling the interconnections among the subsystems with integral quadratic constraints we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities we also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness the sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem