modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

stable trace formula cuspidal tempered terms consider a connected reductive group g over a number field f for technical reasons we assume that the derived group of g is simply connected see l1 in l3 langlands partially stabilizes the trace formula for g after making certain assumptions he writes the elliptic regular part of the trace formula for g as a linear combination of the elliptic g regular parts of the stable trace formulas for the elliptic endoscopic groups h of g the function f used in the stable trace formula forh is obtained from the function f used in the trace formula for g by transferring orbital integrals

depth zero supercuspidal l packets for inner forms of gsp4 abstract we show that for any tame regular discrete series parameter of g s p 4 or its inner form g u 2 d the l packet attached by the local langlands conjecture gan and takeda 2011 14 gan and tantono submitted for publication 15 agrees with the l packet of depth zero supercuspidal representations constructed by debacker and reeder 2009 12

event triggered fuzzy h control for a class of nonlinear networked control systems using the deviation bounds of asynchronous normalized membership functions this paper is concerned with the event triggered h control for a nonlinear networked control system a new event triggered transmission scheme is first proposed to reduce the network bandwidth utilization under this scheme the nonlinear networked control system is formulated as a takagi sugeno fuzzy threshold error dependent system with asynchronous normalized membership functions then by using the deviation bounds of asynchronous normalized membership functions some sufficient conditions on the existence of the parameters of the event triggered transmission scheme and the fuzzy controller are derived such that the takagi sugeno fuzzy threshold error dependent system with asynchronous normalized membership functions is asymptotically stable with a prescribed h attenuation level it is shown that the proposed design method can reduce the conservativeness of some existing results finally two examples are given to demonstrate the effectiveness of the proposed design method and the event triggered transmission scheme

hecke algebras of classical groups over p adic fields and supercuspidal representations let k be a p adic field with involution 0 and let k 0 be its fixed subfield of k let v be a finite dimensional vector space defined over k equipped with e hermitian form v k 0 is large

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

event based robust h filtering for affine fuzzy systems abstract this paper investigates the event based robust h filter design problem for a class of nonlinear systems described by affine fuzzy models different from the existing results an event triggered scheme is introduced to reduce the burden of the communication by judging whether the data transmitted condition is satisfied or not under this scheme the premise variables of fuzzy model and filter to be designed are unsynchronized which will lead to the plant and the filter cannot always evolve in the same region at the same time to solve this problem a novel fuzzy basis dependent nonsynchronized h filter is proposed by using the piecewise quadratic lyapunov functions and the s procedure technique finally a numerical example illustrates the effectiveness of the proposed method

fuzzy adaptive output feedback fault tolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults this paper studies the fuzzy adaptive output feedback fault tolerant control ftc problem for a class of single input and single output uncertain nonlinear systems with time varying nonaffine nonlinear faults in strict feedback form in the design procedure filtered signals are adopted to circumvent algebraic loop problems on implementing the usual controllers by using fuzzy logic systems to approximate the unknown nonlinearity effects and changes in model dynamics due to faults a fuzzy state observer is first presented to estimate the unmeasured states based on the online estimating information from the adaptive mechanism an observer based dynamic output feedback fault tolerant controller is designed via the backstepping technique it is shown that the stability and tracking performances of the closed loop system can be achieved even in the presence of unknown nonlinear faults in comparison with the existing approaches the ftc scheme can handle the nonaffine nonlinear faults effectively finally a simulation example is included to validate the advantages of the proposed approaches

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

depth zero supercuspidal l packets and their stability in this paper we verify the local langlands correspondence for pure inner forms of unramied p adic groups and tame langlands parameters in general position for each such parameter we explicitly construct in a natural way a nite set l packet of depth zero supercuspidal representations of the appropriate p adic group and we verify some expected properties of this l packet in particular we prove with some conditions on the base eld that the appropriate sum of characters of the representations in our l packet is stable no proper subset of our l packets can form a stable combination our l packets are also consistent with the conjectures of b gross and d prasad on restriction from so2n 1 to so2n 24 these l packets are in general quite large for example sp2n has an l packet containing 2 n representations of which exactly two are generic in fact on a quasi split form eachl packet contains exactly one generic representation for every rational orbit of hyperspecial vertices in the reduced bruhattits building when the group has connected center every depth zero generic supercuspidal representation appears in one of these l packets we emphasize that there is nothing new about the representations we construct they are induced from deligne lusztig representations on subgroups of nite

distinguished regular supercuspidal representations based on recent work of kaletha we apply hakim murnaghan s result to study distinguished regular supercuspidal representations of tamely ramified reductive p adic groups assuming p is sufficiently large we obtain a necessary and sufficient condition for regular supercuspidal representations to be distinguished we also investigate the relation between the distinction problem and the langlands functoriality and confirm a conjecture of lapid for regular depth zero or epipelagic supercuspidal representations

finite order automorphisms and a parametrization of nilpotent orbits in p adic lie algebras let k be a field with a nontrivial discrete valuation which is complete and has perfect residue field let g be the group of k rational points of a reductive linear algebraic group bf g equipped with a finite cyclic group l of order m acting on bf g by algebraic automorphisms defined over k we assume that the lie algebra of g decomposes into a direct sum of eigenspaces under the action of l with generator theta we let frak g i denote the eigenspace corresponding to eigenvalue xi i where xi is a primitive m th root of unity that is x in frak g i if and only if theta x xi ix if bf h is a k subgroup of bf g l the group of l fixed points which contains the neutral component of bf g l then h bf h k acts on each eigenspace of frak g let r in bbb r under mild restrictions on the residual characteristic of k the set of nilpotent h orbits in the xi eigenspace frak g 1 is parametrized by equivalence classes of noticed moy prasad cosets of depth r which lie in frak g 1

supercuspidal l packets of positive depth and twisted coxeter elements the local langlands correspondence is a conjectural connection between representations of groups g k for connected reductive groups g over a padic field k and certain homomorphisms langlands parameters from the galois or weil deligne group of k into a complex lie group g which is dual in a certain sense to g and which encodes the splitting structure of g over k more introductory remarks on the local langlands correspondence can be found in 21 wheng gl1 this correspondence should reduce to local abelian class field theory for g gln the langlands correspondence is uniquely determined by local factors 24 and was shown to exist in 23 and 25 so far this correspondence is not completely explicit but much progress has been made in this direction see 9 10 for example for groups other than gln or pgln the theory is much less advanced new phenomena appear arising on the arithmetic side from the difference between conjugacy and stable conjugacy and on the dual side from nontrivial monodromy of langlands parameters this means that a single langlands parameter should determine not just one but a finite set of representations these are the l packets of the title however since local factors have not been defined in general there is no precise characterization of an l packet for general groups one can at present only hope to define finite sets of representations attached to langlands parameters and show that they have properties expected or perhaps unexpected of l packets see 14 chap 3 for some of these properties one is thereby proposing a definition of local factors for the representations in the sets cf 4 chap 3 this paper is a sequel to 14 the aim of both papers is to verify in an explicit and natural way the local langlands correspondence for the simplest kinds of non abelian extensions of k and the simplest kinds of

construction of tame supercuspidal representations the notion of depth is defined by moy prasad mp2 the notion of a generic character will be defined in 9 when g gln or g is the multiplicative group of a central division algebra of dimension n with n p 1 our generic characters are just the generic characters in my where the definition is due to kutzko moreover in these cases our construction literally specializes to howe s construction as formulated in my and it is known that the construction yields all supercuspidal representations my hm notice that the initial datum in our construction consists of very simple objects linear characters and supercuspidal representations of depth zero the latter are well understood by the work of moy prasad and morris see 3 by the work of howe irreducible supercuspidal representations of gln f with n p 1 are parametrized by certain characters of e as e varies through

character expansions and unrefined minimal k types let k be a p adic field let g be the group of k rational points of a connected reductive group g defined over k and let inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i be its lie algebra under certain hypotheses on g and k we get a new character expansion called a asymptotic expansion for representations of positive depth inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i this character expansion is valid on the g domain inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i which is bigger than that where the harish chandra howe character expansion is known to be valid

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

rigid inner forms of real and p adic groups we dene a new cohomology set h 1 u w z g for an ane algebraic group g and a nite central subgroup both dened over a local eld of characteristic zero which is an enlargement of the usual rst galois cohomology set of g we show how this set can be used to give a precise conjectural description of the internal structure and endoscopic transfer of tempered l packets for arbitrary connected reductive groups that extends the well known conjectural description for quasi split groups in the case of real groups we show that this description is correct using shelstad s work

simple modifications for signed roots of likelihood ratio statistics summary in the context of inference about a scalar parameter in the presence of nuisance parameters some simple modifications for the signed root of the log likelihood ratio statistic r are developed that reduce the order of error in the standard normal approximation to the distribution of r from o n 1 2 to o n 1 barndorff nielsen has introduced a variable u such that the error in the standard normal approximation to the distribution of r r r log u r is of order o n 3 2 but calculation of urequires the specification of an exact or approximate ancillary statistic a this paper proposes an alternative variable to u denoted by t that is available without knowledge of a and satisfies t u op n 1 in general thus the standard normal approximation to the distribution of r r log t r has error of order o n 1 and it can be used to construct approximate confidence limits having coverage error of order o n 1 in certain cases however tand uare identical the derivation of tinvolves the bayesian approach to constructing confidence limits considered by welch and peers and peers similar modifications for the signed root of the conditional likelihood ratio statistic are also developed and these modifications are seen to be useful when a large number of nuisance parameters are present several examples are presented including inference for natural parameters in exponential models and inference about location scale models with type ii censoring in each case the relationship between tand u is discussed numerical examples are also given including inference for regression models inference about the means of log normal distributions and inference for exponential lifetime models with type i censoring where barndorff nielsen s variable u is not available

is the improved likelihood ratio statistic really improved in the discrete case summary on the basis of some numerical studies we argue that bartlett adjustment of the likelihood ratio statistic for discrete data does not in general yield an improvement in the asymptotic error rate of the chi squared approximation also we argue that the small sample effect of the bartlett adjustment is unclear and that it is in no way comparable with the improvement obtained for continuous data

theta lifts and distinction for regular supercuspidal representations this article has a twofold purpose first by recent works of kaletha and loke ma we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic orthogonal case second based on this description we show that the local theta correspondence preserves distinction with respect to unramified galois involutions

supercuspidal characters of reductive p adic groups we compute the characters of many supercuspidal representations of reductive p adic groups specifically we deal with representations that arise via yu s construction from data satisfying a certain compactness condition each character is expressed in terms of a depth zero character of a smaller group the linear characters appearing in yu s construction fourier transforms of orbital integrals and certain signs and cardinalities that are described explicitly in terms of the datum associated to the representation and of the element at which the character is evaluated

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

supercuspidal l packets via isocrystals in a recent paper debacker and reeder construct and parameterize l packets on pure inner forms of unramified p adic groups that consist of depth zero supercuspidal representations we generalize their work to non pure inner forms by providing an alternative construction based on the theory of isocrystals with additional structure due to kottwitz furthermore we show the stability and endoscopic transfer for these l packets

endoscopic character identities for depth zero supercuspidal l packets one of the conjectural properties of a langlands correspondence is its compatibility with endoscopic induction debacker and reeder have recently constructed a partial local langlands correspondence for p adic groups focusing on l packets consisting of depth zero supercuspidal representations in this paper we prove the conjectural endoscopic transfer for these l packets

asymptotic behavior of supercuspidal representations and sato tate equidistribution for families abstract we establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes for the tame supercuspidals constructed by j k yu we prove the limit multiplicity property with error terms thereby we obtain a sato tate equidistribution for the hecke eigenvalues of these families the main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p adic group tend to zero uniformly for every noncentral semisimple element

the supercuspidal representations of p adic classical groups let g be a unitary symplectic or special orthogonal group over a locally compact non archimedean local field of odd residual characteristic we construct many new supercuspidal representations of g and bushnell kutzko types for these representations moreover we prove that every irreducible supercuspidal representation of g arises from our constructions

epipelagic l packets and rectifying characters we provide an explicit construction of the local langlands correspondence for general tamely ramified reductive p adic groups and a class of wildly ramified langlands parameters furthermore we verify that our construction satisfies many expected properties of such a correspondence more precisely we show that each l packet we construct admits a parameterization in terms of the langlands dual group contains a unique generic element for a fixed whittaker datum satisfies the formal degree conjecture is compatible with central and cocentral characters provides a stable virtual character and satisfies the expected endoscopic character identities moreover we show that in the case of mathrm gl n our construction coincides with the established local langlands correspondence our techniques provide a general approach to the construction of the local langlands correspondence for tamely ramified groups and regular supercuspidal parameters

event based h filtering for sampled data systems this paper is concerned with event based h filtering for sampled data systems first an event based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated as a result communication resources can be saved significantly while preserving the desired h performance second the resulting filtering error system is modeled as a system with an interval time varying delay by employing the lyapunov krasovskii functional approach a new bounded real lemma brl is established such that the filtering error system is asymptotically stable with the prescribed h performance third by performing an invertible linear transformation on the filtering error system a linear matrix inequality lmi based sufficient condition which is equivalent to the condition in the brl is obtained on the feasibility of the event based h filtering problem consequently suitable h filters and the event parameters in the event condition can be co designed provided that a set of lmis are satisfied finally a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method

epipelagic representations and invariant theory letg be a reductive p adic group we give a new construction of small depth epipelagic supercuspidal representations ofg k using stable orbits in geometric invariant theory git in contrast to previously known methods this construction works without any restrictions on the residue characteristic p we construct appropriate langlands parameters for these representations with some restrictions on p the git arises from graded moy prasad filtrations which we show are isomorphic to the graded lie algebras whose git was analyzed by vinberg and levy this leads to a classification of stable orbits in moy prasad filtrations as well as epipelagic supercuspidal representations in terms of z regular elliptic automorphisms of the absolute root system of g transferred to the l group of g generates the image of tame inertia under the corresponding wild langlands parameter for unramified groups and sufficiently large p we also classify the moy prasad filtrations which have semi stable orbits which solves the long outstanding problem of classifying non degenerate k types for g k

semisimple characters for p adic classical groups let g be a unitary symplectic or orthogonal group over a non archimedean local field of residual characteristic different from 2 considered as the fixed point subgroup in a general linear group of an involution following previous work of bushnell and kutzko and of the author we generalize the notion of a semisimple character for and for g in particular following the formalism of bushnell and henniart we show that these semisimple characters have certain functorial properties finally we show that any positive level supercuspidal representation of g contains a semisimple character

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed methods

a construction of the supercuspidal representations of _ adic let f be a nondiscrete locally compact non archimedean field in this paper we construct all irreducible supercuspidal representations of g gl n f for each such representation which we may as well assume is unitary we give a subgroup j of g that is compact mod the center z of g and a finite dimensional representation of j such that inducing to g gives the proof that all supercuspidals have been constructed appeals to a theorem the matching theorem that has been proved by global methods

branching rules for supercuspidal representations of sl2 k for k a p adic field abstract the restriction of a supercuspidal representation of sl 2 k to a maximal compact subgroup decomposes as a multiplicity free direct sum of irreducible representations we explicitly describe this decomposition and determine how the spectrum of this decomposition varies as a function of the parameters describing the supercuspidal representation

on depth zero l packets for classical groups by computing reducibility points of parabolically induced representations we construct to within at most two unramified quadratic characters the langlands parameter of an arbitrary depth zero irreducible cuspidal representation formula presented of a classical group which may be not quasi split over a non archimedean local field of odd residual characteristic from this we can explicitly describe all the irreducible cuspidal representations in the union of one two or four formula presented packets containing formula presented these results generalize the work of debacker reeder in the case of classical groups from regular to arbitrary tame langlands parameters

the local character expansion near a tame semisimple element consider the character of an irreducible admissible representation of a p adic reductive group the harish chandra howe local expansion expresses this character near a semisimple element as a linear combination of fourier transforms of nilpotent orbital integrals under mild hypotheses we describe an explicit region on which the local character expansion is valid we assume neither that the group is connected nor that the underlying field has characteristic zero

standardized log likelihood ratio statistics for mixtures of discrete and continuous observations on considere des cas ou la statistique exhaustive minimale est partiellement discrete et partiellement continue en particulier on considere des problemes de test associes avec des durees de vie exponentielles censurees

arithmetic invariants of discrete langlands parameters the local langlands correspondence can be used as a tool for making verifiable predictions about irreducible complex representations of p adic groups and their langlands parameters which are homomorphisms from the local weil deligne group to the l group in this article we refine a conjecture of hiraga ichino and ikeda which relates the formal degree of a discrete series representation to the value of the local gamma factor of its parameter we attach a rational function in x with rational coefficients to each discrete parameter which specializes at x q the cardinality of the residue field to the quotient of this local gamma factor by the gamma factor of the steinberg parameter the order of this rational function at x 0 is also an important invariant of the parameter it leads to a conjectural inequality for the swan conductor of a discrete parameter acting on the adjoint representation of the l group we verify this conjecture in many cases when we impose equality we obtain a prediction for the existence of simple wild parameters and simple supercuspidal representations both of which are found and described in this article

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

switching type h filter design for t s fuzzy systems with unknown or partially unknown membership functions this paper is concerned with the h filter design problem for takagi sugeno t s fuzzy systems with unknown or partially unknown membership functions if the membership functions are allowed to be unknown or partially unknown then a fuzzy system may describe a wide class of nonlinear systems however in this case the filter design of fuzzy systems which is based on parallel distributed compensator strategy is infeasible to tackle this difficulty a switching mechanism which depends on the lower and upper bounds of the unknown membership functions is introduced to construct the h filter with varying gains some examples given in the simulation section show that the proposed method can achieve a better disturbance attenuation performance than a simple fixed gain filter design approach

validity of the formal edgeworth expansion when the underlying distribution is partly discrete validity of the formal edgeworth expansion for the distribution of the statistic ng x n n y n n is considered here x n is a continuous variate and y n is a discrete variate in general if x n y n resemble the sum of i i d variables and the partial derivative of g with respect to the first variable has full rank it is possible to establish an edgeworth expansion

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods

unrefined minimal k types for p adic groups via their restriction to compact open subgroups was begun by mautner shalika and tanaka for groups of type ai in contrast to real reductive groups where the representation theory of a maximal compact subgroup k is given in terms of slight modifications to cartan s theory of the highest weight the representation theory of a compact parahoric subgroup is quite complicated there is still no comprehensive theory for classifying the irreducible representa tions in the case of