asymptotic stability of two dimensional digital filters under quantization the stability of 2 d digital filters implemented with two s complement quantization is investigated the difference equation model is considered for the following cases i quantization after each product and ii quantization after a complete sum of products for both cases sufficient conditions are established for asymptotic stability the 2 d state space roesser s 1975 model is also considered under two s complement quantization and a sufficient condition is derived for its stability some examples are given to illustrate the results

lattice topological field theory in two dimensions the lattice definition of a two dimensional topological field theory tft is given generically and the exact solution is obtained explicitly in particular the set of all lattice topological field theories is shown to be in one to one correspondence with the set of all associative algebrasr and the physical hilbert space is identified with the centerz r of the associative algebrar perturbations of tft s are also considered in this approach showing that the form of topological perturbations is automatically determined and that all tft s are obtained from one tft by such perturbations several examples are presented including twistedn 2 minimal topological matter and the case wherer is a group ring

lmi stability tests for the fornasini marchesini model we present a linear matrix inequality lmi for testing the stability of a 2 d system described by the fornasini marchesini first model the test is based on the properties of sum of squares polynomials with matrix coefficients although the test implements a sufficient condition extensive experiments suggest that the gap to necessity is very small we also derive an lmi describing stability conditions around a given model and useful in robust stability testing

stability of 2 d systems described by the fornasini marchesini first model a sufficient condition for the stability of linear two dimensional 2 d systems described by the fornasini marchesini 1976 first model is presented the condition is compared with previously reported conditions

topological higher gauge theory from bf to bfcg theory we study generalizations of three and four dimensional bf theories in the context of higher gauge theory first we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of yetter mackaay and porter under certain conditions we can present their corresponding continuum counterparts in terms of classical lagrangians we then explain that two of these models are already familiar from the literature the ea model of three dimensional gravity coupled to topological matter and also a four dimensional model of bf theory coupled to topological matter

stability and stability margin for a two dimensional system in this paper a necessary and sufficient condition is derived for the stability of the fornasini marchesini fm first model proposed for two dimensional 2 d dynamic system descriptions a connection has been established between the stability of this model and the structured singular value ssv of a constant matrix which is now widely known in control theories based on this connection a novel sufficient condition is obtained for the stability of the fm first model that is more computationally convenient in filter design numerical simulations show that this sufficient condition is usually less conservative than that of moreover the stability margin of the fm first model is also investigated it is shown that a 2 d system remains stable under parametric variations if and only if the ssv of a constant matrix is smaller than one

a stability analysis of two dimensional nonlinear digital state space filters two different methods for a stability analysis of 2 d nonlinear discrete state space systems under zero input conditions are provided the first method reduces the task of testing a 2 d discrete nonlinear or shift varying system to a single 2 d linear stability test of a system matrix with nonnegative system matrix entries the second method is based on a number of norm tests for products of extreme matrices and can be considered the 2 d counterpart of the method for 1 d systems described by k t erickson and a n michel 1985 both of the introduced methods are based on the sector description of the nonlinearity and can be used to analyze digital filter stability under finite word length effects

stability of two dimensional linear systems with singularities on the stability boundary using lmis this paper gives results on stability and asymptotic stability of two dimensional systems using linear matrix inequalities lmis despite a long history of research in this area systems with singularities on the stability boundary ssb have received limited attention because they cannot produce a sign definite solution to the required lmi however 2d systems describing some classes of models of vehicle platoons generically involve an ssb therefore commonly used definitions for asymptotic stability and strict lmi conditions are not suitable to discuss the stability of these systems it is shown that the existence of a negative semidefinite solution together with simple additional conditions is sufficient to guarantee asymptotic stability thus the stability conditions discussed here can be used to study a wider range of dynamical systems including systems with singularities on the stability boundary ssb which cannot be exponentially stable a unified framework is used to analyse continuous continuous continuous discrete and discrete discrete systems simultaneously

necessary and sufficient lmi conditions for stability and performance analysis of 2 d mixed continuous discrete time systems this paper proposes necessary and sufficient conditions for stability and performance analysis of 2 d mixed continuous discrete time systems that can be checked with convex optimization in particular linear matrix inequalities lmis specifically the first contribution of the paper is a condition for exponential stability based on the introduction of a complex lyapunov function depending polynomially on a parameter and on the use of the gram matrix method it is shown that this condition is sufficient for any chosen degree of the complex lyapunov function and necessary for an a priori known degree the second contribution is a non lyapunov condition for exponential stability based on eigenvalue products this condition is necessary and sufficient and has the advantage of requiring a significantly smaller computational burden for achieving necessity lastly the third contribution is to show how upper bounds on the h norm of 2 d mixed continuous discrete time systems can be obtained through a semidefinite program based on complex lyapunov functions a necessary and sufficient condition is provided for establishing the tightness of the found upper bounds

two s complement quantization in two dimensional state space digital filters two dimensional 2 d state space digital filters are investigated for stability with and without quantization a sufficient condition is obtained for the stability of the linear fornasini marchesini 1976 state space model the same model is then studied for stability when implemented using two s complement truncation quantization and a sufficient condition for asymptotic stability of the nonlinear filter is obtained in the process a theorem is proved which gives a sufficient condition for the stability of a one dimensional 1 d state space digital filter under the same type of quantization

on second quantization of quantum groups we construct a deformation of the function algebra on the quantum group slq 2 into a trialgebra in the sense of crane and frenkel we show that this naturally acts on the trialgebraic deformation of the manin plane previously introduced by the authors alternatively one can view it as acting on the trialgebraic deformation of the fermionic manin plane we prove that the trialgebraic deformation of slq 2 defines a 2 c category a structure as needed for the superselection structure of massive two dimensional quantum field theories besides this we investigate another approach to trialgebra deformations of a bialgebra as a deformation of a fock space construction over the bialgebra

fuzzy modeling and h control for general 2d nonlinear systems this paper investigates h control for general 2d nonlinear systems based on a 2d takagi sugeno t s fuzzy model the system under consideration is an extension of the general 2d linear system to a nonlinear case taking the spatial and structural features into consideration a 2d t s fuzzy model is first established in designing the h controller the inputs are regarded as variables independent from the states and then basis dependent free matrices are introduced it has been shown that separation of the input and state variables does not lead to any conservativeness compared with the commonly used method thus a fuzzy h controller is designed using a common free matrix resulting in only r linear matrix inequalities the computational advantage is obvious for fuzzy systems with a large number of fuzzy rules we also demonstrate that the proposed method is less computationally expensive than the approach in which the input variable state variable and its forward stepping state are all separately considered although these two methods can achieve the same optimal h performance simulation examples are used to demonstrate the technique and its advantages

on the bose trautman condition for stability of two dimensional linear systems in this correspondence we give a counterexample that shows that the bose trautman condition for the stability of 2 d linear models is incorrect the correction and equivalent conditions are given together with simple proofs from non negative matrix theory

robust stability and performance analysis of 2d mixed continuous discrete time systems with uncertainty this paper investigates 2d mixed continuous discrete time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set it is shown that a nonconservative linear matrix inequality lmi condition for ensuring robust stability can be obtained by introducing complex lyapunov functions depending polynomially on the uncertain vector and a frequency moreover it is shown that nonconservative lmi conditions for establishing upper bounds of the robust h and h 2 norms can be obtained by introducing analogous lyapunov functions depending rationally on the frequency some numerical examples illustrate the proposed methodology

structural invariants of two dimensional systems in this paper some fundamental structural properties of two dimensional 2 d systems which remain invariant under feedback and output injection transformation groups are identified and investigated for the first time as is well known structural invariants that follow from the definition of controlled and conditioned invariance output nulling input containing self bounded and self hidden subspaces play pivotal roles in many theoretical studies of systems theory and in the solution of several control estimation problems these concepts are developed and studied within a 2 d context in this paper

simple criteria for stability of two dimensional linear systems stability criteria for two dimensional 2 d systems described by the fornasini marchesini state space model are presented the criteria are sharper than the reported results in literature illustrative examples are provided

propositional knowledge base revision and minimal change abstract the semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model theoretic point of view a characterization of all revision schemes that satisfy the gardenfors rationality postulates is given in terms of minimal change with respect to an ordering among interpretations revision methods proposed by various authors are surveyed and analyzed in this framework the correspondences between gardenfors like rationality postulates and minimal changes with respect to other orderings are also investigated

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

structures and diagrammatics of four dimensional topological lattice field theories abstract crane and frenkel proposed a state sum invariant for triangulated 4 manifolds they sketched the definition of a hopf category that was to be used in their construction crane and yetter studied hopf categories and gave some examples using group cocycles that are associated to the drinfeld double of a finite group in this paper we define a state sum invariant of triangulated 4 manifolds using crane yetter cocycles as boltzmann weights our invariant is analogous to the 3 dimensional invariants defined by dijkgraaf and witten and the invariants that are defined via hopf algebras we present diagrammatic methods for the study of such invariants that illustrate connections between hopf categories and moves to triangulations

2 groups trialgebras and their hopf categories of representations a strict 2 group is a 2 category with one object in which all morphisms and all 2 morphisms have inverses 2 groups have been studied in the context of homotopy theory higher gauge theory and topological quantum field theory tqft in the present article we develop the notions of trialgebra and cotrialgebra generalizations of hopf algebras with two multiplications and one comultiplication or vice versa and the notion of hopf categories generalizations of monoidal categories with an additional functorial comultiplication we show that each strict 2 group has a group algebra which is a cocommutative trialgebra and that each strict finite 2 group has a function algebra which is a commutative cotrialgebra each such commutative cotrialgebra gives rise to a symmetric hopf category of corepresentations in the semisimple case this hopf category is a 2 vector space according to kapranov and voevodsky we also show that strict compact topological 2 groups are characterized by their c cotrialgebras of complex valued functions generalizing the gel fand representation and that commutative cotrialgebras are characterized by their symmetric hopf categories of corepresentations generalizing tannaka krei n reconstruction technically all these results are obtained using ideas from functorial semantics by studying models of the essentially algebraic theory of categories in various base categories of familiar algebraic structures and the functors that describe the relationships between them

two s complement quantization in periodic digital filters the stability of periodically shift variant psv filters are studied when implemented with two s complement truncation tct quantization block form and standard nonblock form implementations are considered and two sufficient conditions are established for stability as a special case second order coupled form psv filters are then investigated under tct quantization stability regions are established within the parameter space for block implementations examples are given to illustrate the results

nonmonotonic inference based on expectations abstract we show how nonmonotonic inferences may elegantly be interpreted in terms of underlying expectations the fundamental idea is that when we reason we make use of not only the information that we firmly believe but also expectations that guide our beliefs without quite being part of them we propose two ways of modelling the expectations used in nonmonotonic reasoning by expectation sets equipped with selection functions and by expectation relations for each of these we prove representation theorems and establish relations with several other modellings in the area including poole systems and preferential models we also show that by using the notion of expectation one can unify the treatment of the theory of belief revision and that of nonmonotonic inference relations this is accomplished by viewing the relation of epistemic entrenchment used in gardenfors 18 and gardenfors and makinson 20 as a kind of expectation ordering thus we see belief revision and nonmonotonic reasoning as basically the same process albeit used for two different purposes

a representation theorem for recovering contraction relations satisfying wci a notion of an image structure associated with the canonical epistemic state is introduced based on it we get a representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion wci in terms of f standard epistemic agm states in effect this result establishes a representation theorem for belief contraction functions satisfying agm postulates k 1 k 7 and rott s wci and k 8c and hence generalizes rott s corresponding result in the finite framework

stability of asynchronous two dimensional fornasini marchesini dynamical systems abstract conditions for stability of two dimensional 2d fornasini marchesini fm models with variable shifts are derived using nonnegative matrix theory the conditions are shift independent the stability is proved under a general boundary condition bc

a foundationalist view of the agm theory of belief change abstract we describe an alternative interpretation of the agm postulates for belief change alchourron et al 1985 gardenfors 1988 in a foundational framework of epistemic states suggested by bochman 1997 though foundational contractions constitute a new kind of belief contractions incompatible with agm postulates a broad class of preferential agm contractions is shown to be revision equivalent to foundational contractions and can actually be produced using a modification of the contraction operation on epistemic states it is shown also that revisions of epistemic states determine a natural class of preferential agm revisions and that all the agm postulates for revision can be satisfied by imposing reasonable restrictions on underlying epistemic states as a result the foundational theory of epistemic states is shown to provide a unification of the main approaches to belief change on a foundationalist basis

stability of digital filters implemented with two s complement truncation quantization the stability of digital filters implemented with two s complement truncation quantization is investigated both the direct form and normal form realizations are considered and regions in the parameter plane are obtained where the filters are globally asymptotically stable regions within the stability triangle of a direct form digital filter are also studied where limit cycles of period one and two are possible the results are illustrated with several examples