stability and controller design of switched systems with sequence based average dwell time this paper investigates the stability of both linear and nonlinear switched systems with sequence based average preceding dwell time sbapdt and sequence based average subsequent dwell time sbasd

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

transient dynamics of on line learning in two layered neural networks the dynamics of on line learning in neural networks with continuous units is dominated by plateaux in the time dependence of the generalization error using tools from statistical mechanics we show for a soft committee machine the existence of several fixed points of the dynamics of learning that give rise to complicated behaviour such as cascade like runs through different plateaux with a decreasing value of the corresponding generalization error we find learning rate dependent phenomena such as splitting and disappearing of fixed points of the equations of motion the dependence of plateau lengths on the initial conditions is described analytically and simulations confirm the results

generalization learning in a perceptron with binary synapses we consider the generalization problem for a perceptron with binary synapses implementing the stochastic belief propagation inspired sbpi learning algorithm which we proposed earlier and perform a mean field calculation to obtain a differential equation which describes the behaviour of the device in the limit of a large number of synapses n we show that the solving time of sbpi is of order n sqrt log n while the similar well known clipped perceptron cp algorithm does not converge to a solution at all in the time frame we considered the analysis gives some insight into the ongoing process and shows that in this context the sbpi algorithm is equivalent to a new simpler algorithm which only differs from the cp algorithm by the addition of a stochastic unsupervised meta plastic reinforcement process whose rate of application must be less than sqrt 2 pi n for the learning to be achieved effectively the analytical results are confirmed by simulations

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

variants of newton s method for functions of several variables some variants of newton s method are developed in this work in order to solve systems of nonlinear equations based in trapezoidal and midpoint rules of quadrature we prove the quadratic convergence of one of these methods moreover different numeric tests confirm theoretic results and allow us to compare these variants with newton s classical method

exponential stability analysis for delayed neural networks with switching parameters average dwell time approach this paper is concerned with the problem of exponential stability analysis of continuous time switched delayed neural networks by using the average dwell time approach together with the piecewise lyapunov function technique and by combining a novel lyapunov krasovskii functional which benefits from the delay partitioning method with the free weighting matrix technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time varying delays respectively moreover the decay estimates are explicitly given the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

dwell time based stabilisation of switched linear delay systems using clock dependent lyapunov krasovskii functionals dwell time stability conditions of the switched delay systems are derived using multiple clock dependent lyapunov krasovskii functionals the corresponding conditions are approximated by both using

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

observer design for switched recurrent neural networks an average dwell time approach this paper is concerned with the problem of observer design for switched recurrent neural networks with time varying delay the attention is focused on designing the full order observers that guarantee the global exponential stability of the error dynamic system based on the average dwell time approach and the free weighting matrix technique delay dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities the error state decay estimate is also given then the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results finally four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

on a general class of multipoint root finding methods of high computational efficiency a general class of n point iterative methods for solving nonlinear equations is constructed by combining methods of newton s type and an arbitrary two point method of the fourth order of convergence it is proved that these methods have the convergence order 2 n requiring only n 1 function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class possess as high as possible computational efficiency in the sense of the kung traub hypothesis numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

a third order newton type method to solve systems of nonlinear equations in this paper we present a third order newton type method to solve systems of nonlinear equations in the first we present theoretical preliminaries of the method secondly we solve some systems of nonlinear equations all test problems show the third order convergence of our method

optimal pruning in neural networks we study pruning strategies in simple perceptrons subjected to supervised learning our analytical results obtained through the statistical mechanics approach to learning theory are independent of the learning algorithm used in the training process we calculate the post training distribution mathcal p j of synaptic weights which depends only on the overlap ensuremath rho 0 achieved by the learning algorithm before pruning and the fraction ensuremath kappa of relevant weights in the teacher network from this distribution we calculate the optimal pruning strategy for deleting small weights the optimal pruning threshold grows from zero as ensuremath theta mathrm opt ensuremath rho 0 ensuremath kappa ensuremath propto ensuremath rho 0 ensuremath ensuremath rho c ensuremath kappa 1 2 above some critical value ensuremath rho c ensuremath kappa thus the elimination of weak synapses enhances the network performance only after a critical learning period possible implications for biological pruning phenomena are discussed

remarks on on a general class of multipoint root finding methods of high computational efficiency an oversight on the number of function evaluations of the n point root finding methods proposed in siam j numer anal 47 2010 pp 4402 4414 is discussed to correct this flaw modified methods of optimal computational efficiency are presented by applying higher order hermite interpolatory polynomials

dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension abstract this paper deals with the real dynamical analysis of iterative methods for solving nonlinear systems on vectorial quadratic polynomials we use the extended concept of critical point and propose an easy test to determine the stability of fixed points to multivariate rational functions moreover an scaling theorem for different known methods is satisfied we use these tools to analyze the dynamics of the operator associated to known iterative methods on vectorial quadratic polynomials of two variables the dynamical behavior of newton s method is very similar to the obtained in the scalar case but this is not the case for other schemes some procedures of different orders of convergence have been analyzed under this point of view and some dangerous numerical behavior have been found as attracting strange fixed points or periodic orbits

a new tool to study real dynamics in this paper the author presents a graphical tool that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way this tool gives the information as previous tools such as feigenbaum diagrams and lyapunov exponents for every initial point the convergence plane can be used inter alia to find the elements of a family that have good convergence properties to see how the basins of attraction changes along the elements of the family to study two point methods such as secant method or even to study two parameter families of iterative methods to show the applicability of the tool an example of the dynamics of the damped newton s method applied to a cubic polynomial is presented in this paper

dwell time based stabilisation of switched delay systems using free weighting matrices abstractin this paper we present a quasi convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems piecewise lyapunov krasovskii functionals are introduced and the upper bound for the derivative of lyapunov functionals is estimated by free weighting matrices method to investigate non switching stability of each candidate subsystems then a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system once these conditions are represented by a set of linear matrix inequalities dwell time optimisation problem can be formulated as a standard quasi convex optimisation problem numerical examples are given to illustrate the improvements over previously obtained dwell time bounds using the results obtained in the stability case we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers the algorithm solves the problem with successive linearisation of nonlin

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

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

third order methods from quadrature formulae for solving systems of nonlinear equations we extend to p dimensional problems a modification of the newton method based on quadrature formulas of order at least one which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given these new methods may be more efficient then other third order methods as they do not require the use of the second order frechet derivative

exponential stabilization of a class of stochastic system with markovian jump parameters and mode dependent mixed time delays in this technical note the globally exponential stabilization problem is investigated for a general class of stochastic systems with both markovian jumping parameters and mixed time delays the mixed mode dependent time delays consist of both discrete and distributed delays we aim to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense first by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem then a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality lmi approach finally it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of lmis numerical simulation is carried out to demonstrate the effectiveness of the proposed methods

a novel family of composite newton traub methods for solving systems of nonlinear equations we present a family of three step iterative methods of convergence order five for solving systems of nonlinear equations the methodology is based on the two step traub s method with cubic convergence for solving scalar equations computational efficiency of the new methods is considered and compared with some well known existing methods numerical tests are performed on some problems of different nature which confirm robust and efficient convergence behavior of the proposed methods moreover theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems stability of the methods is tested by drawing basins of attraction in a two dimensional polynomial system

slowly evolving connectivity in recurrent neural networks i the extreme dilution regime we study extremely diluted spin models of neural networks in which the connectivity evolves in time although adiabatically slowly compared to the neurons according to stochastic equations which on average aim to reduce frustration the fast neurons and slow connectivity variables equilibrate separately but at different temperatures our model is exactly solvable in equilibrium we obtain phase diagrams upon making the condensed ansatz i e recall of one pattern these show that as the connectivity temperature is lowered the volume of the retrieval phase diverges and the fraction of mis aligned spins is reduced still one always retains a region in the retrieval phase where recall states other than the one corresponding to the condensed pattern are locally stable so the associative memory character of our model is preserved

dynamic output feedback control of switched linear systems this paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete time domains a particular class of matrix inequalities the so called lyapunov metzler inequalities provides conditions for open loop stability analysis and closed loop switching control using state and output feedback switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the hamilton jacobi bellman inequality an upper bound on the optimal cost associated with a closed loop stabilizing switching strategy is provided as well the solution of the output feedback problem is based on the construction of a full order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule throughout the theoretical results are illustrated by means of academic examples a realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported

technical communique h model reduction for uncertain switched linear discrete time systems in this paper the problem of h model reduction for switched linear discrete time systems with polytopic uncertainties is investigated a reduced order switched model is constructed for a given robustly stable switched system which has the same structural polytopic uncertainties as the original system such that the resulting error system is robustly asymptotically stable and an h error performance is guaranteed a sufficient condition for the existence of the desired reduced order model is derived and formulated in terms of a set of linear matrix inequalities by solving the corresponding convex optimization problem in such existence condition the vertex system of reduced order model can be obtained which also provides an h gain for the error system between the original system and the reduced order model a numerical example is given to show the effectiveness and the potential of the proposed techniques

parallel strategy for optimal learning in perceptrons we developed a parallel strategy for learning optimally specific realizable rules by perceptrons in an online learning scenario our result is a generalization of the caticha kinouchi ck algorithm developed for learning a perceptron with a synaptic vector drawn from a uniform distribution over the n dimensional sphere so called the typical case our method outperforms the ck algorithm in almost all possible situations failing only in a denumerable set of cases the algorithm is optimal in the sense that it saturates bayesian bounds when it succeeds

on the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods a development of an inverse first order divided difference operator for functions of several variables is presented two generalized derivative free algorithms built up from ostrowski s method for solving systems of nonlinear equations are written and analyzed a direct computation of the local order of convergence for these variants of ostrowski s method is given in order to preserve the local order of convergence any divided difference operator is not valid two counterexamples of computation of a classical divided difference operator without preserving the order are presented a rigorous study to know a priori if the new method will preserve the order of the original modified method is presented the conclusion is that this fact does not depend on the method but on the systems of equations and if the associated divided difference verifies a particular condition a new divided difference operator solving this problem is proposed furthermore a computation that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced this study can be applied directly to other newton s type methods where derivatives are approximated by divided differences

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

selecting examples for perceptrons a technique is introduced for analysing the learning process of perceptrons which continually select their own examples the most efficient training algorithm yet devised the authors predict a 42 reduction in the number of examples wasted in training an ising perceptron compared to the case in which examples are random optimally stable spherical perceptrons may also be taught significantly more efficiently and their results compare well with an existing numerical simulation

a fourth order method from quadrature formulae to solve systems of nonlinear equations in this paper we obtain a fourth order convergence method to solve systems of nonlinear equations this method is based on a quadrature formulae a general error analysis providing the fourth order of convergence is given numerical examples show the fourth order convergence this method does not use the second order frechet derivative

on the computational efficiency index and some iterative methods for solving systems of nonlinear equations in this paper two new iterative methods are built up and analyzed a generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited analytic proofs of the local order of convergence based on developments of multilineal functions and numerical concepts that will be used to illustrate the analytic results are given an approximation of the computational order of convergence is computed independently of the knowledge of the root and the necessary time to get one correct decimal is studied in our examples

iterative methods of order four and five for systems of nonlinear equations the adomian decomposition is used in order to obtain a family of methods to solve systems of nonlinear equations the order of convergence of these methods is proved to be p 2 under the same conditions as the classical newton method also numerical examples will confirm the theoretical results

the dynamics of on line principal component analysis the learning dynamics of an on line algorithm for principal component analysis is described exactly in the thermodynamic limit by means of coupled ordinary differential equations for a set of order parameters it is demonstrated that learning is delayed significantly because existing symmetries among student vectors have to be broken a closely related effect is the perfect or partial loss of initial knowledge in the course of learning the analysis shows that different learning rates for the student vectors improve the performance of the algorithm drastically

on the ability of the optimal perceptron to generalise a linearly separable boolean function is derived from a set of examples by a perceptron with optimal stability the probability to reconstruct a pattern which is not learnt is calculated analytically using the replica method

learning drifting concepts with neural networks the learning of time dependent concepts with a neural network is studied analytically and numerically the linearly separable target rule is represented by an n vector whose time dependence is modelled by a random or deterministic drift process a single layer network is trained online using different hebb like algorithms training is based on examples which are chosen randomly and according to a query strategy the evolution of the generalization error can be calculated exactly in the thermodynamic limit n to infinity the rule is never learnt perfectly but can be tracked within a certain error margin the generalization performance of various learning rules is compared and simulations confirm the analytic results

an efficient fifth order method for solving systems of nonlinear equations in this paper we present a three step iterative method of convergence order five for solving systems of nonlinear equations the methodology is based on the two step homeier s method with cubic convergence homeier 2004 computational efficiency in its general form is discussed and a comparison between the efficiency of proposed technique and existing ones is made the performance is tested through numerical examples moreover theoretical results concerning order of convergence and computational efficiency are verified in the examples it is shown that the present method has an edge over existing methods particularly when applied to large systems of equations

an improved newton traub composition for solving systems of nonlinear equations in this paper we present a modified newton traub composition with increasing order of convergence for solving systems of nonlinear equations the idea is based on the recent development by sharma et al 2015 analysis of convergence shows that the presented method has sixth order of convergence computational efficiency of the new method is considered and compared with some well known existing methods numerical tests are performed on some problems of different nature which confirm robust and efficient convergence behavior of the proposed method moreover theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems the basins of attraction of existing methods and the presented method are given to demonstrate their performance

biased learning in boolean perceptrons abstract the generalization ability of hebbian boolean perceptrons can be improved by a kind of feedback mechanism in which the student net judges the difficulty of a new example from its previous experience it is shown that by giving a higher weight to the hard examples both generalization and learning abilities can be increased analytical as well as numerical results are presented for both cases where the examples are drawn at random or selected in an intelligent form

optimal generalization in perceptions a new learning algorithm for the one layer perceptron is presented it aims to maximize the generalization gain per example analytical results are obtained for the case of single presentation of each example the weight attached to a hebbian term is a function of the expected stability of the example in the teacher perceptron this leads to the obtention of upper bounds for the generalization ability this scheme can be iterated and the results of numerical simulations show that it converges within errors to the theoretical optimal generalization ability of the bayes algorithm analytical and numerical results for an algorithm with maximized generalization in the learning strategy with selection of examples are obtained and it is proved that as expected orthogonal selection is optimal exponential decay of the generalization error is obtained for the single presentation of selected examples

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

generalization performance of bayes optimal classification algorithm for learning a perceptron the generalization error of the bayes optimal classification algorithm when learning a perceptron from noise free random training examples is calculated exactly using methods of statistical mechanics it is shown that if an assumption of replica symmetry is made then in the thermodynamic limit the error of the bayes optimal algorithm is less than the error of a canonical stochastic learning algorithm by a factor approaching ensuremath surd 2 as the ratio of the number of training examples to perceptron weights grows in addition it is shown that approximations to the generalization error of the bayes optimal algorithm can be achieved by learning algorithms that use a two layer neutral net to learn a perceptron

some iterative methods for solving a system of nonlinear equations in this paper we suggest and analyze two new two step iterative methods for solving the system of nonlinear equations using quadrature formulas we prove that these new methods have cubic convergence several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods these new iterative methods may be viewed as an extension and generalizations of the existing methods for solving the system of nonlinear equations

a modified newton method with cubic convergence the multivariate case recently a modification of the newton method for finding a zero of a univariate function with local cubic convergence has been introduced here we extend this modification to the multi dimensional case i e we introduce a modified newton method for vector functions that converges locally cubically without the need to compute higher derivatives the case of multiple roots is not treated per iteration the method requires one evaluation of the function vector and solving two linear systems with the jacobian as coefficient matrix where the jacobian has to be evaluated twice since the additional computational effort is nearly that of an additional newton step the proposed method is useful especially in difficult cases where the number of iterations can be reduced by a factor of two in comparison to the newton method this much better convergence is indeed possible as shown by a numerical example also the modified newton method can be advantageous in cases where the evaluation of the function is more expensive than solving a linear system with the jacobian as coefficient matrix an example for this is given where numerical quadrature is involved finally we discuss shortly possible extensions of the method to make it globally convergent

developing high order methods for the solution of systems of nonlinear equations abstract two families of order six for the solution of systems of nonlinear equations are developed and compared to existing schemes of order up to six we have found that one of the methods in the literature has been rediscovered the comparison is based on the total cost of an iteration and the performance on 14 examples of systems of dimensions 2 9