thompson s metric and mixed monotone operators abstract we apply thompson s metric to prove several fixed point theorems of mixed monotone operators by appealing to various generalizations of banach s fixed point theorem

passivity based synchronization of a class of complex dynamical networks with time varying delay this paper proposes a complex delayed dynamical network consisting of n linearly and diffusively coupled identical reaction diffusion neural networks by utilizing some inequality techniques a sufficient condition ensuring the output strict passivity is derived for the proposed network model then we reveal the relationship between output strict passivity and synchronization of the proposed network model moreover based on the obtained passivity result and the relationship between output strict passivity and synchronization a criterion for synchronization is established finally a numerical example is provided to illustrate the correctness and effectiveness of the proposed results

brief paper a robust override scheme enforcing strict output constraints for a class of strictly proper systems this paper presents an override controller which ensures that constrained output variables retain certain prescribed strict bounds the class of nominal closed loop systems considered is strictly proper and minimum phase assuming the first markov parameter to be full rank and for each output measurement constraint there is one available actuator the advantage of the considered class of nominal systems is that an output constraint translates directly into a state constraint for which it is possible to use a particular non smooth lyapunov function the non smooth lyapunov function is defined by the level of the output constraint creating an invariant set for which the strict output constraints are satisfied the override strategy is designed to have only a minimal effect on the nominal control loop when no constraint is violated

dynamics of piecewise linear maps and sets of nonnegative matrices abstract we consider maps f k v min a k av and g k v max a k av where k is a finite set of nonnegative matrices and by min and max we mean component wise minimum and maximum we transfer known results about properties of g k to f k in particular we show existence of nonnegative generalized eigenvectors of f k give necessary and sufficient conditions for existence of strictly positive eigenvector of f k study dynamics of f k on the positive cone we show the existence and construct matrices a and b possibly not in k such that f k n v a n v and g k n v b n v for any strictly positive vector v

global attractivity in monotone and subhomogeneous almost periodic systems abstract a global attractivity theorem is first proved for a class of skew product semiflows then this result is applied to monotone and subhomogeneous almost periodic reaction diffusion equations ordinary differential systems and delay differential equations for their global dynamics

stability analysis and stabilization of 2 d switched systems under arbitrary and restricted switchings in this paper the problems of stability analysis and stabilization are investigated for discrete time two dimensional 2 d switched systems which are formulated by the well known fornasini marchesini local state space model firstly by using the switched quadratic lyapunov function approach a sufficient stability condition is established for such systems under arbitrary switching signal then the extended average dwell time technique combining with the piecewise lyapunov function approach is developed and it is utilized for the stability analysis of the 2 d switched systems for the restricted switching case based on the stability analysis results sufficient conditions are presented to stabilize the 2 d switched systems finally two examples are provided to illustrate the effectiveness of the proposed new design techniques

cooperative systems and time varying discrete diffusion for single species w x the theory of monotone dynamical systems developed by hirsch 2 has proved to be very successful in the study of the asymptotic behavior of solutions of competitive and cooperative systems of differential equations w x w x recently smith 4 and takac 5 7 have partially extended some of hirsch s results in order to study non autonomous periodic equations in this article we complement some of smith and takac results that are applied in order to study a model for single species non linear discrete diffusion with time varying coefficients models for single species linear w x discrete diffusion were studied in 1 3 obtaining results about extinction and persistence of the species the systems studied in these articles are of the form

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

event triggered h filtering of markov jump systems with general transition probabilities abstract this paper investigates the h filtering of markov jump systems with general transition probabilities which are known uncertain and unknown the transmission from sensor to filter is determined by a mode dependent event triggered scheme the advantage of the scheme is that no restriction is imposed on a triggering scalar employing a zero order holder the resulting filtering error system is expressed by markov jump systems with time delay with the aid of a relaxed lyapunov krasovskii functional and the finlser lemma the desired h filter gains and the related triggering parameter are solved in a uniformed framework it is shown that the proposed approach is less conservative than the existing one numerical examples are given to verify the validity of the proposed method

constrained stabilization problems for linear plants linear systems with magnitude and rate constraints on both the state and control variables are considered for such systems semi global and global constrained stabilization problems are formulated when state feedback controllers are used necessary and sufficient conditions for the solvability of the formulated problems are developed moreover design methodologies for such constrained stabilization problems are presented an important aspect of our development here is a taxonomy of constraints to show clearly for what type of constraints what can or cannot be achieved

relative stability for ascending and positively homogeneous operators on banach spaces abstract for a closed convex cone k in a real banach space with a norm increasing on k and a selfmapping t of k which is continuous positively homogeneous and ascending it is shown that the nonlinear eigenvalue problem tx x has a unique solution x k 0 up to a scalar r which is relatively stable in the sense that for a suitable function c of k into r formula moreover an estimate for the speed of convergence is given

concave perron frobenius theory and applications many important results of classical perron frobenius theory can be extended from linear selfmappings of the standard cone in finite dimensional real space to concave selfmappings of this cone this is in particular true for minima of linear mappings albeit the spectrum of these special concave mappings is more intricate than that for linear mappings as classical perron frobenius theory has numerous applications there are many new applications for its concave extension 1991 mathematical subject classification primary 39a11 15a48 secondary 47h07 47h12

l2 l filter design for discrete time singular markovian jump systems with time varying delays the problem of l 2 l filter design for discrete time singular systems with markovian jump and time varying delays is investigated in this paper by using the delay partitioning technique a delay dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l 2 l performance index based on the derived condition the full order and reduced order filters with mode independent characterization are designed in a unified framework the corresponding filter parameters can be obtained by solving a set of linear matrix inequalities the reported results not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism two numerical examples are provided to illustrate the effectiveness of the proposed methods

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

global asymptotics in some quasimonotone reaction diffusion systems with delays abstract both dichotomy and trichotomy on the global asymptotics of some quasimonotone reaction diffusion systems with delays are established in terms of the principal eigenvalue of linear weakly coupled elliptic systems applications to a class of delayed reaction diffusion models of single species growth and to a reaction diffusion system with delay modelling the spread of bacterial infections are provided

cooperative systems of differential equations with concave nonlinearities on considere le systeme dynamique discret engendre par une application monotone concave t r n r n on etudie ensuite des systemes d equations differentielles cooperatifs periodiques x f t x a non linearites concaves

the asymptotic behavior of monotone difference equations of higher order abstract for difference equations which satisfy a strict monotonicity property a comparison principle is shown this is used to prove relative stability for all solutions which implies in particular that all solutions must converge to a limit provided there is at least one bounded nonzero solution

dynamic output feedback control of discrete time markov jump linear systems through linear matrix inequalities this paper addresses the cal h 2 and cal h infty dynamic output feedback control design problems of discrete time markov jump linear systems under the mode dependent assumption which means that the markov parameters are available for feedback the main contribution is the complete characterization of all full order proper markov jump linear controllers such that the cal h 2 or cal h infty norm of the closed loop system remains bounded by a given prespecified level yielding the global solution to the corresponding mode dependent optimal control design problem expressed in terms of pure linear matrix inequalities some academic examples are solved for illustration and comparison as a more consequent practical application the networked control of a vehicle platoon using measurement signals transmitted in a markov channel as initially proposed in p seiler and r sengupta ieee trans automat control 50 2005 pp 356 364 is considered

a variant of the meir keeler type theorem in ordered banach spaces abstract this paper discusses a projective variant of the fixed point theorem for a class of mappings satisfying the meir keeler type contraction condition in ordered banach spaces through projective metric we also prove a result on the chainability of the thompson s metric using an elementary argument

a limit set trichotomy for positive nonautonomous discrete dynamical systems abstract for a sequence tn n n of self mappings of a normal cone in a real banach space conditions are specified which imply a limit set trichotomy for the inhomogeneous iterates tn tn 1 t1 t0

attractor minimal sets for cooperative and strongly convex delay differential systems abstract we study the skew product semiflow induced by a family of convex and cooperative delay differential systems under some monotonicity assumptions we obtain an ergodic representation for the upper lyapunov exponent of a minimal subset in addition when eventually strong convexity at one point is assumed and there exist two completely strongly ordered minimal subsets k1 ck2 we show that k1 is an attractor subset which is a copy of the base the long time behaviour of every trajectory strongly ordered with k2 is then deduced some examples of application of the theory are shown

nonlinear tracking control in the presence of state and control constraints a generalized reference governor this paper proposes a new approach to reference governor design as in prior literature the governor accepts input commands and modifies their evolution so that specified pointwise in time constraints on state and control variables are satisfied the new approach applies to general discrete time and continuous time nonlinear systems with uncertainties it relies on safety properties provided by sublevel sets of equilibria parameterized functions these functions need not be lyapunov functions and the corresponding sublevel sets need not be positively invariant technical conditions that capture the bare essentials of what is needed are identified and the usual desirable properties of reference governors are established the new approach significantly broadens the class of methods available for constructing the nonlinear function that is required in the implementation of the reference governors this advantage is illustrated in a nonlinear control problem where off line computer based simulation is the basis for constructing the nonlinear function

stabilization for markovian jump systems with partial information on transition probability based on free connection weighting matrices this paper focuses on stability and stabilization for a class of continuous time markovian jump systems with partial information on transition probability the free connection weighting matrix method is proposed to obtain a less conservative stability criterion of markovian jump systems with partly unknown transition probability or completely unknown transition probability as a result a sufficient condition for the state feedback controller design is derived in terms of linear matrix inequalities finally numerical examples are given to illustrate the effectiveness and the merits of the proposed method

a nonlinear extension of the birkhoff jentzsch theorem abstract the birkhoff jentzsch theorem for linear positive operators is extended to a certain class of nonlinear positive operators these so called p ascending operators include concave operators and suprema of such operators for the underlying positive cone to be complete for hilbert s metric a necessary and sufficient condition is given from which various criteria for completeness are derived the extension made yields in particular a concave version of jentzsch s theorem

global attractivity in concave or sublinear monotone infinite delay differential equations abstract we study the dynamical behavior of the trajectories defined by a recurrent family of monotone functional differential equations with infinite delay and concave or sublinear nonlinearities we analyze different sceneries which require the existence of a lower solution and of a bounded trajectory ordered in an appropriate way for which we prove the existence of a globally asymptotically stable minimal set given by a 1 cover of the base flow we apply these results to the description of the long term dynamics of a nonautonomous model representing a stage structured population growth without irreducibility assumptions on the coefficient matrices

an affine eigenvalue problem on the nonnegative orthant in this paper we consider the conditional affine eigenvalue problem lambda x ax b lambda is an element of r x 0 parallel to x parallel to 1 where a is an n x n nonnegative matrix b a nonnegative vector and parallel to center dot parallel to a monotone vector norm under suitable hypotheses we prove the existence and uniqueness of the solution lambda x and give its expression as the perron root and vector of a matrix a bc t where c has a maximizing property depending on the considered norm the equation x ax b parallel to ax b parallel to has then a unique nonnegative solution given by the unique perron vector of a bc t c 2005 elsevier inc all rights reserved

the omega limit sets of ray contractive operators abstract in this paper we study the omega limit sets of a ray contractive map t without the compactness assumption on the orbits if there exists a compact subset of k the interior of a closed convex cone k such that t and t k 0 k then we are able to prove that x either consists of a single point or forms a cycle 2 periodic orbit for any x k

inhomogeneous iterates of contraction mappings and nonlinear ergodic theorems this paper is motivated by the nonlinear ergodic theory developed by t fujimoto and krause 6 and nussbaum 11 their works depend heavily on projective metrics this motivates us to consider the convergence problems of inhomogeneous iterates in metric spaces and to apply them to study the nonlinear ergodic problems in ordered banach spaces which are related to certain problems from population biology and economics 3 5 throughout this paper x will be a complete metric space let t x x be a mapping we say t is a generalized contraction 7 if any for 0iaibi there exists l a b 0 1 such that d tx ty l a b d x y 1

the contraction mapping approach to the perron frobenius theory why hilbert s metric the perron frobenius theorem says that if a is a nonnegative square matrix some power of which is positive then there exists an x0 such that anx anx converges to xn for all x 0 there are many classical proofs of this theorem all depending on a connection between positively of a matrix and properties of its eigenvalues a more modern proof due to garrett birkhoff is based on the observation that every linear transformation with a positive matrix may be viewed as a contraction mapping on the nonnegative orthant this observation turns the perron frobenius theorem into a special ease of the banach contraction mapping theorem furthermore it applies equally to linear transformations which are positive in a much more general sense the metric which birkhoff used to show that positive linear transformations correspond to contraction mappings is known as hilbert s projective metric the definition of this metric is rather complicated it is therefore natural to try to define another less complicated m

a presic type contractive condition and its applications abstract we study discrete dynamic systems in a complete metric space m d defined by mappings which satisfy presic type contractive conditions their counterparts in an ordered banach space are investigated and applied to solve the global asymptotic stability of the equilibriums of some nonlinear difference equations

set membership identification of nonlinear systems in the paper the problem of identifying nonlinear dynamic systems described in nonlinear regression form is considered using finite and noise corrupted measurements most methods in the literature are based on the estimation of a model within a finitely parametrized model class describing the functional form of involved nonlinearities a key problem in these methods is the proper choice of the model class typically realized by a search from the simplest to more complex ones linear bilinear polynomial neural networks etc in this paper an alternative approach based on a set membership framework is presented not requiring assumptions on the functional form of the regression function describing the relations between measured input and output but assuming only some information on its regularity given by bounds on its gradient in this way the problem of considering approximate functional forms is circumvented moreover noise is assumed to be bounded in contrast with statistical methods which rely on assumptions such as stationarity ergodicity uncorrelation type of distribution etc whose validity may be difficult to test reliably and is lost in presence of approximate modeling in this paper necessary and sufficient conditions are given for the validation of the considered assumptions an optimal interval estimate of the regression function is obtained providing its uncertainty range for any assigned regressor values the set estimate allows to derive an optimal identification algorithm giving estimates with minimal guaranteed l p error on the assigned domain of the regressors the properties of the optimal estimate are investigated and its worst case l p identification error is evaluated the presented approach is tested and compared with other nonlinear methods on the identification of a water heater a mechanical system with input saturation and a vehicle with controlled suspensions

nonlinear models of diffusion on a finite space the basic convergence theorems for finite state markov chains are extended to the nonlinear case an operatort inl1 of a finite space with counting measure is called nonexpansive if tf tg 1 f g 1 holds for allf g it is shown that for anyf there exists an integer p 1 such thattpnf converges sufficient conditions forp 1 are given in the case of continuous parameter nonexpansive semigrous tt t 0 ttf converges fort

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

laplacians on finitely ramified graph directed fractals a finitely ramified graph directed fractal is approximated by an adapted sequence of increasingly refined graphs the scaling problem for a corresponding sequence of discrete laplacians is rephrased via a renormalization map comparing two subsequent graphs a limit set dichotomy for this map is proved the forward orbit always accumulates at periodic points even if the corresponding models are disconnected thus these periodic points can be numerically approximated by an iteration scheme based on the schur complement this allows to turn numerical information via the short cut test into theorems on the existence of laplacians on fractals

invariance control for a class of cascade nonlinear systems we consider the control of partially linear cascade systems using switching control of the states of the linear subsystem we give sufficient conditions under which feedback of the linear states with switching gains guarantees both exponential stability of the linear subsystem and positive invariance of a prespecified region in state space we refer to a control scheme incorporating these two objectives as invariance control semiglobal asymptotic stabilization follows under some additional conditions the key idea of our design is to keep a given state space region positively invariant by switching on the boundary of the region thus the transient response of the system can be kept within prescribed bounds which is important in many practical applications our approach can also be viewed as an alternative to high gain designs the results in this paper can be extended to nonlinear cascades and even to noncascaded systems

characterizations of linear volterra integral equations with nonnegative kernels abstract we first introduce the notion of positive linear volterra integral equations then we offer a criterion for positive equations in terms of the resolvent in particular equations with nonnegative kernels are positive next we obtain a variant of the paley wiener theorem for equations of this class and its extension to perturbed equations furthermore we get a perron frobenius type theorem for linear volterra integral equations with nonnegative kernels finally we give a criterion for positivity of the initial function semigroup of linear volterra integral equations and provide a necessary and sufficient condition for exponential stability of the semigroups

asymptotic behavior of a nonhomogeneous linear recurrence system consider the nonhomogeneous linear recurrence systemxn 1 a bn xn gn where a and bn n 0 1 are square matrices and gn n 0 1 are column vectors in this paper we describe in terms of the initial condition the asymptotic behavior of the solutions of this equation in the case when a has a simple dominant eigenvalue 0 n 0 bn and n 0 0 n gn the proof is based on the duality between the solutions of the above equation and the solutions of the associated adjoint equation as a consequence we obtain a similar result for higher order scalar equations

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

minimal sets in monotone and concave skew product semiflows i a general theory abstract the long term dynamics of a general monotone and concave skew product semiflow is analyzed paying special attention to the region delimited from below by the graph of a semicontinuous subequilibrium or by a minimal set admitting a flow extension different possibilities arise depending on the existence and number or absence of minimal sets strongly above the initially fixed one as well as on the coexistence or not of bounded and unbounded semiorbits on the region previous results are unified and extended and significative differences with the sublinear case are established some scenarios which are impossible in the autonomous or periodic cases may occur in this setting

convergence and stability for essentially strongly order preserving semiflows abstract this paper is concerned with a class of essentially strongly order preserving semiflows which are defined on an ordered metric space and are generalizations of strongly order preserving semiflows for essentially strongly order preserving semiflows we prove several principles which are analogues of the nonordering principle for limit sets the limit set dichtomy and the sequential limit set trichotomy for strongly order preserving semiflows then under certain compactness hypotheses we obtain some results on convergence quasiconvergence and stability in essentially strongly order preserving semiflows finally some applications are made to quasimonotone systems of delay differential equations and reaction diffusion equations with delay and the main advantages of our results over the classical ones are that we do not require the delicate choice of state space and the technical ignition assumption

nonquadratic lyapunov functions for robust control abstract this paper deals with the problem of controlling a linear continuous time system with structured time varying parameter uncertainties and input disturbances with a lyapunov function approach in contrast with most of the previous results in the literature we do not confine our attention to the class of quadratic lyapunov functions conversely the basic motivation of this paper is to determine whether there exist other functions that can be conveniently used as candidate lyapunov functions this question has a positive answer the proposed class is that of polyhedral norms or more generally of polyhedral minkowski functionals we show that the class of these functions is universal in the sense that if the problem of ultimately bounding the state in an assigned convex set via state feedback control can be solved via a lyapunov function and a continuous state feedback compensator then it can be solved via a polyhedral lyapunov function and a possibly different continuous control moreover we show that the control can be piecewise linear a numerical technique for constructing the controller is presented for the case in which the uncertainty constraint sets are polyhedral

on stability and robust stability of positive linear volterra equations we first introduce the notion of positive linear volterra integrodifferential equations then we give some characterizations of these positive equations an explicit criterion and a perron frobenius type theorem for positive linear volterra integrodifferential equations are given then we offer a new criterion for uniformly asymptotic stability of positive equations finally we study stability radii of positive linear volterra integrodifferential equations it is proved that complex real and positive stability radii of positive linear volterra equations under structured perturbations or affine perturbations coincide and can be computed by explicit formulae to the best of our knowledge most of the results of this paper are new

existence and uniqueness of the solution of a space time periodic reaction diffusion equation this paper is concerned with the study of the periodic solutions and the entire solutions of the equation 1 tu a t x u q t x u f t x u where the diffusion matrix a the advection term q and the reaction term f are periodic in t and x we prove that the sign of the periodic principal eigenvalue associated with the linearized problem determines the existence and the uniqueness of the periodic solution introducing another eigenvalue we are able to state uniqueness conditions for the entire solution and to derive the asymptotic behavior of the solutions of the associated cauchy problem

filtering of two dimensional periodic roesser systems subject to dissipativity abstract in this note the problem of dissipativity based filtering of two dimensional 2d periodic roesser systems is investigated a discrete time periodic roesser model extensively used in practical systems is introduced to describe 2d periodic systems moreover it is assumed that the periods of the augmented system in horizontal and vertical directions are the same which can greatly simplify stability analyses by resorting to the periodic lyapunov functional approach that depends on periodical property of the augmented system less conservative results for the existence of 2d periodic filter are presented to ensure the asymptotic stability and 2d q 1 q 2 q 3 dissipativity particularly the parameters of 2d periodic filter are derived with convex optimization method simulation results are provided to verify the effectiveness and merits of the theoretical findings in addition the correlation between optimal dissipative performance indices and different lyapunov functions is revealed

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

a sliding mode approach to h non fragile observer based control design for uncertain markovian neutral type stochastic systems this paper is focused on designing an h sliding mode control for a class of neutral type stochastic systems with markovian switching parameters and nonlinear uncertainties an h non fragile observer subjected to the transition rates of the switching mode is firstly constructed by some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established then the state estimation based sliding mode control law is designed to guarantee the reachability of the sliding surface in finite time interval furthermore a stochastic stability criterion is established for all admissible uncertainties which can guarantee the error system and sliding mode dynamics to be asymptotically stochastic stable with a given disturbance attenuation level finally an example is provided to illustrate the efficiency of the proposed method

on a class of positive linear differential equations with infinite delay abstract we give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a perron frobenius type theorem for positive equations furthermore a novel criterion for the exponential asymptotic stability of positive equations is presented finally we provide a sufficient condition for the exponential asymptotic stability of positive equations subjected to structured perturbations a simple example is given to illustrate the obtained results

exponential synchronization of delayed markovian jump complex networks with generally uncertain transition rates this paper investigates the exponential synchronization problem for a class of markovian jump complex networks mjcns with generally uncertain transition rates gutrs in this gutr neural network model each transition rate can be completely unknown or only its estimate value is known this new uncertain model could be applied to many practical cases based on the lyapunov functional method and kronecker product technique a sufficient condition on the exponentially synchronization in mean square is derived in terms of linear matrix inequalities lmis which can be easily solved by using the matlab lmi toolbox finally one numerical example is well studied to illustrate the effectiveness of the developed method

an extension of maximum and anti maximum principles to a schrodinger equation in r2 abstract strong maximum and anti maximum principles are extended to weak l2 r 2 solutions u of the schrodinger equation u q x u u f x in l2 r 2 in the following form let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the schrodinger operator a q x in l2 r 2 assume that q x q x f is a sufficiently smooth perturbation of a radially symmetric function f 0 and 0 f 1 c const a e in r 2 then there exists a positive number depending upon f such that for every 1 with 1 the inequality 1 u c 1 holds a e in r 2 where c is a positive constant depending upon f and it is shown that such an inequality is valid if and only if the potential q x which is assumed to be strictly positive and locally bounded has a superquadratic growth as x this result is applied to linear and nonlinear elliptic boundary value problems in strongly ordered banach spaces whose positive cone is generated by the eigenfunction 1 in particular problems of existence and uniqueness are addressed

robust shrinkage estimation of high dimensional covariance matrices we address high dimensional covariance estimation for elliptical distributed samples which are also known as spherically invariant random vectors sirv or compound gaussian processes specifically we consider shrinkage methods that are suitable for high dimensional problems with a small number of samples large p small n we start from a classical robust covariance estimator tyler 1987 which is distribution free within the family of elliptical distribution but inapplicable when n p using a shrinkage coefficient we regularize tyler s fixed point iterations we prove that for all n and p the proposed fixed point iterations converge to a unique limit regardless of the initial condition next we propose a simple closed form and data dependent choice for the shrinkage coefficient which is based on a minimum mean squared error framework simulations demonstrate that the proposed method achieves low estimation error and is robust to heavy tailed samples finally as a real world application we demonstrate the performance of the proposed technique in the context of activity intrusion detection using a wireless sensor network

output regulation of linear plants subject to constraints output regulation problems for continuous time linear systems with state and or input constraints are studied the problems are formulated in global and semi global setting by using state or full information feedback the goal of this paper is to develop solvability conditions for the posed problems moreover appropriate regulators are constructed under the solvability conditions to state the solvability conditions clearly a taxonomy of constraints is introduced which delineates the constraints into several categories such a taxonomy of constraints provides a classification of linear plants with constraints and identifies what types of output regulation problems are solvable results developed here include as a special case the results obtained in the literature for systems with only input constraints the constraint taxonomy also identifies some intrinsically hard constraints non right invertible constraints for which the solvability conditions of global semi global output regulation problems are not clear yet as a special case of output regulation we also consider tracking problems with constraints it is shown that if there exists a state feedback controller with a stabilizing domain of attraction then one can find a regulator with a tracking domain of attraction arbitrarily close to the stabilizing domain

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

minimal sets in monotone and sublinear skew product semiflows i the general case abstract the dynamics of a general monotone and sublinear skew product semiflow is analyzed paying special attention to the long term behavior of the strongly positive semiorbits and to the minimal sets four possibilities arise depending on the existence or absence of strongly positive minimal sets and bounded semiorbits as well as on the coexistence or not of bounded and unbounded strongly positive semiorbits previous results are unified and extended and scenarios which are impossible in the autonomous or periodic cases are described

stability analysis of two dimensional markovian jump state delayed systems in the roesser model with uncertain transition probabilities this paper is concerned with the problem of stochastic stability analysis of discrete time two dimensional 2 d markovian jump systems mjss described by the roesser model with interval time varying delays the transition probabilities of the jumping process markov chain are assumed to be uncertain that is they are not exactly known but can be estimated a lyapunov like scheme is first extended to 2 d mjss with delays based on some novel 2 d summation inequalities proposed in this paper delay dependent stochastic stability conditions are derived in terms of linear matrix inequalities lmis which can be computationally solved by various convex optimization algorithms finally two numerical examples are given to illustrate the effectiveness of the obtained results

fault detection for discrete time markov jump linear systems with partially known transition probabilities in this article the fault detection fd problem for a class of discrete time markov jump linear system mjls with partially known transition probabilities is investigated the proposed systems are more general which relax the traditional assumption in markov jump systems that all the transition probabilities must be completely known a residual generator is constructed and the corresponding fd is formulated as an h filtering problem by which the error between residual and fault are minimised in the h sense the linear matrix inequality based sufficient conditions for the existence of fd filter are derived a numerical example on a multiplier accelerator model economic system is given to illustrate the potential of the developed theoretical results

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

nonlinear perron frobenius theory in finite dimensions abstract a nonlinear perron frobenius theory in finite dimensions is described which applies to positively homogeneous and increasing maps sufficient conditions for the existence and uniqueness of eigenvectors in the interior of a cone are developed even when eigenvectors at the boundary of the cone exist several ways to benefit from nonlinearities are pointed out in order to show that the classical linear theory truly deserves nonlinear generalization the main technical novelties are a link between collatz wielandt numbers and g teaux derivatives and the almost one dimensional dynamics of the nonlinear map

delay dependent stability analysis and controller synthesis for markovian jump systems with state and input delays this paper focuses on the problem of delay dependent robust stochastic stability analysis and controller synthesis for markovian jump systems with state and input delays it is assumed that the delays are constant and unknown but their upper bounds are known by constructing a new lyapunov krasovskii functional and introducing some appropriate slack matrices new delay dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities lmis an important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays memoryless state feedback controllers are designed such that the closed loop system is robustly stochastically stable some numerical examples are provided to illustrate the effectiveness of the proposed method