stability analysis for stochastic differential equations with infinite markovian switchings abstract this paper is concerned with stability analysis of linear ito stochastic differential equations with countably infinite markovian switchings a spectral criterion is proposed for exponential stability of the considered models by means of the established spectral criterion the relationship between exponential stability and stochastic l 2 stability is clarified moreover under the disturbance of random signals with finite energy a sufficient condition is presented for l 2 input output stability of the perturbed stochastic differential equations

maximal versus strong solution to algebraic riccati equations arising in infinite markov jump linear systems abstract we deal with a perturbed algebraic riccati equation in an infinite dimensional banach space which appears for instance in the optimal control problem for infinite markov jump linear systems from now on imjls infinite or finite here has to do with the state space of the markov chain being infinite countable or finite see e g m d fragoso j baczynski optimal control for continuous time lq problems with infinite markov jump parameters siam j control optim 40 1 2001 270 297 by using a certain concept of stochastic stability a sort of l 2 stability we have proved in j baczynski m d fragoso maximal solution to algebraic riccati equations linked to infinite markov jump linear systems internal report lncc no 6 2006 existence and uniqueness of maximal solution for this class of equations as it is noticed in this paper unlike the finite case including the linear case we cannot guarantee anymore that maximal solution is a strong solution in this setting via a discussion on the main mathematical hindrance behind this issue we devise some mild conditions for this implication to hold specifically our main result here is that under stochastic stability along with a condition related with convergence in the infinite dimensional scenario and another one related to spectrum weaker than spectral continuity we ensure the maximal solution to be also a strong solution these conditions hold trivially in the finite case allowing us to recover the result of strong solution of c e de souza m d fragoso on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control systems control lett 14 1990 233 239 set for mjls the issue of whether the convergence condition is restrictive or not is brought to light and together with some counterexamples unveil further differences between the finite and the infinite countable case

on stability and h control of switched systems with random switching signals abstract in this paper the stability analysis and h control problems for a class of continuous time switched systems with a random switching signal are addressed the dwell time of the switched systems is characterized with a fixed part and a random part a new stability criterion which is equivalent to a necessary and sufficient condition developed previously is established first and then it is reformulated in terms of linear matrix inequalities based on the stability analysis result l 2 gain performance analysis and h control problems are studied several numerical examples are given to illustrate the effectiveness of our results

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

modelling and simulating higher dimensional chaotic data abstract we consider time series data whose estimated lyapunov exponents are positive this data is represented by a probability density function on a suitably fine partition of the phase space an algorithm is presented for constructing a transformation which has a unique absolutely continuous invariant measure whose density function is and which has the same lyapunov exponents as the original time series an example is given

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

on unordered codes by extending the results obtained by d e knuth 1986 a parallel unordered coding scheme with 2 sup r information bits is described balanced codes in which each codeword contains equal amounts of zeros and ones with r check bits and up to 2 sup r 1 r 2 information bits are constructed unordered codes with r check bits and up to 2 sup r 2 sup r 1 1 information bits are designed codes capable of detecting 2 sup r 1 2 sup r 2 1 unidirectional errors using r check bits are also described a review of previous work is presented

knuth s balanced codes revisited in 1986 don knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of 1 s and 1 s called balanced codes knuth s algorithm is well suited for use with large codewords the redundancy of knuth s balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords in this paper we will present results of our attempts to improve the performance of knuth s balanced codes

coding for delay insensitive communication with partial synchronization assume that information is transmitted in parallel among many lines in such a way that an electrical transition represents a 1 and an absence of a transition represents a 0 the propagation delay in the wires varies and results in asynchronous reception the challenge is to find an efficient communication scheme that will be delay insensitive one of the common solutions to this problem is to use a handshake mechanism namely the transmitter sends the next vector only after getting an acknowledgment that the current vector was received a natural question is how does the receiver know that reception of the current vector is complete this problem was solved by verhoeff 1988 by using the so called unordered codes however in practice it is common that the communication lines are arranged in pairs double rail such that the propagation delay on the lines within a pair is identical in general the lines can be arranged in groups of size larger than 1 where transmission within a group is synchronized the authors have created a few delay insensitive schemes that take advantage of partial synchronization within groups to achieve that they have generalized to arbitrary alphabets the following known results sperner s theorem on unordered sets henry knuth s henry 1982 knuth 1986 construction of balanced codes and berger s 1961 construction of unordered codes finally they have focused on practice and constructed a code that uses double rail channels but has the advantage that it is a rate 3 4 code as opposed to the rate 1 2 double rail code that is the common code being used in real systems

codes for zero spectral density at zero frequency corresp in pulse amplitude modulation pam digital transmission systems line encoding is used for shaping the spectrum of the encoded symbol sequence to suit the frequency characteristics of the transmission channel in particular it is often required that the encoded symbol sequence have a zero mean and spectral density vanishing at zero frequency we show that the finite running digital sum condition is a necessary and sufficient condition for this to occur the result holds in particular for alphabetic codes which are the most widely used line codes

stabilizability and insensitivity of switched linear systems this note identifies two types of stabilizability for switched systems the pointwise stabilizability and the consistent stabilizability necessary conditions and sufficient conditions for both types are presented for switched linear systems insensitivity issues are briefly addressed as well

performance of efficient balanced codes the problem of appraising the spectral performance of codes based on a new algorithm for generating zero disparity codewords presented by d e knuth 1986 is addressed in order to get some insight into the efficiency of knuth s construction technique the authors evaluate the spectral properties of its code streams the structure of knuth codes allows the derivation a simple expression for an approximation to the sum of variance of these codes this quantity plays a key role in the spectral performance characterization of dc balanced codes the authors evaluate this expression and compare the sum variance of knuth codes with the sum variance of the polarity bit codes for fixed redundancy under the premise that the sum variance can serve as a quantity to judge the width of the spectral notch the authors conclude that codes based on knuth s algorithm offer less spectral suppression than polarity bit codes with the same redundancy

almost sure and moments stability of jump linear systems abstract the stability of piecewise deterministic linear systems driven by an underlying finite markov chain is analyzed necessary and sufficient conditions for moment stability are obtained by means of an explicit formula for the corresponding liapunov exponent the relationship between almost sure and moment stability is elucidated revealing the possible occurrence of high order moment instability and large deviations from a stable sample path behavior

a result on almost sure stability of linear continuous time markovian switching systems this work investigates the almost sure stability for linear markovian switching systems in continuous time by using lyapunov function method the distribution of switching points is combined into constructing the lyapunov function which gives rise to the fluctuation in bounding the transient phase over the time interval confined between two successive switching points due to the randomness of their locations showing that the influence of the accumulated fluctuations by averaging it out will be negligible is the key step in proving our stability result illustrative examples are included to show the effectiveness of the theoretical result

balancing sets of vectors for n 0 d or 0 n identical to d mod 2 let k n d denote the minimal cardinality of a family v of or 1 vectors of dimension n such that for any or 1 vector w of dimension n there is a v in v such that mod v w mod

stability and stabilization of a class of stochastic switching systems with lower bound of sojourn time abstract this paper is concerned with the stability and stabilization issues for a family of discrete time stochastic switching systems with bounded sojourn time the stochastic switching systems are modeled by semi markov jump linear systems and the semi markov kernel approach is employed to handle the stability and stabilization problems the sojourn time of each system mode is considered to have both upper and lower bounds which is more general than the scenarios in previous literature that only consider the upper bound of sojourn time the concept of error mean square stability is put forward in a new form by taking into account the lower bounds of sojourn time for all system modes by virtue of a lyapunov function that not only depends on the current system mode but also on the elapsed time the system has been in the current mode together with certain techniques eliminating powers of matrices numerically testable stability and stabilization criteria in the sense of the proposed error mean square stability are obtained for the closed loop stochastic switching system finally a numerical example and a practical example of a dc motor are utilized to demonstrate the effectiveness of the proposed control strategy and the superiority of allowing for the lower bound of sojourn time

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

feedback control of switched stochastic systems using randomly available active mode information almost sure asymptotic stabilization of a discrete time switched stochastic system is investigated information on the active operation mode of the switched system is assumed to be available for control purposes only at random time instants we propose a stabilizing feedback control framework that utilizes the information obtained through mode observations we first consider the case where stochastic properties of mode observation instants are fully known we obtain sufficient asymptotic stabilization conditions for the closed loop switched stochastic system under our proposed control law we then explore the case where exact knowledge of the stochastic properties of mode observation instants is not available we present a set of alternative stabilization conditions for this case the results for both cases are predicated on the analysis of a sequence valued process that encapsulates the stochastic nature of the evolution of active operation mode between mode observation instants finally we demonstrate the efficacy of our results with numerical examples

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

recognizing chaotic time waveforms in terms of a parametrized family of nonlinear predictors abstract consider a chaotic dynamical system which exhibits a variety of chaotic time waveforms with a change in the bifurcation parameters this paper presents an algorithm for estimating the underlying bifurcation parameters of the chaotic time waveforms in experimental situation in which no a priori analytical knowledge of the dynamical system is available first we construct qualitatively similar parametrized family of nonlinear predictors only from several sets of chaotic time waveforms qualitatively similar parametrized family means that the family of nonlinear predictors exhibits qualitatively similar bifurcation phenomena as the original chaotic time waveforms are then characterized in terms of the qualitatively similar bifurcation parameters of the nonlinear predictors we call the characterization of chaotic time waveforms in terms of the underlying bifurcation parameters chaotic time waveform recognition several numerical experiments using the rossler equations show the efficiency of the algorithm the effect of observational noise included in chaotic time waveforms is also considered

approximating threshold circuits by rational functions motivated by the problem of understanding the limitations of threshold networks for representing boolean functions we consider size depth trade offs for threshold circuits that compute the parity function using a fundamental result in the theory of rational approximation we show how to approximate small threshold circuits by rational functions of low degree we apply this result to establish an almost optimal lower bound of n2 ln2n on the number of edges of any depth 2 threshold circuit with polynomially bounded weights that computes the parity function we also prove that any depth 3 threshold circuit with polynomially bounded weights requires n1 2 ln5 3n edges to compute parity on the other hand we give a construction of a depth d threshold circuit that computes parity with n1 1 d edges where 1 5 2 is the golden ratio we conjecture that there are no linear size bounded depth threshold circuits for computing parity

analysis of positive lyapunov exponents from random time series abstract the conventional method for estimating lyapunov spectra can give spurious positive lyapunov exponents when applied to random time series we analyze this phenomenon by considering a situation in which the method is applied to completely random time series produced by a simple stochastic model we show that the possible estimation of spurious positive lyapunov exponents is due to the statistical nature and the finiteness of data we also derive an upper bound of the largest lyapunov exponent for the model which is useful in testing positive lyapunov exponents with random shuffled surrogate data the results suggest that the method should be applied very carefully to experimentally obtained chaotic time series with possible random contamination so as to avoid spurious estimation of positive lyapunov exponents as evidences of deterministic chaos

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

optimal unidirectional error detecting correcting codes in this correspondence a class of t error correcting and multiple unidirectional error detecting systematic codes is presented these codes are significantly more efficient than the earlier codes the efficiency of these codes approaches the efficiency of the bch codes asymptotically furthermore it is shown that these codes can be easily decoded also in this correspondence we have presented a generalization of berger codes over zq these new codes are also shown to be optimal

measurement of the lyapunov spectrum from a chaotic time series the exponential divergence or convergence of nearby trajectories lyapunov exponents is conceptually the most basic indicator of deterministic chaos we propose a new method to determine the spectrum of several lyapunov exponents including positive zero and even negative ones from the observed time series of a single variable we have applied the method to various known model systems and also to the rayleigh b enard experiment and have elucidated the dependence of the lyapunov exponents on the rayleigh number

event triggered control for semi global stabilisation of systems with actuator saturation abstractthis paper investigates the problem of event triggered control for semi global stabilisation of null controllable systems subject to actuator saturation first for a continuous time system novel event triggered low gain control algorithms based on riccati equations are proposed to achieve semi global stabilisation the algebraic riccati equation with a low gain parameter is utilised to design both the event triggering condition and the linear controller a minimum inter event time based on the riccati ordinary differential equation is set a priori to exclude the zeno behaviour in addition the high low gain techniques are utilised to extend the semi global results to event based global stabilisation furthermore for a discrete time system novel low gain and high low gain control algorithms are proposed to achieve event triggered stabilisation numerical examples are provided to illustrate the theoretical results

m ary balanced codes with parallel decoding an m ary block code m 2 3 4 ldots of length n in mathbf i mathbf i mskip 7mu mathbf n is called balanced if and only if every codeword is balanced that is the real sum of the codeword components or weight is equal to left lfloor m 1 n 2 right rfloor this paper presents efficient encoding schemes to m ary balanced codes with parallel hence fast decoding in fact the decoding time complexity is o 1 digit operations these schemes are a generalization to the m ary alphabet of knuth s complementation method with parallel decoding let binom n w m indicate the number of m ary words of length n and weight w in 0 1 ldots m 1 n for any m in mathbf i mathbf i mskip 7mu mathbf n m geq 2 a simple implementation of the method is given which uses r in mathbf i mathbf i mskip 7mu mathbf n check digits to balance k leq binom r left lfloor m 1 r 2 right rfloor vphantom r r m m bmod 2 m 1 k bmod 2 m 1 information digits with an encoding time complexity of o mk log m k digit operations a refined implementation of the parallel decoding method is also given with r check digits and k leq m r 1 m 1 information digits where the encoding time complexity is o k sqrt log m k thus the proposed codes are less redundant than the m ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

a statistical framework for testing chaotic dynamics via lyapunov exponents abstract one common criticism of the existing lyapunov exponents algorithms is the absence of a distributional theory which provides a framework for the statistical hypothesis testing for the calculated lyapunov exponents this paper presents a methodology to calculate the empirical distributions of lyapunov exponents by using a bootstrapping technique the methodology of the paper provides a formal test of chaos under the null hypothesis the numerical examples show that the method works well with small data sets

on symmetric error correcting and all unidirectional error detecting codes the design of binary block codes that are capable of correcting up to t symmetric errors and detecting all unidirectional errors is discussed a class of systematic t symmetric error correcting all unidirectional error detecting t syec aued codes are proposed when t 0 the proposed codes become berger codes for t 1 the proposed codes are shown to be of asymptotically optimal order methods to construct nonsystematic t syec aued codes for t 2 and 3 are also presented

stability of nonlinear discrete repetitive processes with markovian switching repetitive processes are a class of 2d systems that operate over a subset of the upper right quadrant of the 2d plane applications include iterative learning control where experimental verification has been reported based on a linear time invariant model approximation of the dynamics this paper considers discrete nonlinear repetitive processes with markovian switching and applies as one application the resulting stability theory to iterative learning control for a class of networked systems where time varying dynamics arise

stabilization of continuous time jump linear systems we investigate almost sure and moment stabilization of continuous time jump linear systems with a finite state markov jump form process we first clarify the concepts of spl delta moment stabilizability exponential spl delta moment stabilizability and stochastic spl delta moment stabilizability we then present results on the relationships among these concepts coupled riccati equations that provide necessary and sufficient conditions for mean square stabilization are given in detail and an algorithm for solving the coupled riccati equations is proposed moreover we show that individual mode controllability implies almost sure stabilizability which is not true for other types of stabilizability finally we present some testable sufficient conditions for spl delta moment stabilizability and almost sure stabilizability

on efficient balanced codes over the mth roots of unity let spl phi sub m spl sube spl copf be the set of all mth roots of unity m spl isin in a balanced code over spl phi sub m is a block code over the alphabet spl phi sub m such that each code word is balanced that is the complex sum of its components or weight is equal to 0 let b sub m n be the set of all balanced words of length n over spl phi sub m in this correspondence it is shown that when m is a prime number the set b sub m n is not empty if and only if m divides n in this case the minimum redundancy for a balanced code over spl phi sub m of length n is on the other hand it is shown that when m 4 the set b sub 4 n is not empty if and only if n is even and in this case the minimum redundancy for a balanced code over spl phi sub 4 of length n is further this correspondence completely solves the problem of designing efficient coding methods for balanced codes over spl phi sub m when m 4 in fact it reduces the problem of designing efficient coding schemes for balanced codes over spl phi sub 4 to the design of efficient balanced codes over the usual bipolar alphabet spl phi sub 2 1 1

capacity approaching non binary balanced codes using auxiliary data it is known that for large user word lengths the auxiliary data can be used to recover most of the redundancy losses of knuth s simple balancing method compared with the optimal redundancy of balanced codes for the binary case here this important result is extended in a number of ways first an upper bound for the amount of auxiliary data is derived that is valid for all codeword lengths this result is primarily of theoretical interest as it defines the probability distribution of the number of balancing indices that results in optimal redundancy this result is equally valid for particular non binary generalizations of knuth s balancing method second an asymptotically exact expression for the amount of auxiliary data for the ternary case of a variable length realization of the modified balanced code construction is derived that in all respects is the analogue of the result obtained for the binary case the derivation is based on a generalization of the binary random walk to the ternary case and a simple modification of an existing generalization of knuth s method for the non binary balanced codes finally a conjecture is proposed regarding the probability distribution of the number of balancing indices for any alphabet size

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

statistics for mathematical properties of maps between time series embeddings we develop a set of statistics which are intended to characterize in terms of probabilities or confidence levels whether two data sets are related by a mapping with certain mathematical properties given these statistics we can ask how confident we can be that the mapping is continuous injective differentiable or has a differentiable inverse the intended use is for experimental or numerical situations in which multiple time series are generated and one wants to know what relation exists among them but the mapping between them is unknown or intractable examples of applications are testing filtered chaotic data for continuity and differentiability testing two data sets for synchronization in the most general sense testing one data set for determinism forward and backward in time and determining when transformations on two or three dimensional images are well behaved diffeomorphisms we test the statistics on several of these cases and show that they are useful for characterizing relations between data sets and for shedding light on phenomena which occur when data are transformed for example a dimension increase on filtering a chaotic data set

detecting determinism in short time series using a quantified averaged false nearest neighbors approach we propose a criterion to detect determinism in short time series this criterion is based on the estimation of the parameter e 2 defined by the averaged false neighbors method for analyzing time series cao physica d 110 43 1997 using surrogate data testing with several chaotic and stochastic simulated time series we show that the variation coefficient of e 2 over a few values of the embedding dimension d defines a suitable statistic to detect determinism in short data sequences this result holds for a time series generated by a high dimensional chaotic system such as the mackey glass one different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real world data we also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise

on stability of randomly switched nonlinear systems this note is concerned with stability analysis and stabilization of randomly switched systems these systems may be regarded as piecewise deterministic stochastic systems the discrete switches are triggered by a stochastic process which is independent of the state of the system and between two consecutive switching instants the dynamics are deterministic our results provide sufficient conditions for almost sure stability and stability in the mean using lyapunov based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds this slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants this condition is shown to hold for switching signals coming from the states of finite dimensional continuous time markov chains our results therefore hold for markovian jump systems in particular for systems with control inputs we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems

the problem of spurious lyapunov exponents in time series analysis and its solution by covariant lyapunov vectors we briefly recall the methods for the determination of lyapunov exponents from time series data and their limitations one particular problem is given by the fact that reconstructed phase spaces have usually extra dimensions compared to the true phase space of a dynamical system leading to extra so called spurious lyapunov exponents several methods to identify the true ones have been proposed which do not give satisfactory results we show that the geometric information contained in covariant lyapunov vectors can be used to identify the true exponents we illustrate its use and its limitations by applying it to experimental nmr laser data this article is part of a special issue of journal of physics a mathematical and theoretical devoted to lyapunov analysis from dynamical systems theory to applications

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

optimal asymmetric error detecting codes some of the properties of codes capable of detecting errors when used on a binary asymmetric or z channel are examined and in fact the maximum cardinality codes are determined these results are extended to the q ary asymmetric channel introduced by varshamov 1973 ieee trans inform theory 19 92 95

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

almost sure stabilization for feedback controls of regime switching linear systems with a hidden markov chain this work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown markov chain the control system displays continuous dynamics represented by differential equations and discrete events given by a hidden markov chain in the previous investigation on this class of problems averaging criteria were used which provides only the system behavior in some expectation sense a closer scrutiny of the system behavior necessarily requires the consideration of sample path properties different from previous work on stabilization of adaptive controlled systems with a hidden markov chain where average criteria were considered this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes under simple conditions it is shown that as long as the feedback controls have linear growth in the continuous component the resulting process is regular moreover by appropriate choice of the lyapunov functions it is shown that the adaptive system is stabilizable almost surely as a by product it is also established that the controlled process is positive recurrent

lie algebraic stability criteria for switched systems it was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable lie algebra possesses a quadratic common lyapunov function which implies that the corresponding switched linear system is exponentially stable for arbitrary switching in this paper we prove that the same properties hold under the weaker condition that the lie algebra generated by given matrices can be decomposed into a sum of a solvable ideal and a subalgebra with a compact lie group the corresponding local stability result for nonlinear switched systems is also established moreover we demonstrate that if a lie algebra fails to satisfy the above condition then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable relevant facts from the theory of lie algebras are collected at the end of the paper for easy reference

full informationh control for discrete time infinite markov jump parameter systems abstract in this paper we consider the full information discrete timeh control problem for the class of linear systems with markovian jumping parameters the state space of the markov chain is assumed to take values in a countably infinite set full information here means that the controller has access to both the state variables and jump variables a necessary and sufficient condition for the existence of a feedback controller that makes the l 2 induced norm of the system less than a prespecified bound is obtained this condition is written in terms of a set of infinite coupled algebraic riccati equations

almost sure stability of switching markov jump linear systems recently a special hybrid system called switching markov jump linear system smjls is studied a smjls is subject to a deterministic switching and a stochastic markovain switching to extend the results already obtained and to investigate some new aspects of such systems our main contributions in this paper are i transient analysis of markov process i e the expectations of the sojourn time the activation number of any mode and the number of switchings between any two modes and ii two sufficient conditions of the exponential almost sure stability for a general smjls different from previous work which is a special case of our study the transition rate matrix for the random markov process in our study is not fixed but varies when a deterministic switching takes place

binary transmission codes with higher order spectral zeros at zero frequency corresp a method is presented for designing binary channel codes in such a way that both the power spectral density function and its low order derivatives vanish at zero frequency the performance of the new codes is compared with that of channel codes designed with a constraint on the unbalance of the number of transmitted positive and negative pulses some remarks are made on the error correcting capabilities of these codes

lyapunov exponents of random time series the conventional method for estimating lyapunov spectra can give spurious positive lyapunov exponents when applied to random time series we analyze this phenomenon by using a simple stochastic model which produces completely random time series with no temporal correlation we show that the possible estimation of spurious positive lyapunov exponents is due to the statistical nature and finiteness of data we also derive an upper bound of the largest lyapunov exponent for the model textcopyright 1996 the american physical society

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

distinguishing between low dimensional dynamics and randomness in measured time series the success of current attempts to distinguish between low dimensional chaos and random behavior in a time series of observations is considered first we discuss stationary stochastic processes which produce finite numerical estimates of the correlation dimension and k2 entropy under naive application of correlation integral methods we then consider several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory this determines whether the methods are applicable to a given series if they are we evaluate the significance of a particular result for example by considering the results of the analysis of stochastic signals with statistical properties similar to those of observed series from the examples considered it is clear that the correlation integral should not be used in isolation but as one of a collection of tools to distinguish chaos from stochasticity

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

improved multicovering bounds from linear inequalities and supercodes the multicovering radii of a code are natural generalizations of the covering radius in which the goal is to cover all m tuples of vectors for some m as cheaply as possible in this correspondence we describe several techniques for obtaining lower bounds on the sizes of codes achieving a given multicovering radius our main method is a generalization of the method of linear inequalities based on refined weight distributions of the code we also obtain a linear upper bound on the 2 covering radius we further study bounds on the sizes of codes with a given multicovering radius that are subcodes of a fixed code we find for example constraints on parity checks for codes with small ordinary covering radius

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

on balanced codes in a balanced code each codeword contains equally many 1 s and 0 s parallel decoding balanced codes with 2 sup r or 2 sup r 1 information bits are presented where r is the number of check bits the 2 sup 2 r 1 construction given by d e knuth ibid vol 32 no 1 p 51 3 1986 is improved the new codes are shown to be optimal when knuth s complementation method is used

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

lq control of discrete time jump systems with markov chain in a general borel space in this technical note it is studied the lq optimal control problem for discrete time markov jump linear systems considering the case in which the markov chain takes values in a general borel space cal m it is shown that the solution of the lq optimal control problem is obtained in terms of the positive semi definite solution s ell ell in cal m of cal m coupled algebraic riccati equations by cal m coupled we mean that the algebraic riccati equations are coupled via an integral over a transition probability kernel cal g cdot vert cdot having a density g cdot vert cdot with respect to a sigma finite measure mu on cal m it is obtained sufficient conditions based on the concept of stochastic stabilizability and stochastic detectability for the existence and uniqueness of this positive semi definite solution these results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

variable length unordered codes in an unordered code no code word is contained in any other code word unordered codes are all unidirectional error detecting aued codes in the binary case it is well known that among all systematic codes with k information bits berger codes are optimal unordered codes with r log2 k 1 log2k check bits this paper gives some new theory on variable length unordered codes and introduces a new class of systematic instantaneous unordered codes with variable length check symbols the average redundancy of the new codes presented here is r 1 2 log2k c where c 1 0470 1 1332 ir and k in is the number of information bits when k is large it is shown that such redundancy is at most 0 6069 bits off the redundancy of an optimal systematic unordered code design with fixed length information symbols and variable length check symbols and at most 2 8075 bits off the redundancy of an optimal variable length unordered code design the generalization is also given for the nonbinary case and it is shown that similar results hold true

stability of switched systems on randomly switching durations with random interaction matrices in this paper we investigate the almost sure stability of switched systems on randomly switching durations simultaneously with randomly switching interaction matrices we not only allow the interaction matrix on each switching duration to take values randomly from either a countable an uncountable or even an unbounded state space but also allow the corresponding probability density function to be time varying with the switching we provide an example to show the difference between the almost sure stability and the moment stability then we establish several practical stability criteria for switched systems which may have linear or nonlinear subsystems these stability criteria also enable us to find suitable conditions for realizing almost sure synchronization in complex networks such as small world networks with both randomly switching durations and a few switching couplings that take values randomly in either an uncountable or an unbounded state space

design of some new efficient balanced codes a balanced code with r check bits and k information bits is a binary code of length k r and cardinality 2 sup k such that each codeword is balanced that is it has k r 2 1 s and k r 2 0 s this paper contains new methods to construct efficient balanced codes to design a balanced code an information word with a low number of 1 s or 0 s is compressed and then balanced using the saved space on the other hand an information word having almost the same number of 1 s and 0 s is encoded using the single maps defined by knuth s 1986 complementation method three different constructions are presented balanced codes with r check bits and k information bits with k spl les 2 sup r 1 2 k spl les 3 spl times 2 sup r 8 and k spl les 5 spl times 2 sup r 10r c r c r spl isin 15 10 5 0 5 are given improving the constructions found in the literature in some cases the first two constructions have a parallel coding scheme