control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

irreducible representations of nongraded witt type lie algebras abstract from his classification of quadratic conformal algebras corresponding to certain hamiltonian pairs in integrable systems xu gave an explicit construction of seven types of nongraded infinite dimensional simple lie algebra related to a finite set of locally finite derivations on certain commutative associative algebras in this paper we construct a family of irreducible generalized weight modules for the nongraded witt type lie algebras based on finite dimensional irreducible modules of general linear lie algebras our results are nongraded generalizations of rao s work on irreducible representations of the derivation lie algebra of the algebra of laurent polynomials in several variables

2 cocycles on the algebra of differential operators soit c t t 1 l anneau des polynomes de laurent sur un corps complexe c soit a c t t 1 d l algebre des operateurs differentiels sur c t t 1 soit 7b u l algebre des operateurs differentiels 7b u a gl u c sur c t t 1 gl u c tout 2 cocycle sur a est equivalent a un multiple de tout 2 cocycle sur 7b u est equivalent a un multiple de

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

quantum automata and quantum grammars abstract to study quantum computation it might be helpful to generalize structures from language and automata theory to the quantum case to that end we propose quantum versions of finite state and push down automata and regular and context free grammars we find analogs of several classical theorems including pumping lemmas closure properties rational and algebraic generating functions and greibach normal form we also show that there are quantum context free languages that are not context free so qcfl cfl

quantum finite automata we first outline main steps and achievements along bertoni s research path in quantum finite automata theory from the very basic definitions of the models of quantum finite automata throughout the investigation of their computational and descriptional power next we choose to focus on bertoni s studies on quantum finite automata descriptional complexity in particular we expand on a statistical framework for the synthesis of succinct quantum finite automata discussing its adaptation to the case of multiperiodic events and languages we then improve such a framework to obtain even more succinct quantum finite automata for some multiperiodic languages finally we introduce some promise problems for multiperiodic inputs showing that even on this class of problems the descriptional power of quantum finite automata greatly outperforms that of equivalent classical finite automata we build small size monte carlo quantum finite automata for multiperiodic languages we analyze the modular architecture of such monte carlo quantum finite automata we solve promise problems on multiperiodic inputs by small quantum finite automata

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

time varying input and state delay compensation for uncertain nonlinear systems a robust controller is developed for uncertain second order nonlinear systems subject to simultaneous unknown time varying state delays and known sufficiently small time varying input delays in addition to additive sufficiently smooth disturbances an integral term composed of previous control values facilitates a delay free open loop error system and the development of the feedback control structure a stability analysis based on lyapunov krasovskii lk functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying numerical simulations illustrate robustness of the developed method to various combinations of simultaneous input and state delays

robustness and safe sampling of distributed delay control laws for unstable delayed systems in the control of delayed systems by a finite spectrum assignment fsa in the control law the integral over the time delay of a function of past control appears this assignment is in fact available for continuous delayed process independently of the stability of the latter which is very interesting since smith predictor is usually only used with stable processes nevertheless in case of fsa control implementation this integral control should be sampled so that spectrum assignment is not necessarily preserved and an unstable discrete closed loop can be obtained in this technical note fsa integral control robustness with respect to prediction time uncertainty is analyzed for an unstable continuous linear system a transformation approach is also proposed to understand the effects of different ways of sampling control laws in a last part a case study shows how simpson approximation of integral control law leads to an unstable digital closed loop

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

deformations of lie algebras using σ derivations in this article we develop an approach to deformations of the witt and virasoro algebras based on sigma derivations we show that sigma twisted jacobi type identity holds for generators of such deformations for the sigma twisted generalization of lie algebras modeled by this construction we develop a theory of central extensions we show that our approach can be used to construct new deformations of lie algebras and their central extensions which in particular include naturally the q deformations of the witt and virasoro algebras associated to q difference operators providing also corresponding q deformed jacobi identities c 2005 elsevier inc all rights reserved

with central charge n we study representations of the central extension of the lie algebra of differential operators on the circle the algebra we obtain complete and specialized character formulas for a large class of representations which we call primitive these include all quasi finite irreducible unitary representations we show that any primitive representation with central chargen has a canonical structure of an irreducible representation of the with the same central charge and that all irreducible representations of with central chargen arise in this way we also establish a duality between integral modules of and finite dimensional irreducible modules ofgl n and conjecture their fusion rules

brief paper lyapunov tools for predictor feedbacks for delay systems inverse optimality and robustness to delay mismatch we consider lti finite dimensional completely controllable but possibly open loop unstable plants with arbitrarily long actuator delay and the corresponding predictor based feedback for delay compensation we study the problem of inverse optimal re design of the predictor based feedback law we obtain a simple modification of the basic predictor based controller which employs a low pass filter and has been proposed previously by mondie and michiels for achieving robustness to discretization of the integral term in the predictor feedback law the key element in our work is the employment of an infinite dimensional backstepping transformation and the resulting lyapunov function for the infinite dimensional systems consisting of the state of the ode plant and the delay state the lyapunov function allows us to quantify the lyapunov stability properties under the modified feedback the inverse optimality of the feedback and its disturbance attenuation properties for the basic predictor feedback the availability of the lyapunov function also allows us to prove robustness to small delay mismatch in both positive and negative directions

quasifinite highest weight modules over the lie algebra of matrix differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t tm 1 the unitary ones are classified as well similar results are obtained for the sin algebras

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

extremum seeking for static maps with delays in this paper we address the design and analysis of multi variable extremum seeking for static maps subject to arbitrarily long time delays both gradient and newton based methods are considered multi input systems with different time delays in each individual input channel as well as output delays are dealt with the phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation based averaging based estimate of the hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point even in the presence of delays the stability analysis is carried out using backstepping transformation and averaging in infinite dimensions capturing the infinite dimensional state due the time delay in particular a new backstepping like transformation is introduced to design the predictor for the gradient based extremum seeking scheme with multiple and distinct input delays the proposed newton based extremum seeking approach removes the dependence of the convergence rate on the unknown hessian of the nonlinear map to be optimized being user assignable as in the literature free of delays a source seeking example illustrates the performance of the proposed delay compensated extremum seeking schemes

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

representations of the twisted affine nappi witten algebras in this paper we study verma modules for the twisted affine nappi witten algebras h4 1 and h4 2 the vertex operator representations of the affine nappi witten algebras h4 1 h4 2 and h4 are also constructed furthermore the irreducible non zero level quasifinite modules over the affine nappi witten algebras are classified

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

classification of quasifinite representations of a lie algebra related to block type abstract a well known theorem of mathieu s states that a harish chandra module over the virasoro algebra is either a highest weight module a lowest weight module or a module of the intermediate series it is proved in this paper that an analogous result also holds for the lie algebra b related to block type with basis l i c i z i 0 and relations l i l j i 1 j 1 l i j 0 i j 0 3 12 c namely an irreducible quasifinite b module is either a highest weight module a lowest weight module or a module of the intermediate series

an adaptive smith controller for time delay systems with relative degree n 2 abstract this paper addresses the control of time delay systems whose relative degree does not exceed two an adaptive smith controller together with an adaptive law similar to the delay free case is proposed by using lyapunov krasovskii functionals for an appropriate model transformation of the original system semiglobal stability of the closed loop system and asymptotic convergence of the output error is established strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties robustness properties of the adaptive controller are briefly discussed

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

classification of quasifinite modules over the lie algebras of weyl type abstract for a nondegenerate additive subgroup of the n dimensional vector space f n over an algebraically closed field f of characteristic zero there is an associative algebra and a lie algebra of weyl type w n spanned by all differential operators ud1m1 dnmn for u f the group algebra and m1 mn 0 where d1 dn are degree operators in this paper it is proved that an irreducible quasifinite w z 1 module is either a highest or lowest weight module or else a module of the intermediate series furthermore a classification of uniformly bounded w z 1 modules is completely given it is also proved that an irreducible quasifinite w n module is a module of the intermediate series and a complete classification of quasifinite w n modules is also given if is not isomorphic to z

zeta values and differential operators on the circle abstract the fock representation of the virasoro lie algebra is extended to a larger graded lie subalgebra of the algebra of differential operators on the circle the central cocycle is related to values of the riemann zeta function at odd negative integers the corresponding generating function is related to eisenstein series for sl 2 z an analogous result is obtained for values of l series associated to even dirichlet characters using differential operators of infinite order

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

improved constructions of quantum automata we present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata our automata use email protected states to recognize a language that requires p states classically the construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction our construction is by a probabilistic argument we consider the possibility to derandomize it and present some results in this direction

classification of harish chandra modules over some lie algebras related to the virasoro algebra abstract in this paper we provide a uniform method to thoroughly classify all harish chandra modules over some lie algebras related to the virasoro algebras we first classify such modules over the lie algebra w s for s 0 1 2 with this result and method we can also do such works for some lie algebras related to the virasoro algebra including the several kinds of schrodinger virasoro lie algebras which are open up to now

character and determinant formulae of quasifinite representation of thew1 algebra we diagonalize the hilbert space of some subclass of the quasifinite module of thew1 algebra states are classified according to their eigenvalues for infinitely many commuting charges and the young diagrams the parameter dependence of their norms is explicitly derived the full character formulae of the degenerate representations are given as summation of the bilinear combinations of the schur polynomials

dense quantum coding and quantum finite automata we consider the possibility of encoding m classical bits into many fewer n quantum bits qubits so that an arbitrary bit from the original m bits can be recovered with good probability we show that nontrivial quantum codes exist that have no classical counterparts on the other hand we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding the proof is based on an entropy coalescence principle that is obtained by viewing holevo s theorem from a new perspective in the existing implementations of quantum computing qubits are a very expensive resource moreover it is difficult to reinitialize existing bits during the computation in particular reinitialization is impossible in nmr quantum computing which is perhaps the most advanced implementation of quantum computing at the moment this motivates the study of quantum computation with restricted memory and no reinitialization that is of quantum finite automata it was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata here we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata

on distributed delay in linear control laws part i discrete delay implementations this note proposes two approaches to approximate distributed delay in linear control laws and furthermore to implement it in the z domain and in the s domain the h sup spl infin norm of the approximation error converges to 0 when the number n of approximation steps approaches spl infin hence the instability problem due to the approximation error which has been widely studied in recent years does not exist provided that n is large enough moreover the static gain is guaranteed so that no extra efforts are needed to retain the steady state performance as by products two new formulas for the forward and backward rectangular rules are obtained these formulas are more accurate than the conventional ones when the integrand has an exponential term

quasifinite representations of a lie algebra of block type abstract let b be the lie algebra of block type over c with basis l i c i z i 1 and relations l i l j i 1 j 1 l i j 0 i j 2c c l i 0 in this paper it is proved that a quasifinite irreducible b module is a highest or lowest weight module furthermore the quasifinite irreducible highest weight modules are classified and the unitary ones are proved to be trivial

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

stabilization of nonlinear delay systems using approximate predictors and high gain observers we provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only the solution is global employs the predictor approach over the period that combines the input and output delays addresses nonlinear systems with sampled measurements and with control applied using a zero order hold and requires that the sampling holding periods be sufficiently short though not necessarily constant our approach considers a class of globally lipschitz strict feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map a high gain sampled data observer and a linear stabilizing feedback for the delay free system the obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered the approach is specialized to linear systems where the predictor is available explicitly

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

quasifinite representations of classical lie subalgebras of w1 we show that there are precisely two up to conjugation anti involutions of the algebra of differential operators on the circle preserving the principal gradation we classify the irreducible quasifinite highest weight representations of the central extension d of the lie subalgebra of this algebra fixed by and find the unitary ones we realize them in terms of highest weight representations of the central extension of the lie algebra of infinite matrices with finitely many non zero diagonals over the algebra c u um 1 and its classical lie subalgebras ofb canddtypes character formulas forpositive primitiverepresentations of d including all the unitary ones are obtained we also realize a class of primitive representations of d in terms of free fields and establish a number of duality results between these primitive representations and finite dimensional irreducible representations of finite dimensional lie groups and supergroups we show that the vacuum modulevcof d carries a vertex algebra structure and establish a relationship betweenvcforc 12z and w algebras

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given

state succinctness of two way finite automata with quantum and classical states two way finite automata with quantum and classical states 2qcfa were introduced by ambainis and watrous in 2002 in this paper we study state succinctness of 2qcfa for any email protected z and any e 1 2 we show that 1 there is a promise problem a e q m which can be solved by a 2qcfa with one sided error e in a polynomial expected running time with a constant number that depends neither on m nor on e of quantum states and o email protected classical states whereas the sizes of the corresponding deterministic finite automata dfa two way nondeterministic finite automata 2nfa and polynomial expected running time two way probabilistic finite automata 2pfa are at least 2m 2 logm and logm b3 respectively 2 there exists a language l t w i n m wcw email protected a b w m over the alphabet s a b c which can be recognized by a 2qcfa with one sided error e in an exponential expected running time with a constant number of quantum states and o email protected classical states whereas the sizes of the corresponding dfa 2nfa and polynomial expected running time 2pfa are at least 2 m m and m b3 respectively where b is a constant

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy

classification of harish chandra modules over the higher rank virasoro algebras we classify the harish chandra modules over the higher rank virasoro and super virasoro algebras it is proved that a harish chandra module i e an irreducible weight module with finite weight multiplicities over a higher rank virasoro or super virasoro algebra is either a module of the intermediate series or a finitely dense module as an application it is also proved that an indecomposable weight module with finite weight multiplicities over a generalized witt algebra is either a uniformly bounded module i e a module with weight multiplicities uniformly bounded with all nonzero weights having the same multiplicity or a finitely dense module as long as the generalized witt algebra satisfies one minor condition

representations of the schrodinger virasoro algebras in this paper it is proved that an irreducible weight module with finite dimensional weight spaces over the schrodinger virasoro algebras is a highest lowest weight module or a uniformly bounded module furthermore indecomposable modules of the intermediate series over these algebras are completely determined