patterns of relation triples in inversion and ascent sequences abstract recently martinez and savage carried out the systematic study of inversion sequences avoiding triples of relations they reported many nice connections with familiar combinatorial families and posed several enumeration conjectures all of their conjectures have already been solved except those related to the oeis sequence a098746 in this paper we address those remaining conjectures which completes a picture for all the suspected connections arising in their investigation as one of the most important subsets of inversion sequences ascent sequences were introduced by bousquet melou et al in bijection with 2 2 free posets and their pattern avoidance properties have been extensively studied we investigate some classical eulerian and stirling statistics on ascent sequences avoiding triples of relations this leads us to find two new interpretations of the catalan numbers and its refinements and to interpret combinatorially a natural refinement of the binomial transformation of catalan numbers the latter discovery answers a challenging open problem posed by pudwell

controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

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

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

model matching and factorization for nonlinear systems a structural approach the model matching and the left factorization problems for nonlinear systems are investigated using an approach based on the structural algorithm sufficient conditions for the solvability of the f

implicit discrete time systems and accessibility an intrinsic description for dynamic systems whose evolution along discrete time is governed by nonlinear implicit difference equations in one independent variable and zero order algebraic equations is presented by means of differential geometrical methods where systems are associated with appropriate geometric objects reflecting their dynamics dynamic systems given in implicit form have the peculiarity that they may contain so called hidden restrictions a normal form is presented which is characterized by the circumstances that there are no further restrictions in addition it is illustrated that such a normal form allows for an equivalent system representation in explicit form based on the geometric picture of implicit discrete time systems the qualitative property of accessibility along a fixed trajectory is discussed by applying symmetry groups of discrete time systems and studying invariants of these groups a formal approach is provided that allows us to gather local accessibility criteria successively which can be tested by computer algebra several examples illustrate the results

generalized controlled invariance for nonlinear systems a general setting is developed which describes controlled invariance for nonlinear control systems and which incorporates the previous approaches dealing with controlled invariant co distributions a special class of controlled invariant subspaces called controllability cospaces is introduced these geometric notions are shown to be useful for deriving a geometric solution to the dynamic disturbance decoupling problem and for characterizing the so called fixed dynamics for noninteracting control these fixed dynamics are a central issue in studying noninteracting control with stability the class of quasi static state feedbacks is used

bijections for inversion sequences ascent sequences and 3 nonnesting set partitions abstract set partitions avoiding k crossing and k nesting have been extensively studied from the aspects of both combinatorics and mathematical biology by using the generating tree technique the obstinate kernel method and zeilberger s algorithm lin confirmed a conjecture due independently to the author and martinez savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3 nonnesting partitions have the same cardinality in this paper we provide a bijective proof of this conjecture our bijection also enables us to provide a new bijective proof of a conjecture posed by duncan and steingrimsson which was proved by the author via an intermediate structure of growth diagrams for 01 fillings of ferrers shapes

the magnetic weyl calculus in the presence of a variable magnetic field the weyl pseudodifferential calculus must be modified the usual modification based on the minimal coupling principle at the level of the classical symbols does not lead to gauge invariant formulas if the magnetic field is not constant we present a gauge covariant quantization relying on the magnetic canonical commutation relations the underlying symbolic calculus is a deformation defined in terms of the magnetic flux through triangles of the classical moyal product

block decoupling of non linear systems by static measurement feedback in this paper the block input output decoupling problem for non linear systems is stated and solved by static feedback of measured variables only in contrast with standard solutions which assume that the full state is available for feedback

robust stability of feedback systems a geometric approach using the gap metric a geometric framework for robust stabilization of infinite dimensional time varying linear systems is presented the uncertainty of a system is described by perturbations of its graph and is measured in the gap metric necessary and sufficient conditions for robust stability are generalized from the time invariant case an example is given to highlight an important difference between the obstructions which limit the size of a stabilizable gap ball in the time varying and time invariant cases several results on the gap metric and the gap topology are established that are central in a geometric treatment of the robust stabilizability problem in the gap in particular the concept of a graphable subspace is introduced in the paper subspaces that fail to be graphable are characterized by an index condition on a certain semi fredholm operator

local input output decoupling of discrete time non linear systems a local treatment of the restricted block input output decoupling problem is given the major tools employed are the invariant and locally controlled invariant distributions which have recently been extended to the discrete time domain

invariant codistributions and the feedforward form for discrete time nonlinear systems the goal of this paper is two fold first given an arbitrary n dimensional discrete time nonlinear dynamical system necessary and sufficient conditions for the existence of a one dimensional invariant codistribution are obtained second it is shown that the previous conditions can be used iteratively to obtain a nested sequence of n invariant codistributions with the properties that each codistribution contains the previous one and the last one coincides with the cotangent bundle of the state manifold as a byproduct necessary and sufficient conditions are obtained for a discrete time nonlinear dynamical system to be equivalent to the so called feedforward form

non linear non interacting control with stability in discrete time a dynamic solution the geometric approach proposed in califano et al nonlinear noninteracting control with stability in discrete time a geometric approach int j control 75 1 pp 11 22 2002 for non linear non interacting control with stability via static state feedback in discrete time is now used to find a dynamic solution for systems characterized by an invertible drift geometric necessary and sufficient conditions are given a constructive procedure for the computation of the dynamic compensator solving the problem is proposed

adaptive control and robustness in the gap metric we consider the construction of adaptive controllers for minimum phase linear systems that achieve nonzero robustness margins in the sense of the gap metric the gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties working in both and settings and within the framework of the nonlinear gap metric universal adaptive controllers are first given achieving stabilization for first order nominal plants and the results are then generalized to relative degree one nominal plants a notion of a semiuniversal control design is introduced which is the property that a bound on performance exists that is independent of the a priori known uncertainty level and a characterization is given for when semiuniversal designs outperform the class of memoryless controllers and the class of linear time invariant controllers robust semiuniversal adaptive control designs are given for nominal plants under the classical assumptions of adaptive control in both the and settings the results are applied throughout to explicit classes of unmodeled dynamics including the rohrs example

interconnection of nonlinear causal systems for nonlinear systems it is not a mathematically obvious fact that the simplest feedback system yields equations which are solvable even when the gain in the loop is

positive quantization in the presence of a variable magnetic field starting with a previously constructed family of coherent states we introduce the berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural poisson algebra the phase space reinterpretation involves a magnetic version of the bargmann space and leads naturally to berezin toeplitz operators

toeplitz algebras and rieffel deformations we establish a representation theorem for toeplitz operators on the segal bargmann fock space ofc n whose symbols have uniform radial limits as an application of this result we show that toeplitz algebras on the open ball inc n are strict deformation quantizations in the sense of m rieffel of the continuous functions on the corresponding closed ball

non linear non interacting control with stability in discrete time a geometric framework the aim of the paper is to set the non linear non interacting control problem with stability in discrete time in a correct geometric framework so providing a solution which recalls the continuous approach and to point out the peculiarities of discrete time dynamics geometric necessary and sufficient conditions for the solvability of the problem are given and a constructive method figures out the regular static state feedback solution it is shown that if the given dynamics is feedback equivalent to a decoupled system characterized by an invertible drift the computation of the distributions involved can be carried out in a simple and elegant way the main results are thus proved exhaustively in this case and then generalized to submersive systems

non perturbative deformation quantization of cartan domains abstract we construct families of non commuting c algebras of quantized functions for bounded irreducible hermitian symmetric spaces for this procedure we use algebras of toeplitz operators defined with respect to a perturbation of the ordinary bergman metric we prove the deformation quantization conditions for these algebras

non linear systems stabilization and coprimeness a theory of coprimeness is developed for non linear systems with the intention of constructing analytic tools for the solution of the problem of stabilizing a non linear system through the application of additive non linear feedback the qualitative features of the resulting theory are strikingly similar to the situation in the linear case

robustness in the graph topology of a common adaptive controller for any m input m output finite dimensional linear minimum phase plant p with first markov parameter having spectrum in the open right half complex plane it is well known that the adaptive output feedback control c given by u ky dot k y 2 yields a closed loop system p c for which the state converges to zero the signal k converges to a finite limit and all other signals are of class l 2 it is first shown that these properties continue to hold in the presence of l 2 input and l 2 output disturbances working within the conceptual framework of the nonlinear gap metric approach to robust stability and by establishing gain function stability of an appropriate closed loop operator it is proved that these properties also persist when the plant p is replaced with a stabilizable and detectable linear plant p 1 within a sufficiently small neighborhood of p in the graph topology provided that the plant initial data and the l 2 magnitude of the disturbances are sufficiently small example 9 of georgiou and smith ieee trans automat control 42 1997 pp 1200 1221 is revisited unstable behavior for large initial conditions and or large l 2 disturbances is shown demonstrating that the bounds obtained from the l 2 theory are qualitatively tight this contrasts with the l infty robustness analysis of georgiou and smith which is insufficiently tight to predict the stable behavior for small initial conditions and zero disturbances

coprime fractional representations and stability of non linear feedback systems fractional representation methods for finite dimensional linear time invariant fdlti systems have been developed in an algebraic framework of principal ideal domains the concept of coprime fractional representations has been generalized to discrete time non linear systems by hammer 1985 1987 by viewing the bezout identity as the basis of the definition of coprimeness in this paper we view the role of right coprime fractional representation in representing the set of all stable input output pairs of a possibly unstable non linear system this notion of coprimeness is shown to be equivalent to that of fdlti systems using coprime fractional representations of non linear systems we obtain a characterization of the stability of non linear feedback systems this characterization is similar to that obtained in the case of fdlti systems we also obtain a parameterization of all non linear and time varying stabilizing controllers for linear possibly time varying plants which has the same form as t

simple sufficient conditions for reachability of discrete time polynomial systems we consider reachability of discrete time polynomial systems the reachability of such systems can be interpreted as the surjectivity of the polynomial mappings defined by the systems for a polynomial mapping between suitable spaces of the same dimensions it has been shown that the injectivity of the mapping also implies the surjectivity by utilizing this fact we derive sufficient conditions for the reachability of the polynomial systems which essentially check the injectivity of the polynomial mappings

a complete characterization of decoupling control laws for a general class of nonlinear systems in the past decade conditions for feedback decoupling of nonlinear systems have been studied extensively the class of control laws which decouple has received relatively little attention in this paper a characterization of the whole class of nonlinear decoupling control laws for real analytic nonlinear systems is obtained this result is important from both mathematical and engineering viewpoints for instance we present an example where former results do not allow stable decoupling while our result does the main result is proved and several examples which illustrate its generality are presented

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

the immersion under feedback of a multidimensional discrete time non linear system into a linear system this paper deals with the problem of finding conditions which ensure the reproducibility of the input output behaviour of a linear analytic discrete time system by means of a linear discrete time system on this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved

pattern avoiding inversion sequences and open partition diagrams abstract by using the generating tree technique and the obstinate kernel method kim and lin confirmed a conjecture due to martinez and savage which asserts that inversion sequences e e 1 e 2 e n containing no three indices i j k such that e i e j e j e k and e i e k are counted by baxter numbers in this paper we provide a bijective proof of this conjecture via an intermediate structure of open partition diagrams in answer to a problem posed by beaton bouvel guerrini rinaldi moreover we show that two new classes of pattern avoiding inversion sequences are also counted by baxter numbers

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

on the gap metric and coprime factor perturbations abstract new conditions are derived for when the distance between two linear systems in the gap metric is less than one by including a coprimeness assumption in the coprime factor uncertainty description it is shown that an open ball in the gap metric is equivalent to an open ball phrased in terms of coprime factor perturbations a new criterion is given for robust stabilization

the necessity of the small gain theorem for time varying and nonlinear systems it is shown that an appropriately modified version of the small gain theorem which uses the asymptotic gain of a fading memory system leads to a necessary and sufficient condition for the stable invertibility of certain feedback operators this modified small gain theorem is then used to obtain conditions for robust finite energy input output stability of 1 nonlinear plants subject to nonlinear time varying perturbations and 2 linear time varying plants subject to linear time varying perturbations these conditions are shown to be necessary as well as sufficient

frequency domain uncertainty and the graph topology a new metric on linear time invariant systems is defined this metric is no greater than the gap metric and is in fact the smallest metric for which a certain robust stabilization result holds unlike other known metrics which induce the graph topology it has a clear frequency response interpretation this allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric

continuity of magnetic weyl calculus abstract we investigate continuity properties of the operators obtained by the magnetic weyl calculus on nilpotent lie groups using modulation spaces associated with unitary representations of certain infinite dimensional lie groups

brief paper on the observability of discrete time dynamic systems a geometric approach a coordinate free description for dynamic systems described by explicit nonlinear difference equations in one independent variable via a differential geometric framework is presented based on this covariant approach suitable geometric objects for discrete time dynamics are introduced especially the observability along a trajectory is discussed and transformations to normal forms are derived in addition the obtained local observability criteria can be checked by computer algebra algorithms some examples illustrate the proposed approach

vincular patterns in inversion sequences abstract inversion sequences have intriguing applications in combinatorics computer sciences and polyhedral geometry ascent sequences as one of the most important subsets of inversion sequences were introduced by bousquet melou claesson dukes and kitaev to encode the 2 2 free posets pattern avoidance in ascent sequences was first studied by ducan and steingrimsson in 2011 while the systematic study of patterns in inversion sequences was initiated only recently by corteel martinez savage weselcouch and mansour shattuck in this paper we investigate systematically the enumeration of inversion or ascent sequences avoiding vincular patterns of length 3 where two of the three letters are required to be adjacent our results connect restricted inversion sequences and ascent sequences to a number of well known combinatorial sequences including bell numbers fishburn numbers powered catalan numbers semi baxter numbers and the number of 3 noncrossing partitions a variety of combinatorial bijections known or newly constructed are applied to achieve these interesting connections

linearization and input output decoupling for general nonlinear systems necessary and sufficient conditions are obtained for the linearization and input decoupling by state feedback of general nonlinear systems it is shown how these conditions can be derived from the already known conditions for affine nonlinear systems thereby also elucidating the existing theory for affine systems

reversible linear and nonlinear discrete time dynamics it is shown that any causal discrete time system can be realized with a reversible or invertible state variable representation this bridges the gap with continuous time where flows always satisfy this property and settles an old debate on the relevance of invertibility in nonlinear discrete dynamics as the result applies to the linear case it is shown how the classic approach should be slightly modified and several examples of the benefits that can be obtained are given difference algebra is employed for nonlinear systems it leads to a most elegant characterization of causality which enables reversibility to be demonstrated module theory suffices in the linear case which is supplemented by elementary matrix manipulations

joint state and parameter estimation of non linearly parameterized discrete time nonlinear systems abstract simultaneous state and parameter estimation of nonlinear discrete time systems is addressed the developed procedure is dedicated to multiple input multiple output mimo bounded state nonlinear systems subject to either linear or nonlinear parametrization it is shown that under the persistent excitation condition the unmeasured states along with the system parameters can be reproduced asymptotically if the upper and the lower bounds of the system states are assumed to be known the existence of the observer gain is conditioned by the solvability of a linear matrix inequality lmi simulation results are provided to highlight the efficacy of the developed theoretical results

spectral and propagation results for magnetic schrodinger operators a c algebraic framework abstract we study generalized magnetic schrodinger operators of the form h h a v h a v where h is an elliptic symbol a i a with a a vector potential defining a variable magnetic field b and v is a scalar potential we are mainly interested in anisotropic functions b and v the first step is to show that these operators are affiliated to suitable c algebras of magnetic pseudodifferential operators a study of the quotient of these c algebras by the ideal of compact operators leads to formulae for the essential spectrum of h h a v expressed as a union of spectra of some asymptotic operators supported by the quasi orbits of a suitable dynamical system the quotient of the same c algebras by other ideals give localization results on the functional calculus of the operators h h a v which can be interpreted as non propagation properties of their unitary groups

invariant distributions for discrete time nonlinear systems the purpose of this paper is to introduce some notions of invariant distributions for the class of linear analytic discrete time systems and to give an algebraic characterization of them a brief final discussion motivates the usefulness of the notions introduced in the study of the geometric properties of the system

robust output tracking for non linear systems the problem of output tracking for a single input single output non linear system in the presence of uncertainties is studied the notions relative degree and minimum phase for non linear systems are reviewed given a bounded desired tracking signal with bounded derivatives a control law is designed for minimum phase non linear systems which results in tracking of this signal by the output this control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors two types of uncertainties are considered those satisfying a generalized matching condition but otherwise unstructured and linear parametric uncertainties it is shown that for systems with the first type of uncertainty high gain control laws can result in small tracking errors of o where e is a small design parameter an alternative scheme based on variable structure control strategy is shown to yield zero tracking errors adaptive control te

generalized controlled invariance for discrete time nonlinear systems with an application to the dynamic disturbance decoupling problem in analogy with the continuous time case a general notion of controlled invariance with respect to quasi static state feedback is introduced for discrete time nonlinear systems which incorporates the earlier definition of controlled invariance with respect to regular static state feedback this new notion is used to derive a geometric solution to the dynamic disturbance decoupling problem the proposed solution is a natural generalization of the geometric solution to the static disturbance decoupling problem

the parallel projection operators of a nonlinear feedback system abstract this paper defines and studies a pair of nonlinear parallel projection operators associated with a nonlinear feedback system these operators have been seen to play an important role in the robustness and design of linear systems especially in the theory of the gap metric the use of weighted gaps in control system design and glover mcfarlane loop shaping we show that the input output l 2 stability of a feedback system amounts to a coordinatization of the input and output spaces which is also equivalent to the existence of a pair of nonlinear parallel projection operators onto the graph of the plant and the inverse graph of the controller respectively these projections are shown to have equal norms whenever one of the feedback elements is linear a bound on this norm is given in the case of passive systems with unity negative feedback

the measure algebra of the heisenberg group abstract irreducible representations of the convolution algebram h n of bounded regular complex borel measures on the heisenberg group h nare analyzed for the segal bargmann representation thec algebra generated by m h n is just thec algebra generated by berezin toeplitz operators with positive definite symbols this algebra is a deformation of the sup norm algebra generated by positive definite functions on complexn space c n

robustness analysis of nonlinear feedback systems an input output approach this paper presents an approach to robustness analysis for nonlinear feedback systems we pursue a notion of model uncertainty based on the closeness of input output trajectories which is not tied to a particular uncertainty representation such as additive parametric structured etc the basic viewpoint is to regard systems as operators on signal spaces we present two versions of a global theory where stability is captured by induced norms or by gain functions we also develop local approaches over bounded signal sets and give a treatment for systems with potential for finite time escape we compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations e g small time delays we also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations the paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection

enumerating five families of pattern avoiding inversion sequences and introducing the powered catalan numbers abstract the first problem addressed by this article is the enumeration of some families of pattern avoiding inversion sequences we solve some enumerative conjectures left open by the foundational work on the topics by corteel et al some of these being also solved independently by lin and kim and lin the strength of our approach is its robustness we enumerate four families f 1 f 2 f 3 f 4 of pattern avoiding inversion sequences ordered by inclusion using the same approach more precisely we provide a generating tree with associated succession rule for each family f i which generalizes the one for the family f i 1 the second topic of the paper is the enumeration of a fifth family f 5 of pattern avoiding inversion sequences containing f 4 this enumeration is also solved via a succession rule which however does not generalize the one for f 4 the associated enumeration sequence which we call the powered catalan numbers is quite intriguing and further investigated we provide two different succession rules for it denoted p c a t and s t e a d y and show that they define two types of families enumerated by powered catalan numbers among such families we introduce the steady paths which are naturally associated with s t e a d y they allow us to bridge the gap between the two types of families enumerated by powered catalan numbers indeed we provide a size preserving bijection between steady paths and valley marked dyck paths which are naturally associated with p c a t along the way we provide several nice connections to families of permutations defined by the avoidance of vincular patterns and some enumerative conjectures

a mathcal b invariant distributions and disturbance decoupling of nonlinear systems the concept of a b invariant subspaces has resulted in a unified approach to many of the basic structural properties of time invariant linear systems w m wonham lecture notes in economics and mathematical systems vol 101 springer verlag new york 1974 the purpose of this paper is to introduce the more general notion of a mathcal b invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds

deformation estimates for the berezin toeplitz quantization deformation estimates for the berezin toeplitz quantization ofcn are obtained these estimates justify the description of ccr k as a first order quantum deformation of ap c0 where ccr is the usualc algebra of boson canonical commutation relations k is the full algebra of compact operators ap is the algebra of almost periodic functions andc0 is the algebra of continuous functions which vanish at infinity

crossings and nestings of matchings and partitions we present results on the enumeration of crossings and nestings for matchings and set partitions using a bijection between partitions and vacillating tableaux we show that if we fix the sets of minimal block elements and maximal block elements the crossing number and the nesting number of partitions have a symmetric joint distribution it follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of n as well as over all matchings on 2n as a corollary the number of k noncrossing partitions is equal to the number of k nonnesting partitions the same is also true for matchings an application is given to the enumeration of matchings with no k crossing or with no k nesting mathematics subject classification primary 05a18 secondary 05e10 05a15

fixed modes and nonlinear noninteracting control with stability the existence of a fixed internal dynamics inherent to the noninteraction requirement is identified when unstable this represents an obstruction to the achievement of noninteracting control with stability by means of static state feedback remarkably whenever one leaves the class of linear systems this obstruction cannot in general be removed by dynamic state feedback

remarks on robustness analysis of nonlinear feedback systems an input output approach in our previous paper 1999 sec vii contains two examples of adaptive controllers examples 8 and 9 for which the nonlinear gap robustness margin is zero and which are destabilized by arbitrarily small perturbations in the gap metric the proof that the robustness margin is zero makes use of the fact that the parameter estimate spl theta t tends to infinity as t spl rarr spl infin when there is a constant input disturbance of size spl epsi 0 the purpose of this present note is a to complete the argument given in the above paper to prove the unboundedness of spl theta t and b to give an alternative proof that the convergence of the state x t spl rarr 0 is a consequence of the unboundedness of spl theta t in example 9

product rule for gauge invariant weyl symbols and its application to the semiclassical description of guiding centre motion we derive a product rule for gauge invariant weyl symbols which provides a generalization of the well known moyal formula to the case of non vanishing electromagnetic fields applying our result to the guiding centre problem we expand the guiding centre hamiltonian into an asymptotic power series with respect to both planck s constant and an adiabaticity parameter already present in the classical theory this expansion is used to determine the influence of quantum mechanical effects on guiding centre motion

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

on graphs conic relations and input output stability of nonlinear feedback systems this paper presents necessary and sufficient conditions for the stability of general interconnected dynamical systems the results are expressed in terms of the graphs of the interconnection s subsystems conditions for robustness of stability for an interconnection with additive disturbances are also provided finally the paper gives sufficient conditions for stability using conic sector conditions that generalize earlier conditions and that incorporate a recent nonlinear small gain idea

toeplitz operators on the segal bargmann space in this paper we give a complete characterization of those functions on 2n dimensional euclidean space for which the berezin toeplitz quantizations admit a symbol calculus modulo the compact operators the functions in question are characterized by a condition of small oscillation at infinity

nonlinear morgan s problem case of p 1 inputs and p outputs noninvertible static state feedback solutions of the row by row decoupling problem are investigated for the class of nonlinear systems having one more input component than output components the analysis involves a combination of geometric and algebraic tools but notably avoids the use of regular or degenerate controllability distribution subspaces the main tools used to date for the class of linear systems the main idea is finding within the system a chain of integrators that may be attached to one of the inputs in order to appropriately modify the system s structure at infinity

internally exponentially stable non linear discrete time non interacting control via static feedback the problem of discrete time block non interacting control with internal exponential stability is treated by identifying the linearized fixed modes common to every non interactive closed loop a necessary condition for achieving an exponentially stable solution to the problem is provided also through a special decomposition of the given system a sufficient condition is obtained owing to peculiarities intrinsic to discrete time non linear systems the development of the solution is not completely parallel to that of the solution for the class of continuous time systems

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear