symmetry and phaselocking in chains of weakly coupled oscillators weakly coupled chains of oscillators with nearest neighbor interactions are analyzed for phaselocked solutions it is shown that the symmetry properties of the coupling affect the qualitative form of the phaselocked solutions and the scaling behavior of the system as the number of oscillators grows without bound it is also shown that qualitative behavior of these solutions depends on whether the coupling is diffusive or i synaptic terms defined in the paper the methods include the demonstration that the equations for phaselocked solutions can be approximated by a singularly perturbed two point continuum boundary value problem that is easier to analyze the issue of convergence of the phaselocked solutions to solutions of the continuum equation is closely related to questions involving numerical entropy in computation schemes for a conservation law an application to the neurophysiology of motor behavior is discussed briefly

towards possible q generalizations of the malthus and verhulst growth models abstract tsallis entropy introduced in 1988 based on the equation s q 1 i p i q q 1 has been considered to obtain new possibilities for constructing a generalized thermodynamical basis for statistical physics expanding classical boltzmann gibbs thermodynamics for non equilibrium states during the last two decades this q generalized theory has been successfully applied to a considerable amount of physically interesting complex phenomena the authors wish to present a mathematical analysis of the possible q generalizations of the malthus and the verhulst growth models based on tsallis definitions of the q logarithm and the q exponential

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

on the number of limit cycles near a homoclinic loop with a nilpotent singular point abstract in this article we study the expansion of the first melnikov function appearing by perturbing an integrable and reversible system with a homoclinic loop passing through a nilpotent singular point and obtain formulas for computing the first coefficients of the expansion based on these coefficients we obtain a lower bound for the maximal number of limit cycles near the homoclinic loop moreover as an application of our main results we consider a type of integrable and reversible polynomial systems obtaining at least 3 4 or 5 limit cycles respectively

lower order h_ infty filter design for bilinear systems with bounded inputs we propose an optimization based method for designing a lower order luenberger type state estimator while providing l 2 gain guarantees on the error dynamics when the estimator is used with the higher order system suitable filter parameters can be computed by modelling the bilinear system as a linear differential inclusion and solving a set of bilinear matrix inequality constraints since these constraints are nonconvex in general we also show that one can solve a suitably defined semi definite program to compute a bound on the level of suboptimality the design method also allows one to explicitly take account of linear parameter uncertainties in order to provide a priori robustness guarantees the h infinity estimator not only has lower real time computational requirements compared with a kalman filter but also does not require knowledge of the noise spectrum for a numerical example we consider the estimation of the radiation force for a wave energy converter where a low order model is used to approximate the radiation dynamics

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

effective carrying capacity and analytical solution of a particular case of the richards like two species population dynamics model abstract we consider a generalized two species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions these two species models can be simplified to a one species model with a time dependent extrinsic growth factor with a one species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one species model the equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case the gompertz model here we unveil important aspects of sigmoid growth curves which are relevant to growth processes and population dynamics

robust spl hscr sub spl infin filtering for continuous time varying uncertain systems with deterministic input signals many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals when spl lscr sub 2 or spl hscr sub spl infin filters that were designed based on a nominal model of the system are applied the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal and the latter may be very appreciable we introduce a finite horizon robust spl hscr sub spl infin filtering method that provides a guaranteed spl hscr sub spl infin bound for the estimation error in the presence of both parameter uncertainty and a known input signal this method is developed by using a game theoretic approach and the results generalize those obtained for cases without parameter uncertainty or without a known input signal it is also demonstrated via an example that the proposed method provides significantly improved signal estimates

a one dimensional model of population growth abstract in this work a one dimensional population growth model is proposed the model based on the cooperative and competitive individual individual distance dependent interaction allows us to get a full analytical solution with this analytical approach it was possible to investigate the dynamics of the population according to some parameters as intrinsic growth rate strength of the interaction between individuals and the distance dependent interaction as a consequence of the individuals interaction a rich phase diagram to which the population has access was observed the phases observed are convergence to carrying capacity exponential growth divergence at finite time and extinction moreover it was also observed that some phases are strictly dependent on the initial condition for instance in the cooperative regime with negative intrinsic growth rate the population can diverge or become extinct according to the initial population size the phases accessible to the population can be seen as a macroscopic behavior which emerges from the interaction among the individuals the microscopic level

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

phase chaos in coupled oscillators a complex high dimensional chaotic behavior phase chaos is found in the finite dimensional kuramoto model of coupled phase oscillators this type of chaos is characterized by half of the spectrum of lyapunov exponents being positive and the lyapunov dimension equaling almost the total system dimension intriguingly the strongest phase chaos occurs for intermediate size ensembles phase chaos is a common property of networks of oscillators of very different natures such as phase oscillators limit cycle oscillators and chaotic oscillators e g r ossler systems

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

phase locking in chains of multiple coupled oscillators phase locking in chains of weakly coupled oscillators with coupling beyond nearest neighbors is studied starting with a piecewise linear coupling function a homotopy method is applied to prove the existence of phase locked solutions numerical examples are provided to illustrate the existence and the properties of the solutions differences between multiple coupling and nearest neighbor coupling are also discussed 2000 elsevier science b v all rights reserved

reversibility vs synchronization in oscillator lattices abstract we consider the dynamics of a lattice of phase oscillators with a nearest neighbor coupling the clustering hierarchy is described for the case of linear distribution of natural frequencies we demonstrate that for small couplings prior to the appearance of the first cluster the dynamics is quasi hamiltonian the phase volume is conserved in average and the spectrum of the lyapunov exponents is symmetric we explain this unexpected for a dissipative system phenomenon using the concept of reversibility we show that for a certain coupling a smooth transition from the quasi hamiltonian to the dissipative dynamics occurs which is a novel type of chaos chaos transition

generalized exponential function and discrete growth models abstract here we show that a particular one parameter generalization of the exponential function is suitable to unify most of the popular one species discrete population dynamic models into a simple formula a physical interpretation is given to this new introduced parameter in the context of the continuous richards model which remains valid for the discrete case from the discretization of the continuous richards model generalization of the gompertz and verhulst models one obtains a generalized logistic map and we briefly study its properties notice however that the physical interpretation for the introduced parameter persists valid for the discrete case next we generalize the scramble competition ricker discrete model and analytically calculate the fixed points as well as their stabilities in contrast to previous generalizations from the generalized ricker model one is able to retrieve either scramble or contest models

stability of an n 2 dimensional invariant torus in the kuramoto model at small coupling abstract when the natural frequencies are allocated symmetrically in the kuramoto model there exists an invariant torus of dimension n 2 1 n is the population size a global phase shift invariance allows us to reduce the model to n 1 dimensions using the phase differences and doing so the invariant torus becomes n 2 dimensional by means of perturbative calculations based on the renormalization group technique we show that this torus is asymptotically stable at small coupling if n is odd if n is even the torus can be stable or unstable depending on the natural frequencies and both possibilities persist in the small coupling limit

on the phenomenon of mixed dynamics in pikovsky topaj system of coupled rotators abstract a one parameter family of time reversible systems on three dimensional torus is considered it is shown that the dynamics is not conservative namely the attractor and repeller intersect but not coincide we explain this as the manifestation of the so called mixed dynamics phenomenon which corresponds to a persistent intersection of the closure of the stable periodic orbits and the closure of the completely unstable periodic orbits we search for the stable and unstable periodic orbits indirectly by finding non conservative saddle periodic orbits and heteroclinic connections between them in this way we are able to claim the existence of mixed dynamics for a large range of parameter values we investigate local and global bifurcations that can be used for the detection of mixed dynamics

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

collective phase slips and phase synchronizations in coupled oscillator systems phase synchronization dynamics in coupled limit cycles with distributed natural frequencies are explored a synchronization tree from free oscillations to local clustering and global phase locking is found a desynchronization induced transition to chaos is shown near the onset of various phase synchronization points a simultaneous quantized stick slip feature of the phases of oscillators is observed on the desynchronization side and heuristically interpreted in terms of a heteroclinic path instability

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

continuous growth models in terms of generalized logarithm and exponential functions abstract consider the one parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non symmetrical hyperboles these generalizations coincide to the one obtained in the context of non extensive thermostatistics we show that these functions are suitable to describe and unify the great majority of continuous growth models which we briefly review physical interpretation to the generalization function parameter is given for the richards model which has an underlying microscopic model to justify it

combining convex concave decompositions and linearization approaches for solving bmis with application to static output feedback a novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality bmi constraints the key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings at each iteration of the algorithm the concave part is linearized leading to a convex subproblem applications to various output feedback controller synthesis problems are presented in these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality lmi constraints the performance of the algorithm has been benchmarked on the data from the compleib library

logistic equation of arbitrary order abstract the paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems x vs number of tasks n operating at limited resources k at non extensive heterogeneous self organization processes characterized by parameter f in contrast to the classical logistic equation which exclusively relates to the special case of sub extensive homogeneous self organization processes at f 1 the proposed model concerns both homogeneous and heterogeneous processes in sub extensive and super extensive areas the parameter of arbitrary order f where f depends on both the coefficient of external resource utilization u n k where 0 u 1 and the internal microscopic character of realized processes related to the depth of feedback the coefficient directly influences self organization of processes by the change of microscopic parameters v i s i i and z where v i is the number of references visit to the i th component of the system during the service of each task s i is the time of serving the task by the i th component and z is the think time of a given process in the general case of complex system parameters v i s i i and z can have values in the range from 0 to in this way the new equation includes all possible cases of a complex executive system s operation furthermore it allows us to define the optimal matching point between x and n with f as the parameter it also helps to balance the load in complex systems and to equip artificial systems with self optimization mechanisms similar to those observed in natural systems

robust output feedback controller design via local bmi optimization the problem of designing a globally optimal full order output feedback controller for polytopic uncertain systems is known to be a non convex np hard optimization problem that can be represented as a bilinear matrix inequality optimization problem for most design objectives in this paper a new approach is proposed to the design of locally optimal controllers it is iterative by nature and starting from any initial feasible controller it performs local optimization over a suitably defined non convex function at each iteration the approach features the properties of computational efficiency guaranteed convergence to a local optimum and applicability to a very wide range of problems furthermore a fast but conservative lmi based procedure for computing an initially feasible controller is also presented the complete approach is demonstrated on a model of one joint of a real life space robotic manipulator

cal h _ infty filter for bilinear systems using lpv approach the aim of this technical note is to present a linear paramater varying lpv approach for the design of a functional filter for bilinear systems with a disturbance attenuation specification the unbiasedness requirement on the observation error is guaranteed by the solution of sylvester equations obtained by parametrizing the filter gain matrix this parametrization leads to a non convex optimization problem which is overcome by introducing a constraint on the gain matrix to take into account the whole set of the inputs in the filter design an lpv approach is used to obtain the gain matrix guaranteeing the quadratic stability of the observation error and a given level of disturbance attenuation this approach is then applied to the high gain observer design in order to consider the level of disturbance attenuation

brief paper when is the discretization of a spatially distributed system good enough for control this paper describes a new and straightforward method for controlling spatially distributed plants based on low order models obtained from spatial discretization techniques a suitable level of discretization is determined by computing the sequence of n gaps between weighted models of successively finer spatial resolution and bounding this by another sequence with an analytic series it is proved that such a series forms an upper bound on the n gap between a weighted model in the initial sequence and the spatially distributed weighted plant this enables the synthesis on low order models of robust controllers that are guaranteed to stabilize the actual plant a feature not shared by most model reduction methods where the gap between the high order model and plant is often not known and where the gap between high order and reduced models may be too expensive to compute since the calculation of the current bound is based on weighted models of small state dimension the new method avoids the numerical problems inherent in large scale model reduction based approaches the ideas presented in this paper are demonstrated on a disturbance rejection problem for a 1d heat equation

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

robust h reduced order filtering for uncertain bilinear systems this paper investigates both the h and robust h reduced order unbiased filtering problems for respectively a nominal bilinear system and a bilinear system affected by norm bounded structured uncertainties in all the system matrices first an algebraic framework is used to solve the unbiasedness condition and second a change of variable is introduced on the inputs of the system to reduce the conservatism inherent to the requirement of exponential convergence of the filter then the reduced order filtering solution is obtained through lmi with an equality constraint by transforming the problem into a robust state feedback in the nominal case and a robust static output feedback in the presence of uncertainties in the last case an additional bilinear matrix equality must also be solved

convergent relaxations of polynomial matrix inequalities and static output feedback using a moment interpretation of recent results on sum of squares decompositions of nonnegative polynomial matrices we propose a hierarchy of convex linear matrix inequality lmi relaxations to solve nonconvex polynomial matrix inequality pmi optimization problems including bilinear matrix inequality bmi problems this hierarchy of lmi relaxations generates a monotone sequence of lower bounds that converges to the global optimum results from the theory of moments are used to detect whether the global optimum is reached at a given lmi relaxation and if so to extract global minimizers that satisfy the pmi the approach is successfully applied to pmis arising from static output feedback design problems

robust reduced order unbiased filtering for uncertain systems this paper presents a simple solution to the robust unbiased functional reduced order filtering problem in the case of uncertain systems described by integral quadratic constraint iqc the existence condition of the unbiased filter is expressed through a rank relation then the filter is designed via linear matrix inequalities coupled with an equality constraint the results obtained in this paper are applicable to unstable systems the approach is illustrated by a numerical example

data collapse scaling functions and analytical solutions of generalized growth models we consider a nontrivial one species population dynamics model with finite and infinite carrying capacities time dependent intrinsic and extrinsic growth rates are considered in these models through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included with this data collapse all the models studied become independent from the parameters and initial condition analytical solutions are found when time dependent coefficients are considered these solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition s critical exponents considering an extrinsic growth rate as a cancer treatment we show that the relevant quantity depends not only on the intensity of the treatment but also on when the cancerous cell growth is maximum