brief paper bounded nash type controls for uncertain linear systems this paper deals with multicriteria controls for systems coping with polytopic uncertainties the proposed controls are inspired by a nash strategy for exactly known systems reformulated as a nonconvex coupling between semi definite programming problems the extension to the uncertain case duplicates the linear matrix inequalities for all vertices of the polytope a new iterative algorithm using semi definite programming is provided to design bounded nash type controls for uncertain systems a numerical example is given to illustrate the design method

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

sobolev bounds on functions with scattered zeros with applications to radial basis function surface fitting in this paper we discuss sobolev bounds on functions that vanish at scattered points in a bounded lipschitz domain that satisfies a uniform interior cone condition the sobolev spaces involved may have fractional as well as integer order we then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions rbfs these estimates include situations in which the target function does not belong to the native space of the rbf

the zak transform and sampling theorems for wavelet subspaces the zak transform is used for generalizing a sampling theorem of g waiter see ieee trans informat theory vol 38 p 881 884 1992 for wavelet subspaces cardinal series based on signal samples f a n n in z with a possibly unequal to 0 waiter s case are considered the condition number of the sampling operator and worst case aliasing errors are expressed in terms of zak transforms of scaling function and wavelet this shows that the stability of the resulting interpolation formula depends critically on a

spreading speeds and traveling waves for periodic evolution systems abstract the theory of spreading speeds and traveling waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case then these abstract results are applied to a periodic system modeling man environment man epidemics a periodic time delayed and diffusive equation and a periodic reaction diffusion equation on a cylinder

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

brief paper stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper is to study the discrete time stochastic h 2 h control with state and external disturbance dependent noise a necessary and sufficient condition for the existence of h 2 h control is presented which transforms the h 2 h controller design into solving four coupled matrix valued equations moreover a recursive algorithm for solving the four coupled matrix valued equations is also given

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

multiobjective boldmath ht hf control design an important question in feedback control design is how to achieve desired performance for dynamical systems subject to both model uncertainties and white noise for this purpose it is desirable to develop a systematic design technique that combines the good aspects of both cal h 2 lqg and cal h infty methods which provides the motivation for the development of multiobjective design framework in this paper encouraged by a time domain game approach for cal h 2 cal h infty control design two multiobjective control design problems are formulated and solved in the time domain results for both the finite time horizon and the infinite time horizon are presented it is shown that all the results can be obtained by solving the corresponding set of coupled riccati equations

robust state estimation for uncertain systems with averaged integral quadratic constraints this paper considers a robust state estimation problem for a new class of uncertain systems the new uncertainty class introduced in the paper involves structured uncertainties which are required to satisfy a certain averaged integral quadratic constraint this uncertainty class combines aspects of norm bounded and stochastic uncertainty descriptions the solution to the robust state estimation problem is obtained by solving a parametrized riccati differential equation of the game type

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

optimal discrete time h γ 0 filtering and control under unknown covariances abstractnew stochastic 0 and mixed h 0 filtering and control problems for discrete time systems under completely unknown covariances are introduced and solved the performance measure 0 is the worst case steady state averaged variance of the error signal in response to the stationary gaussian white zero mean disturbance with unknown covariance and identity variance the performance measure h 0 is the worst case power norm of the error signal in response to two input disturbances in different channels one of which is the deterministic signal with a bounded energy and the other is the stationary gaussian white zero mean signal with a bounded variance provided the weighting sum of disturbance powers equals one in this framework it is possible to consider at the same time both deterministic and stochastic disturbances highlighting their mutual effects our main results provide the complete characterisations of the above performance measures in terms of linear matrix inequalities and therefore both th

h sub spl infin differential riccati equations convergence properties and finite escape phenomena the paper studies the transient and asymptotic behavior of the solution of the sign indefinite differential riccati equation dre arising in finite horizon h sub spl infin filtering and control problems differently from the sign definite h sub spl infin dre the solution of the h sub spl infin dre can have finite escape times even for nonnegative initial conditions sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the h sub spl infin norm attenuation level spl gamma finally a stepwise spl gamma switching strategy is devised to guarantee boundedness as well as asymptotic performance

nonlinear stochastic h_2 h_ infty control with x u v dependent noise infinite horizon case for general nonlinear stochastic ito systems with state control and external disturbance dependent noise the infinite horizon mixed h2 hinfin control is studied it turns out that in order to solve the h2 hinfin control one only needs to solve four cross coupled hamilton jacobi equations a necessary condition and a sufficient condition for the existence of the solution of h2 hinfin controlis respectively presented which extends the previous results to more general models

wiener s lemma for infinite matrices in this paper we introduce a class of infinite matrices related to the beurling algebra of periodic functions and we show that it is an inverse closed subalgebra of mathcal b ell q w the algebra of all bounded linear operators on the weighted sequence space ell q w for any 1 q and any discrete muckenhoupt aq weight w

on the structure and interpolation properties of quasi shift invariant spaces abstract the structure of certain types of quasi shift invariant spaces which take the form v x span l 2 x j j z for an infinite discrete set x x j r is investigated additionally the relation is explored between pairs x and y such that interpolation of functions in v x via interpolants in v y solely from the samples of the original function is possible and stable some conditions are given for which the sampling problem is stable and for which recovery of functions from their interpolants from a family of spaces v y is possible

sampling theorems for shift invariant spaces gabor frames and totally positive functions we study nonuniform sampling in shift invariant spaces and the construction of gabor frames with respect to the class of totally positive functions whose fourier transform factors as hat g xi prod j 1 n 1 2 pi i delta j xi 1 e c xi 2 for delta 1 ldots delta n in mathbb r c 0 in which case g is called totally positive of gaussian type in analogy to beurling s sampling theorem for the paley wiener space of entire functions we prove that every separated set with lower beurling density 1 is a sampling set for the shift invariant space generated by such a g in view of the known necessary density conditions this result is optimal and validates the heuristic reasonings in the engineering literature using a subtle connection between sampling in shift invariant spaces and the theory of gabor frames we show that the set of phase space shifts of g with respect to a rectangular lattice alpha mathbb z times beta mathbb z forms a frame if and only if alpha beta 1 this solves an open problem going back to daubechies in 1990 for the class of totally positive functions of gaussian type the proof strategy involves the connection between sampling in shift invariant spaces and gabor frames a new characterization of sampling sets without inequalities in the style of beurling new properties of totally positive functions and the interplay between zero sets of functions in a shift invariant space and functions in the bargmann fock space

gabor super frames with hermite functions we investigate vector valued gabor frames sometimes called gabor superframes based on hermite functions hn let h h0 h1 hn be the vector of the first n 1 hermite functions we give a complete characterization of all lattices lambda subseteq mathbb r 2 such that the gabor system rm e 2 pi i lambda 2 t bf h t lambda 1 lambda lambda 1 lambda 2 in lambda is a frame for l 2 mathbb r mathbb c n 1 as a corollary we obtain sufficient conditions for a single hermite function to generate a gabor frame and a new estimate for the lower frame bound the main tools are growth estimates for the weierstrass function a new type of interpolation problem for entire functions on the bargmann fock space and structural results about vector valued gabor frames

traveling wave solutions of lotka volterra competition systems with nonlocal dispersal in periodic habitats this paper is concerned with space periodic traveling wave solutions of the following lotka volterra competition system with nonlocal dispersal and space periodic dependence partial derivative u 1 partial derivative t integral r n kappa y x u 1 t y dy u 1 t x u 1 a 1 x b 1 x u 1 c 1 x u 1 x is an element of r n partial derivative u 2 partial derivative t integral r n kappa y x u 2 t y dy u 1 t x u 2 a 2 x b 2 x u 2 c 2 x u 2 x is an element of r n under suitable assumptions the system admits two semitrivial space periodic equilibria u 1 x 0 and 0 u 2 x where u 1 x 0 is linearly and globally stable and 0 u 2 x is linearly unstable with respect to space periodic perturbations by sub and supersolution techniques and comparison principals we show that for any given xi is an element of sn 1 there exists a continuous periodic traveling wave solution of the form u 1 t x u 2 t x phi 1 x ct xi ct xi 4 phi 2 x ct xi ct xi connecting u 1 0 and 0 u 2 and propagating in the direction of xi with speed c c xi where c xi is the spreading speed of the system in the direction of moreover for c c xi we also prove the asymptotic stability and uniqueness of traveling wave solution using squeezing techniques c 2016 elsevier inc all rights reserved

robust stochastic maximum principle for multi model worst case optimization this paper develops a version of the robust maximum principle applied to the minimax mayer problem formulated for stochastic differential equations with a control dependent diffusion term the parametric families of first and second order adjoint stochastic processes are introduced to construct the corresponding hamiltonian formalism the hamiltonian function used for the construction of the robust optimal control is shown to be equal to the sum of the standard stochastic hamiltonians corresponding to each possible value of the parameter the cost function is defined on a finite horizon and contains the mathematical expectation of a terminal term a terminal condition given by a vector function is also considered the optimal control strategies adapted for available information for the wide class of multi model systems given by a stochastic differential equation with parameters from a given finite set are constructed this problem belongs to the class of minimax stochastic optimization problems the p

h norm computation for ltv systems using nonlinear optimal control algorithms we discuss the computation for 2 induced norms of finite horizon linear time varying systems it is well known that 2 induced norm calculating problems can be converted into optimal control problems so with the help of optimal control algorithms we propose a numerical technique for 2 induced norm computation our approach is as follows first we present a new computational method for nonlinear optimal control problems that is numerically reliable stable and robust analysing the convergence property under some assumptions next by modifying the presented method we propose an algorithm for the 2 induced norm calculation of finite horizon linear time varying systems which is essentially different from all other existing methods finally the effectiveness of our algorithm is demonstrated by simulation

propagation speed of travelling fronts in non local reaction diffusion equations abstract the object of this paper is to provide variational formulas characterizing the speed of travelling front solutions of the following nonlocal diffusion equation u t j u u f u where j is a dispersion kernel and f is any of the nonlinearities commonly used in various models ranging from combustion theory of ecology in several situations such as population dynamics it is indeed natural to model the dispersion of a population using such operators furthermore since travelling front solutions are expected to give the asymptotic behaviour in large time for solutions of the above equation it is of the interest to characterize their speed our results based on elementary techniques generalize known results obtained for models involving local diffusion operators

h sup spl infin optimal control for singularly perturbed systems ii imperfect state measurements for pt i see ibid vol 29 no 2 p 401 423 1993 in this paper we study the h sup spl infin optimal control of singularly perturbed linear systems under general imperfect measurements for both finite and infinite horizon formulations using a differential game theoretic approach we first show that as the singular perturbation parameter say spl epsiv 0 approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by and in some cases equal to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions with the bound being computable independently of e and knowing only the slow and fast dynamics of the system we then construct a controller based on the slow subsystem only and obtain conditions under which it delivers a desired performance level even though the fast dynamics are completely neglected the ultimate performance level achieved by this slow controller can be uniformly improved upon however by a composite controller that uses some feedback from the output of the fast subsystem we construct one such controller via a two step sequential procedure which uses static feedback from the fast output and dynamic feedback from an appropriate slow output each one obtained by solving appropriate spl epsiv independent lower dimensional h sup spl infin optimal control problems under some informational constraints we provide a detailed analysis of the performance achieved by this lower dimensional spl epsiv independent composite controller when applied to the full order system and illustrate the theory with some numerical results on some prototype systems

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

traveling waves and spreading speeds for time space periodic monotone systems abstract in this paper we first establish the existence of traveling waves and spreading speeds for time space periodic monotone systems with monostable structure via the poincare maps approach combined with an evolution viewpoint our construction of time space periodic wave profiles also gives rise to a family of almost pulsating waves which is a new observation in time and space periodic media we then apply the developed theory to two species competitive reaction advection diffusion systems and prove that the minimal wave speed exists and coincides with the single spreading speed for such a system no matter whether the spreading speed is linearly determinate we further obtain a set of sufficient conditions for the linear determinacy

h and mixed h2 h control of discrete time t s fuzzy systems with local nonlinear models abstract this paper addresses the h and mixed h 2 h control synthesis problems of nonlinear discrete time systems which are represented by a new type of t s fuzzy models the fuzzy systems consist of local nonlinear models and are with fewer fuzzy rules than the conventional t s fuzzy systems with local linear models a fuzzy control scheme with local nonlinear feedbacks is proposed and h and mixed h 2 h control synthesis conditions are given in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing conditions for designing fuzzy controllers the new ones can be used to design fuzzy controllers based on fewer control rules as well as are with less computational burden in particular the new methods can also give less conservative results a numerical example is given to illustrate the effectiveness of the proposed methods

slanted matrices banach frames and sampling in this paper we present a rare combination of ab stract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sam pling problems we show that for a large class of slanted matrices boundedness below of the corresponding operator in p for some p implies boundedness below in p for all p we use the established result to enrich our understanding of banach frames and obtain new results for irregular sampling problems we also present a version of a non commutative wiener s lemma for slanted matri ces

sampled data h optimal control of time varying systems the sampled data h optimal control problem is studied for time varying systems the problem consists of finding all sampled data controllers with a piece wise constant control signal for which the l2 induced norm from the continuous time disturbance to the continuous time output is less than a specified bound a game theoretic approach is used to obtain a complete solution to the problem in the finite horizon time varying case the solution involves a mixed discrete continuous riccati equation and a variable transformation which takes the problem to a standard discrete finite dimensional h filtering problem

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

the speed of propagation for kpp type problems ii general domains this paper is devoted to nonlinear propagation phenomena in general unbounded domains of rn for reaction diffusion equations with kolmogorov petrovsky piskunov kpp type nonlinearities this article is the second in a series of two and it is the follow up of the paper 7 which dealt which the case of periodic domains this paper is concerned with general domains and we give various definitions of the spreading speeds at large times for solutions with compactly supported initial data we study the relationships between these new notions and analyze their dependence on the geometry of the domain and on the initial condition some a priori bounds are proved for large classes of domains the case of exterior domains is also discussed in detail lastly some domains which are very thin at infinity and for which the spreading speeds are infinite are exhibited the construction is based on some new heat kernel estimates in such domains

pareto suboptimal controllers in multi objective disturbance attenuation problems abstract a multi objective disturbance attenuation problem is considered as a novel framework for control and filtering problems under multiple exogenous disturbances there are n potentially possible disturbance inputs of a system on each of which may act a disturbance from a certain class a disturbance attenuation level is defined for each channel as an induced norm of the operator mapping signals of the corresponding class to the objective output of the system necessary conditions of the pareto optimality are derived it is established that the optimal solutions with respect to a multi objective cost parameterized by weights from an n dimensional simplex are pareto suboptimal solutions and their relative losses compared to the pareto optimal ones do not exceed 1 n n these results are extended to the case when the disturbances acting on different inputs are combined into coalitions the approach is applied to multiple classes of l 2 bounded and impulsive disturbances for which the h 0 optimal controllers as the pareto suboptimal solutions are synthesized in terms of linear matrix inequalities lmis illustrative examples demonstrate the effectiveness of the approach proposed

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

continuous time tracking problems in an h sub spl infin setting a game theory approach this paper investigates the problem of finite horizon h sub spl infin tracking for linear time varying systems three tracking problems are considered depending on whether the reference signal is perfectly known in advance measured on line or previewed in fixed interval of time ahead no a priori knowledge of a dynamic model for the reference signal is assumed a game theory approach to the latter tracking problems is presented where given a specific reference signal the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise necessary and sufficient conditions for the existence of a saddle point equilibrium are determined and h sub spl infin tracking controllers for both the cases of state and output feedback are derived tracking problems for time invariant systems on infinite horizon are also analyzed and time invariant tracking controllers are obtained for zero initial conditions

mixed control the discrete time case abstract a stochastic h and a mixed stochastic h 2 h control problem for discrete time systems are considered and solved conditions for existence of a solution are derived based on the solvability of an equivalent minimax problem in this framework it is possible to consider at the same time both stochastic and deterministic disturbances highlighting their mutual effects the controller can be designed by solving a system of three coupled riccati equations such equations display how the h 2 type minimization problem and the h type constraint influence each other

principal lyapunov exponents and principal floquet spaces of positive random dynamical systems ii finite dimensional systems abstract this is the second part in a series of papers concerned with principal lyapunov exponents and principal floquet subspaces of positive random dynamical systems in ordered banach spaces the current part focuses on applications of general theory developed in the authors paper j mierczy ski w shen principal lyapunov exponents and principal floquet spaces of positive random dynamical systems i general theory trans amer math soc in press http dx doi org 10 1090 s0002 9947 2013 05814 x preprint available at http arxiv org abs 1209 3475 to positive random dynamical systems on finite dimensional ordered banach spaces it is shown under some quite general assumptions that measurable linear skew product semidynamical systems generated by measurable families of positive matrices and by strongly cooperative or type k strongly monotone systems of linear ordinary differential equations admit measurable families of generalized principal floquet subspaces generalized principal lyapunov exponents and generalized exponential separations

deformation of gabor systems abstract we introduce a new notion for the deformation of gabor systems such deformations are in general nonlinear and in particular include the standard jitter error and linear deformations of phase space with this new notion we prove a strong deformation result for gabor frames and gabor riesz sequences that covers the known perturbation and deformation results our proof of the deformation theorem requires a new characterization of gabor frames and gabor riesz sequences it is in the style of beurling s characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of gabor frames without inequalities from lattices to non uniform sets

a game theory approach to mixed h2 h control for a class of stochastic time varying systems with randomly occurring nonlinearities this paper is concerned with the mixed h2 h1 control problem for a class of stochastic time varying systems with nonlinearities the nonlinearities are described by statistical means and could cover several kinds of well studied nonlinearities as special cases the occurrence of the addressed nonlinearities is governed by two sequences of bernoulli distributed white sequences with known probabilities such nonlinearities are named as randomly occurring nonlinearities rons as they appear in a probabilistic way the purpose of the problem under investigation is to design a controller such that the closed loop system achieves the expected h2 performance requirements with a guaranteed h1 disturbance attenuation level a su cient condition is given for the existence of the desired controller by means of the solvability of certain coupled matrix equations by resorting to the game theory approach an algorithm is developed to obtain the controller gain at each sampling instant a numerical example is presented to show the efiectiveness and applicability of the proposed method

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

entire solutions in nonlocal dispersal equations with bistable nonlinearity abstract we consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one dimensional spatial domain a two dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed furthermore we show that such an entire solution is unique up to space time translations and liapunov stable a key idea is to characterize the asymptotic behaviors of the solutions as t in terms of appropriate subsolutions and supersolutions we have to emphasize that a lack of regularizing effect occurs

dilation of the weyl symbol and balian low theorem the key result of this paper describes the fact that for an important class of pseudodifferential operators the property of invertibility is preserved under minor dilations of their weyl symbols this observation has two implications in time frequency analysis first it implies the stability of general gabor frames under small dilations of the time frequency set previously known only for the case that the time frequency set is a lattice secondly it allows us to derive a new balian low theorem blt for gabor systems with window in the standard window class and with general time frequency families in contrast to the classical versions of blt the new blt does not only exclude orthonormal bases and riesz bases at critical density but indeed it even excludes irregular gabor frames at critical density

on a nonlocal equation arising in population dynamics we study a one dimensional nonlocal variant of fisher s equation describing the spatial spread of a mutant in a given population and its generalization to the so called monostable nonlinearity the dispersion of the genetic characters is assumed to follow a nonlocal diffusion law modelled by a convolution operator we prove that as in the classical local problem there exist travelling wave solutions of arbitrary speed beyond a critical value and also characterize the asymptotic behaviour of such solutions at infinity our proofs rely on an appropriate version of the maximum principle qualitative properties of solutions and approximation schemes leading to singular limits

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

principal lyapunov exponents and principal floquet spaces of positive random dynamical systems i general theory this series of papers is concerned with principal lyapunov exponents and principal floquet subspaces of positive random dynamical systems in ordered banach spaces the current part of the series focuses on the development of general theory first the notions of generalized principal floquet subspaces generalized principal lyapunov exponents and generalized exponential separations for general positive random dynamical systems in ordered banach spaces are introduced which extend the classical notions of principal floquet subspaces principal lyapunov exponents and exponential separations for strongly positive deterministic systems in strongly ordered banach to general positive random dynamical systems in ordered banach spaces under some quite general assumptions it is then shown that a positive random dynamical system in an ordered banach space admits a family of generalized principal floquet subspaces a generalized principal lyapunov exponent and a generalized exponential separation we will consider in the forthcoming part s the applications of the general theory developed in this part to positive random dynamical systems arising from a variety of random mappings and differential equations including random leslie matrix models random cooperative systems of ordinary differential equations and random parabolic equations institute of mathematics and computer science wroc law university of technology wybrzeze wyspianskiego 27 pl 50 370 wroc law poland url http www im pwr wroc pl mierczyn index html e mail address mierczyn pwr wroc pl department of mathematics and statistics auburn university auburn university al 36849 usa e mail address wenxish auburn edu 2010 mathematics subject classification primary 37h15 37l55 37a30 secondary 15b52 34f05 35r60

towards a less conservative model predictive control based on mixed ℋ2 ℋ control approach a novel approach to the design of a less conservative model predictive control is proposed using mixed 2 design method for time invariant discrete time linear systems the controller has the form of a state feedback satisfies input and state constraints and is constructed from the solution of a set of feasibility linear matrix inequalities the control law takes into account the disturbances naturally and the input constraint is less conservative in the sense that the full control is used numerical examples comparing the proposed algorithm with some existing techniques are provided to demonstrate the applicability and the advantage of the proposed algorithm

frames in the bargmann space of entire functions we look at the decomposition of arbitrary f in l2 r in terms of the family of functions cp x w exp iimnab iman i x nb 2 with a b 0 we derive bounds and explicit formulas for the minimal expansion coefficients in the case where ab 2w n n an integer 2 2 transported to the hilbert space f of entire functions introduced by v bargmann these results are expressed as inequalities of the form

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

robust stabilization subject to structured uncertainties and mean power constraint abstract this paper deals with a robust stabilization problem for discrete time systems subject to multiple disturbances occurring in controller and actuating channel where both linear structured uncertainties and white gaussian noises are included the desired control law is aimed to robustly stabilize the system and to satisfy some pre specified mean power constraint simultaneously by the philosophy of the mixed h 2 h control a solvability condition is first derived for single input systems that reveals the intrinsic relation between the unstable poles of the plant and the disturbance parameters together with two cross coupled algebraic riccati equations the result is further generalized to multiple input systems with a sufficient condition given again by the unstable poles of the plant an example is included to illustrate the current results

spreading speeds and linear determinacy of time dependent diffusive cooperative competitive systems abstract the current paper is devoted to the study of spreading speeds and linear determinacy of diffusive cooperative competitive systems of the form u t t x a u t x f t u t x x h where h r n or z n a is a random or nonlocal dispersal operator in the cases h r n and is a discrete dispersal operator in the case h z n f t u is cooperative or competitive in u and is recurrent in t which includes f t u is periodic and almost periodic in t as special cases first the notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds and some basic spreading properties are established next some principal lyapunov exponent and principal floquent bundle theory for linear cooperative systems of ordinary differential equations is developed which plays an important role in the study of spreading speeds of diffusive cooperative competitive systems with time dependence and is also of independent interest in terms of the principal lyapunov exponent and principal floquent bundle theory some upper and lower bounds for the spreading speed intervals for diffusive cooperative systems are then established under certain conditions it is proved that a diffusive cooperative system has a single spreading speed and is linearly determinant finally by transforming a diffusive competitive system to a diffusive cooperative system and applying established results for diffusive cooperative systems upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained and linearly determinacy for such systems is discussed

mixed control design numerical optimization approaches this paper presents some new approaches to mixed performance control problems of linear systems the design techniques proposed in this paper are based on numerical search of the norm bounded stable transfer matrix q in the and suboptimal controller parameterizations so that the additional performance specifications are satisfied the design problems are then converted to some finite dimensional non linear unconstrained optimization problems by explicitly parameterizing the or norm bounded stable transfer matrix q for any fixed order finally some two stage optimization algorithms are applied to find the optimal parameters numerical examples have shown significant performance improvements of the proposed algorithms over those in the existing literature

h optimal sampled data control in continuous time systems we consider the design of h optimal discrete time digital controllers in continuous time systems an apparent difficulty especially in utilizing modern transform domain analysis in this context stems from the absence of an appropriate transfer function model for the hybrid time discrete and continuous closed loop system this difficulty is overcome through the introduction of an equivalent difference equation model for the continuous time system with distributed inputs and outputs equivalence being in the sense that the continuous and discrete time inputs and outputs are essentially identical using the interplay between the discrete and the continuous time models solutions of the well known purely continuous time and purely discrete time standard problems extend to solutions of the problem at hand they comprise riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed loop induced input output norm and parameterization of compensators we consid