determinative vertices of interval family with ωθ stability abstract in this article we pay attention to the stability of interval polynomials with regard to the region an analysis on how to generate the finite set whose stability implies robust stability of the entire family is given those results are intuitive and convenient to operate

on robust hurwitz polynomials in this note kharitonov s theorem on robust hurwitz polynomials is simplified for low order polynomials specifically for n 3 4 and 5 the number of polynomials required to check robust stability is one two and three respectively instead of four furthermore it is shown that for n geq 6 the number of polynomials for robust stability checking is necessarily four thus further simplification is not possible the same simplifications arise in robust schur polynomials by using the bilinear transformation applications of these simplifications to two dimensional polynomials as well as to robustness for single parameters are indicated

beyond the poisson renewal process a tutorial survey after sketching the basic principles of renewal theory and recalling the classical poisson process we discuss two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of mittag leffler and of wright type we compare these three processes with each other

density approach to ballistic anomalous diffusion an exact analytical treatment this paper addresses the problem of deriving the probability distribution density of a diffusion process generated by a nonergodic dichotomous fluctuation using the liouville equation density method the velocity of the diffusing particles fluctuates from the value of 1 to the value of 1 and back with the distribution density of time durations of the two states proportional to 1 in the asymptotic time limit the adopted density method allows us to establish an exact analytical expression for the probability distribution density of the diffusion process generated by these fluctuations contrary to intuitive expectations the central part of the diffusion distribution density is not left empty when moving from 2 ergodic condition to cr the monomodal distribution density with a minimum at the origin is turned into a bimodal one with a central bump whose intensity increases for 2 the

scale invariant motion in intermittent chaotic systems we investigate the dynamics generated from iterated maps and analyze the motion in terms of the probabilistic continuous time random walk ctrw approach two different ctrw models are considered i particles jump between sites turning points or ii particles move at a constant velocity between sites and choose a new direction at random for both models we study the mean squared displacement mathit r 2 t and the propagator p r t the probability to be at location r at time t having started at the origin at t 0 iterated maps are used to generate both dispersive and enhanced diffusion and the results are analyzed using the ctrw framework and scaling arguments for the case of dispersive motion we discuss the problem of the stationary state and point out its relevance

a new fast algorithm for robust stability analysis of linear control systems with linearly dependent parametric uncertainties abstract in this paper a fast algorithm is proposed for the computation of stability margins in parameter space for linear control systems subject to structured uncertainties the case in which plant transfer function coefficients are affine in a set of physical uncertain parameters is considered the paper shows also how the proposed algorithm can be used to solve another interesting problem in robust control analysis i e the determination of the region of pole location of a closed loop control system including an entire family of uncertain plants

on the relation between white shot noise gaussian white noise and the dichotomic markov process it is shown that the dichotomic markov process converges to a white shot noise interpreted according to the stratonovich integration rule in the joint limit in which the average duration of one of the states goes to zero and the value at this state goes to infinity a further limit procedure allows us to obtain gaussian white noise from white shot noise these results are applied to the problem of noise induced transitions it is shown that white shot noise can give rise to transitions which do not occur for gaussian white noise the above results are finally generalized in introducing compound dichotomic markov processes

extreme point results for robust stabilization of interval plants with first order compensators it has been shown previously that a first order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants these extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients in this work the authors prove a stronger result namely that it is necessary and sufficient to stabilize only sixteen of the extreme plants these sixteen plants are generated using the kharitonov polynomials associated with the numerator and denominator furthermore when additional information about the compensator is specified sign of the gain and signs and relative magnitudes of the pole and zero then in some cases it is necessary and sufficient to stabilize eight critical plants while in other cases it is necessary and sufficient to stabilize twelve critical plants

counter example to a recent result on the stability of interval matrices by s bialas abstract in bialas 1983 a condition is given which is supposedly necessary and sufficient for the stability of interval matrices we demonstrate via a counter example that the condition given is in fact not sufficient

nonergodicity of a time series obeying levy statistics time averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied such a process called a levy walk describes dynamical behaviors of many physical systems fluorescence intermittency of semiconductor nanocrystals under continuous laser illumination being one example when the mean sojourn time diverges the process is non ergodic in that case the time average autocorrelation function is not equal to the ensemble averaged autocorrelation function instead it remains random even in the limit of long measurement time several approximations for the distribution of this random autocorrelation function are obtained for different parameter ranges and favorably compared to monte carlo simulations nonergodicity of the power spectrum of the process is briefly discussed and a nonstationary wiener khintchine theorem relating the correlation functions and the power spectrum is presented the considered situation is in full contrast to the usual assumptions of ergodicity and stationarity

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

a random telegraph signal of mittag leffler type a general method is presented to explicitly compute autocovariance functions for non poisson dichotomous noise based on renewal theory the method is specialized to a random telegraph signal of mittag leffler type analytical predictions are compared to monte carlo simulations non poisson dichotomous noise is non stationary and standard spectral methods fail to describe it properly as they assume stationarity

scaling breakdown a signature of aging we prove that the levy walk is characterized by bilinear scaling this effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions

the generalized cattaneo equation for the description of anomalous transport processes the cattaneo equation which describes a diffusion process with a finite velocity of propagation is generalized to describe anomalous transport three possible generalizations are proposed each one supported by a different scheme continuous time random walks non local transport theory and delayed flux force relation the properties of these generalizations are studied in both the long time and the short time regimes in the long time limit we recover the mean square displacement which is characteristic for these anomalous processes as expected the short time behaviour is modified in comparison to generalized diffusion equations

nonergodic complexity management linear response theory the backbone of nonequilibrium statistical physics has recently been extended to explain how and why nonergodic renewal processes are insensitive to simple perturbations such as in habituation it was established that a permanent correlation results between an external stimulus and the response of a complex system generating nonergodic renewal processes when the stimulus is a similar nonergodic process this is the principle of complexity management whose proof relies on ensemble distribution functions herein we extend the proof to the nonergodic case using time averages and a single time series hence making it usable in real life situations where ensemble averages cannot be performed because of the very nature of the complex systems being studied

polytopes of polynomials with zeros in a prescribed set in the publication by a c bartlett c v holot and h lin proc amer contr conf minneapolis mn 1987 a fundamental result is established on the zero locations of a family of polynomials it is shown that the zeros of a polytope p of nth order real polynomials are contained in a simply connected set d if and only if the zeros of all polynomials along the edges of p are contained in d the present authors are motivated by the fact that the requirement of simple connectedness of d may be too restrictive and applications such as dominant pole assignment and filter design where the separation of zeros is required they extend the edge criterion of bartlett et al to handle any set d whose complement d sup c has the following property every point d in d sup c lies on some continuous path which remains within d sup c and is unbounded this requirement is typically verified by inspection and allows for a large class of disconnected sets

linear response to perturbation of nonexponential renewal processes we study the linear response of a two state stochastic process obeying the renewal condition by means of a stochastic rate equation equivalent to a master equation with infinite memory we show that the condition of perennial aging makes the response to coherent perturbation vanish in the long time limit

stochastic processes driven by dichotomous markov noise some exact dynamical results stochastic processes defined by a general langevin equation of motion where the noise is the non gaussian dichotomous markov noise are studied a non fokker planck master differential equation is deduced for the probability density of these processes two different models are exactly solved in the second one a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time critical slowing down does not appear in this point but in another one

a kharitonov like theorem for interval polynomial matrices abstract as an extension of kharitonov s theorem robust stability of interval polynomial matrices is studied here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts the present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row column has only one element that involves kharitonov edge polynomials and all the other elements take on one of the four kharitonov vertex polynomials

generalized edge theorem abstract in this paper we shall show that a family of analytic functions constructed from the convex hull of a finite number of vertex functions will have no zeros within a simply connected region in the complex plane if and only if all its edge functions have no zeros within the simply connected region the result is in fact a generalization of the edge theorem which has been derived for polynomial functions 1 2 7

power spectra and random walks in intermittent chaotic systems abstract we investigate anomalous diffusion and the corresponding power spectra generated by iterated maps and analyze the motion in terms of the probabilistic continous time random walk approach both stationary and non stationary conditions are considered demonstrating the dependence of the mean squared displacement and of the power spectra on the initial conditions the theoretical results are corroborated by numerical calculations and excellent and agreement is obtained

subordination to periodic processes and synchronization abstract we study the subordination to a process that is periodic in the natural time scale and equivalent to a clock with n states the rationale for this investigation is given by a set of many interacting clocks with n states the natural time scale representation corresponds to the dynamics of an individual clock with no interaction with the other clocks of this set we argue that the cooperation among the clocks of this set has the effect of generating a global clock whose times of sojourn in each of its n states are described by a distribution density with an inverse power law form and power index 2 this is equivalent to extending the widely used subordination method from fluctuation dissipation processes to periodic processes thereby raising the question of whether special conditions exist of perfect synchronization signaled by regular oscillations and especially by oscillations with no damping we study first the case of a poisson subordination function we show that in spite of the random nature of the subordination method the procedure has the effect of creating damped oscillations whose damping vanishes in the limiting case of n 1 thereby suggesting a condition of perfect synchronization in this limit the bateman s mathematical arguments h bateman higher transcendental functions vol iii robert k krieger publishing company inc krim fr drive malabar fl copyright 1953 by mcgraw hill book company inc indicate that the condition of perfect synchronization is possible also in the non poisson case with 2 although it may lie beyond the range of computer simulation to make the theoretical predictions accessible to numerical simulation we use a subordination function whose survival probability is a mittag leffler exponential function this method prevents us from directly establishing the macroscopic coherence emerging from 2 which generates a perfect form of 1 f noise however it affords indirect evidence that perfect synchronization signaled by undamped regular oscillations may be produced in this case furthermore we explore a condition characterized by an excellent agreement between theory and numerical simulation where the long time region relaxation with a perfect inverse power law decay emerging from the subordination to ordinary fluctuation dissipation processes is replaced by exponentially damped regular oscillations

monte carlo simulation of uncoupled continuous time random walks yielding a stochastic solution of the space time fractional diffusion equation we present a numerical method for the monte carlo simulation of uncoupled continuous time random walks with a levy stable distribution of jumps in space and a mittag leffler distribution of waiting times and apply it to the stochastic solution of the cauchy problem for a partial differential equation with fractional derivatives both in space and in time the one parameter mittag leffler function is the natural survival probability leading to time fractional diffusion equations transformation methods for mittag leffler random variables were found later than the well known transformation method by chambers mallows and stuck for levy stable random variables and so far have not received as much attention nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the mittag leffler distribution combining the two methods we obtain an accurate approximation of space and time fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes

generalization of strong kharitonov theorems to the left sector the zero locations of interval polynomials are examined in particular it is shown that a family of interval polynomials will have only zeros in a certain class of left sector if and only if a finite number of specially chosen vertex polynomials have only zeros in the left sector this finite number of vertex polynomials is dependent on the damping margins of the left sector but is independent of the orders of the polynomials the exact number of vertex polynomials to be checked will depend on the damping margins but it will be independent of the orders of the polynomials these specially chosen vertex polynomials are independent of the order of the polynomials the importance of the result lies with the great reduction in computation cost associated with checking the zero locations of interval polynomials