about the notion of truth in quantum mechanics the meaning of truth in quantum mechanics is considered in order to respond to some objections raised by b d espagnat against a logical interpretation of quantum mechanics recently proposed by the author a complete answer is given it is shown that not only can factual data be said to be true but also some of their logical consequences so that the definition of truth given by heisenberg is both extended and refined some nontrue but reliable propositions may also be used but they are somewhat arbitrary because of the complementarity principle for instance the propositions expressing wave packet reduction can be either true or reliable according to the case under study separability is also discussed as far as the true properties of an individual system are concerned quantum mechanics is separable

poincare invariance for continuous time histories we show that the relativistic analog of the two types of time translation in a nonrelativistic history theory is the existence of two distinct poincare groups the internal poincare group is analogous to the one that arises in the standard canonical quantization scheme the external poincare group is similar to the group that arises in a lagrangian description of the standard theory in particular it performs explicit changes of the space time foliation that is implicitly assumed in standard canonical field theory

robust h control for uncertain discrete stochastic time delay systems this paper deals with the problems of robust stabilization and robust h control for discrete stochastic systems with time varying delays and time varying norm bounded parameter uncertainties for the robust stabilization problem attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed loop system for all admissible uncertainties while for the robust h control problem a state feedback controller is designed such that in addition to the requirement of the robust stochastic stability a prescribed h performance level is also required to be satisfied a linear matrix inequality lmi approach is developed to solve these problems and delay dependent conditions for the solvability are obtained it is shown that the desired state feedback controller can be constructed by solving certain lmis an example is provided to demonstrate the effectiveness of the proposed approach

are there realistically interpretable local theories although it rests on strongly established proofs the statement that no realistically interpretable local theory is compatible with some experimentally testable predictions of quantum mechanics seems at first sight to be incompatible with a few general ideas and clear cut statements occurring in recent theoretical work by griffiths omnes and ballentine and jarrett it is shown here that in fact none of the developments due to these authors can be considered as a realistically interpretable local theory so that there is no valid reason for suspecting that the existing proofs of the statement in question are all flawed

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

robust passivity and passification of stochastic fuzzy time delay systems in this paper the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time varying delays the fuzzy system is based on the takagi sugeno t s model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system both the parameter uncertainties and the stochastic disturbances are considered where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a brownian motion we first propose the definition of robust passivity in the sense of expectation then by utilizing the lyapunov functional method the ito differential rule and the matrix analysis techniques we establish several sufficient criteria such that for all admissible parameter uncertainties and stochastic disturbances the closed loop stochastic fuzzy time delay system is robustly passive in the sense of expectation the derived criteria which are either delay independent or delay dependent are expressed in terms of linear matrix inequalities lmis that can be easily checked by using the standard numerical software illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

razumikhin method and exponential stability of hybrid stochastic delay interval systems this paper deals with the exponential stability of hybrid stochastic delay interval systems also known as stochastic delay interval systems with markovian switching the known results in this area see e g x mao exponential stability of stochastic delay interval systems with markovian switching ieee trans automat control 47 10 2002 1604 1612 require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics the main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only the razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay

non regular feedback linearization of nonlinear systems via a normal form algorithm in this paper the problem of non regular static state feedback linearization of affine nonlinear systems is considered first of all a new canonical form for non regular feedback linear systems is proposed using this form a recursive algorithm is presented which yields a condition for single input linearization then the left semi tensor product of matrices is introduced and several new properties are developed using the recursive framework and new matrix product a formula is presented for normal form algorithm based on it a set of conditions for single input approximate linearizability is presented

stability of interval matrices the real eigenvalue case c v hollot and a c bartlett 1987 showed that testing at most 2 to the n sup 2 certain matrices for stability is sufficient for verifying stability of an n n interval matrix with real eigenvalues it is proven that this upper bound can be reduced to 2 sup 2n 1 and a special case where testing only two matrices is needed is considered

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

contraction based stabilisation of nonlinear singularly perturbed systems and application to high gain feedback abstractrecent development of contraction theory based analysis has opened the door for inspecting differential behaviour of singularly perturbed systems in this paper a contraction theory based framework is proposed for stabilisation of singularly perturbed systems the primary objective is to design a feedback controller to achieve bounded tracking error for both standard and non standard singularly perturbed systems this framework provides relaxation over traditional quadratic lyapunov based method as there is no need to satisfy interconnection conditions during controller design algorithm moreover the stability bound does not depend on smallness of singularly perturbed parameter and robust to additive bounded uncertainties combined with high gain scaling the proposed technique is shown to assure contraction of approximate feedback linearisable systems these findings extend the class of nonlinear systems which can be made contracting

finite time dissipative control for stochastic interval systems with time delay and markovian switching the finite time stochastically boundedness ftsb and the finite time strictly stochastically exponential dissipative ftssed control problems for the stochastic interval systems which are encountered the time delay and markovian switching are investigated in this paper the stochastic delayed interval systems with markovian switching sdisswms are equivalently transformed into a kind of stochastic uncertain time delay systems with markovian switching by interval matrix transformation some sufficient conditions of ftsb and ftssed for the stochastic delayed interval systems with markovian switching are obtained and the ftsb and ftssed controllers are designed by solving a series of linear matrix inequalities which are solvable by lmis toolbox finally a numerical example with simulations is given to illustrate the correctness of the obtained results and the effectiveness of the designed controller

approximate state feedback linearization using spline functions abstract this paper presents two numerical methods for synthesizing an approximate feedback linearizing control for single input nonlinear systems both techniques use part of the pseudo linearizing coordinate transformation as an output function t1 the first synthesis uses a well known recursive algorithm to compute the control given t1 splines represent functions that cannot be computed in closed form the second method yields a simplified controller that can be computed regardless of the plant s complexity experimental results from a rotating inverted pendulum show an improved performance of the approximate feedback linearization compared with pseudo linearization while highlighting the practical numerical difficulties that arise in the first method simulations of an acrobot illustrate the second method which is also improved over pseudo linearization

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

stabilization of approximately feedback linearizable systems using singular perturbation we consider a stabilization problem of approximately feedback linearizable systems we introduce a perturbation parameter by applying high gain feedback and use both the feedback linearization method and the singular perturbation method for the controller design through this we can overcome the rigorous conditions of the feedback linearization method and can reduce the dimension of the slow model of the singularly perturbed system

stability results for stochastic delayed recurrent neural networks with discrete and distributed delays we present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays our approach is based on the method using fixed point theory which do not resort to any liapunov function or liapunov functional our results neither require the boundedness monotonicity and differentiability of the activation functions nor differentiability of the time varying delays in particular a class of neural networks without stochastic perturbations is also considered examples are given to illustrate our main results

on delay dependent stability for a class of nonlinear stochastic systems with multiple state delays abstract global asymptotic stability conditions for nonlinear stochastic systems with multiple state delays are obtained based on the convergence theorem for semimartingale inequalities without assuming the lipschitz conditions for nonlinear drift functions the lyapunov krasovskii and degenerate functionals techniques are used the derived stability conditions are directly expressed in terms of the system coefficients nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given

nonlinear repetitive control repetitive controllers are generally applied to reject periodic disturbances and to track periodic reference signals with a known period their design is based on the internal model principle proposed by francis and wonham 1975 this paper describes a new finite dimensional siso repetitive controller for two different classes of nonlinear plants simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the nth harmonic frequency a proof of robustness of the repetitive control system to small nonlinearities like actuator nonlinearities is provided

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

approximate linearization of nonlinear control systems abstract the paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback the main result proved is that if the fast k d relative degrees are equal to each other then the input output response of a nonlinear control system can be linearized to degree k any system having linear d relative degree can be linearized to any degree by dynamic feedbacks one example of signal tracking using dynamic feedback linearization method to improve the performance is also given

robust stochastic stabilization and h control of uncertain neutral stochastic time delay systems this paper investigates the problems of robust stochastic stabilization and robust h control for uncertain neutral stochastic time delay systems with time varying norm bounded parameter uncertainties appearing in both the state and input matrices the time delay is assumed to be unknown sufficient conditions for the existence of state feedback controllers are proposed which ensure mean square asymptotic stability of the resulting closed loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties a linear matrix inequality approach is employed to design the desired state feedback controllers furthermore in the case when time delays appear in both the state and control input results on the robust stochastic stabilization and robust h control are also presented an illustrative example is provided to show the potential of the proposed techniques

stabilization of feedback linearizable systems using a radial basis function network the main obstacle in the practical use of the feedback linearization is the difficulty in obtaining a linearizing feedback and a coordinate transformation map finding a desired transformation map and feedback turns out to be finding an integrating factor for an annihilating one form in this work we develop numerical algorithms for an integrating factor and the corresponding zero form employing a radial basis function rbf neural network as an interpolation method for the data resulted from the numerical algorithms the authors obtained an approximate integrating factor and zero form in closed forms finally they construct a stabilizing controller based on a linearized system with the use of the approximate integrating factor and zero form

some numerical aspects of approximate linearization of single input non linear systems we characterize approximate linearization to order m of a single input non linear system in terms of the existence of an integrating factor to order m 2 which is equivalent to the well known condition that a system of vector fields be order m 1 involutive we present a constructive method to obtain the required transformation for approximate linearization which results in substantial computational savings

logical reformulation of quantum mechanics i foundations the basic rules of quantum mechanics are reformulated they deal primarily with individual systems and do not assume that every ket may represent a physical state the customary kinematic and dynamic rules then allow to construct consistent boolean logics describing the history of a system following essentially griffiths proposal logical implication is defined within these logics the multiplicity of which reflects the complementary principle only one interpretative rule of quantum mechanics is necessary in such a framework it states that these logics providebona fide foundations for the description of a quantum system and for reasoning about it one attempts to build up classical physics including classical logic on these quantum foundations the resulting theory of measurement needs not to statea priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction both these properties can be obtained as consequences of the basic rules one also needs not to postulate that every observable is measurable even in principle a proposition calculus is obtained allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations

complex probabilities on r n as real probabilities on c n and an application to path integrals we establish a necessary and sufficient condition for averages over complex valued weight functions on r n to be represented as statistical averages over real non negative probability weights on c n using this result we show that many path integrals for time ordered expectation values of bosonic degrees of freedom in real valued time can be expressed as statistical averages over ensembles of paths with complex valued coordinates and then speculate on possible consequences of this result for the relation between quantum and classical mechanics

synchronization control of stochastic delayed neural networks abstract in this paper synchronization control of stochastic neural networks with time varying delays has been considered a novel control method is given using the lyapunov functional method and linear matrix inequality lmi approach several sufficient conditions have been derived to ensure the global asymptotical stability in mean square for the error system and thus the drive system synchronize with the response system also the estimation gains can be obtained with these new and effective methods synchronization can be achieved simulation results are given to verify the theoretical analysis in this paper

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

necessary and sufficient conditions for the hurwitz and schur stability of interval matrices establishes a set of new sufficient conditions for the hurwitz and schur stability of interval matrices the authors use these results to establish necessary and sufficient conditions for the hurwitz and schur stability of interval matrices the authors relate the above results to the existence of quadratic lyapunov functions for linear time invariant systems with interval valued coefficient matrices using the above results the authors develop an algorithm to determine the hurwitz and the schur stability properties of interval matrices the authors demonstrate the applicability of their results by means of two specific examples

exponential stability of stochastic delay interval systems abstract although deterministic interval systems have received a great deal of attention so far there is no work on stochastic interval systems the main aim of this paper is to initiate the study of stochastic interval systems of course there are many properties of such systems to be investigated but this paper will concentrate on the study of exponential stability of stochastic interval systems with time varying delays the main technique used in this paper is the razumikhin type theorem established recently by mao stochastic process appl 65 1996 233 250

robust stability of two time scale systems with nonlinear uncertainties this note is concerned with the robust stability problem of uncertain two time scale systems where the only information available for system uncertainties is their norm upper bounds the stability bound spl epsiv sup is derived via a state transformation and the constructive use of a lyapunov function finally examples are given to illustrate the applications of the proposed results

on delay dependent stability for vector nonlinear stochastic delay difference equations with volterra diffusion term global asymptotic stability conditions for discrete vector nonlinear stochastic systems with state delay and volterra diffusion term are obtained based on the convergence theorem for semimartingale inequalities without assuming the lipschitz conditions for nonlinear drift functions the derived stability conditions are directly expressed in terms of the system coefficients a number of nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given the obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems

input output linearization of nonlinear systems using multivariable legendre polynomials this contribution presents a new approach for the numeric computation of the input output linearizing feedback law which is obtained exactly in an analytical form by using a state space embedding technique the nonlinear system to be controlled is described by a higher order system with solely polynomial nonlinearities consequently the nonlinearities of this system can be represented by multivariable legendre polynomials so that the derivation of the input output linearizing feedback controller can be accomplished using the operational matrices of multiplication and of differentiation for legendre polynomials

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction