relating h sub 2 and h sub spl infin norm bounds for sampled data systems we relate the h sub spl infin and h sub 2 norms for multi input multi output sampled data feedback control systems where a continuous time plant is controlled by a digital compensator with hold and sampler upper bounds on both h sub 2 and h sub spl infin norms are obtained based on fundamental relations derived by two different approaches namely the hybrid state space approach and the fast sampling and lifting approach

energy type estimates and global solvability in a two dimensional chemotaxis haptotaxis model with remodeling of non diffusible attractant this paper deals with the coupled chemotaxis haptotaxis model ut u u v u w u 1 u w x t 0 0 v u v x t 0 wt vw w 1 w u x t 0 which was initially proposed by chaplain and lolas 2006 10 to describe the interactions between cancer cells the matrix degrading enzyme and the host tissue in a process of cancer cell invasion of tissue extracellular matrix here r2 is a bounded domain with smooth boundary and and are positive parameters as compared to previous mathematical studies the novelty here consists of allowing for positive values of reflecting processes of self remodeling of the extracellular matrix under zero flux boundary conditions it is shown that for any sufficiently smooth initial data u0 w0 satisfying first order compatibility conditions the model admits a unique global smooth solution a crucial ingredient in the proof is an energy like inequality which given t 0 yields boundedness of u t in llogl this serves as a starting point for a bootstrap argument used to derive higher regularity estimates sufficient for global extensibility of solutions

comparison of peak and rms gains for discrete time systems abstract a convolution system can have a frequency response which is small for all frequencies yet still greatly amplify the peaks of signals passing though it for finite dimensional systems however we establish the simple bound h 1 2 n 1 h h h where h 1 is the peak gain of the system h h is the maximum frequency response of the system and n its dimension the same result for continuous time systems is due to gohberg and doyle and it is mentioned in 6 the bound implies that h optimal controllers which minimize the maximum of some disturbance to error transfer function cannot have very large peak gains from the disturbance to error

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

global existence and boundedness of solutions to a chemotaxis system with singular sensitivity and logistic type source abstract we consider the fully parabolic keller segel system with singular sensitivity and logistic type source u t u u v v r u u k v t v v u under the non flux boundary conditions in a smooth bounded convex domain r n r 0 k 1 a global very weak solution for the system with n 2 is obtained under one of the following conditions i r 2 4 for 0 2 or r max 2 4 1 p 0 2 1 for 2 with p 0 4 k 1 4 2 k k 2 if k 2 1 n 2 ii 2 min 2 r r 2 k 4 k k 1 k 2 if k 2 furthermore this global very weak solution should be globally bounded in fact provided r and the initial data u 0 l 2 v l 4 suitably small for n 2 3 in addition if k 3 n 2 n 4 replaces k 2 in the condition ii the system admits globally bounded classical solutions all these describe the influence of the exponent k 1 in the logistic type source r u u k to the behavior of solutions for the considered fully parabolic keller segel system with singular sensitivity

on the state space and frequency domain characterization of h norm of sampled data systems this paper studies the problem of characterization and computation of the h norm of sampled data systems using the time invariant function space model via lifting with the advantage of time invariance the treatment gives an eigenvalue type characterization first in the operator form in the frequency domain and then in the hamiltonian type finite dimensional form the form obtained can be adopted for use with the bisection algorithm for actual computation

l sub 2 optimal filter reduction a closed loop approach this paper is concerned with the problem of order reduction of a full order kalman filter for a stable linear signal model so that the steady state filtering error variance associated with the reduced order filter is minimized by an orthogonal parameterization the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices both continuous and iterative algorithms are derived to compute an optimal reduced order filter the algorithms are shown to possess good properties including the desirable convergence property the proposed algorithms are simple and effective numerical examples are presented to demonstrate the effectiveness and the significant advantages of the proposed algorithms over the existing open loop methods such as the well known balanced truncation method

a hybrid state space approach to sampled data feedback control this paper develops a state space theory for the study of linear shift invariant finite dimensional hybrid dynamical systems by hybrid system we mean an inputoutput operator relating hybrid signals that is signals which consist of two parts a continuous time part and a discrete time part we first introduce the hybrid state space model and show the closedness properties under the fundamental operations we next investigate the standard basic issues associated with this formalism reachability observability and internal stability we define the notion of hz norm of the hybrid system and show how to evaluate it since the analysis result can be applied to any hybrid system with the proposed hybrid state space model we apply the analysis result to the optimal digital control problem for standard four block configuration with h norm performance measure the solution with computational algorithm is derived for the time delay case

spectral analysis in linear process identification a new look at an old problem the problem of estimating the transfer function frequency response of a linear process by means of a modified spectral analysis method is treated a method of determining the maximum time lags of the correlation functions which makes use of the available a priori physical knowledge about the process and the input signal is proposed this leads in a natural way to the use of an asymmetrical window technique some simulation results are used to illustrate the method based on the asymptotic properties of the estimate the input design is studied finally it will be shown that this work can be used for the estimation of an upper bound of the model uncertainty in the frequency domain

global existence for a kinetic model of pattern formation with density suppressed motilities abstract in this paper we consider global existence of classical solutions to the following kinetic model of pattern formation 0 1 u t v u u 1 u v v u in a smooth bounded domain r n n 1 with no flux boundary conditions here 0 is any given constant the function represents a signal dependent diffusion motility and is decreasing in v which models a density suppressed motility in the process of stripe pattern formation through the self trapping mechanism 9 20 the major difficulty in analysis lies in the possible degeneracy of diffusion as v in the present contribution based on a subtle observation of the nonlinear structure we develop a new method to rule out finite time degeneracy in any spatial dimension for all smooth motility functions satisfying v 0 and v 0 for v 0 then we prove global existence of classical solution for 0 1 in the two dimensional setting with any 0 moreover the global solution is proven to be uniform in time bounded if either 1 satisfies certain polynomial growth condition or 0 besides we pay particular attention to the specific case v e v with 0 under the circumstances system 0 1 becomes of great interest because it shares the same set of equilibria as well as the lyapunov functional with the classical keller segel model a novel critical phenomenon in the two dimensional setting is observed that with any initial datum of sub critical mass the global solution is proved to be uniform in time bounded while with certain initial datum of super critical mass the global solution will become unbounded as time goes to infinity namely blowup takes place in infinite time rather than finite time in our model which is distinct from the well known fact that certain initial data of super critical mass will enforce a finite time blowup for the classical keller segel system

new relations between norms of system transfer functions it is well known that the h2 norm and h norm of a transfer function can differ arbitrarily since both norms reflect fundamentally different properties however if the pole structure of the transfer function is known it is possible to bound the h norm from above by a constant multiple of the h2 norm it is desirable to compute this constant as tightly as possible in this article we derive a tight bound for the h norm given knowledge of the h2 norm and the poles of a transfer function we compute the bound in closed form for multiple input multiple output transfer functions in continuous and discrete time furthermore we derive a general procedure to compute the bound given a weighted l2 norm

how strong a logistic damping can prevent blow up for the minimal keller segel chemotaxis system in this paper we study the minimal keller segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient especially chemotactic aggregation to guarantee boundedness and convergence more specifically we establish how precisely strong a logistic source can prevent blow up and then we obtain an explicit relationship between logistic damping and other ingredient especially chemotactic aggregation so that convergences are ensured and their respective convergence rates are explicitly calculated out known results in the literature are completed and refined furthermore our findings provide clues on how to produce blowup solutions for ks chemotaxis models with logistic sources

global boundedness in a quasilinear chemotaxis system with signal dependent sensitivity abstract this paper deals with a quasilinear parabolic elliptic chemotaxis system with signal dependent sensitivity u t u u u v v x t 0 0 v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n n 2 with nonnegative initial data 0 u 0 c 0 where the given functions u and v are the nonlinear diffusion and chemotactic sensitivity function respectively firstly under the case of non degenerate diffusion u it is proved that the corresponding initial boundary value problem possesses a unique global classical solution that is uniformly bounded in 0 moreover under the case of degenerate diffusion u we prove that the corresponding problem asserts at least one nonnegative global in time bounded weak solution

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity abstract this paper establishes the nonlinear stability of traveling wave solutions to a chemotaxis model with singular or logarithmic sensitivity and its transformed parabolic hyperbolic system depending on the parameter signs we discuss the linear instability of traveling wave solutions using the spectral analysis and nonlinear asymptotic stability of traveling wave solutions with zero end state by the weighted energy estimates where the latter result solves the open question left in a previous work li and wang 2009 7

motion segmentation based on motion brightness integration and oscillatory correlation a segmentation method based on the integration of motion and brightness is proposed for image sequences the method is composed of two parallel pathways that process motion and brightness respectively inspired by the visual system the motion pathway has two stages the first stage estimates local motion at locations with reliable information the second stage performs segmentation based on local motion estimates in the brightness pathway the input scene is segmented into regions based on brightness distribution subsequently segmentation results from the two pathways are integrated to refine motion estimates the final segmentation is performed in the motion network based on refined estimates for segmentation locally excitatory globally inhibitory oscillator network legion architecture is employed whereby the oscillators corresponding to a region of similar motion brightness oscillate in synchrony and different regions attain different phases results on synthetic and real image sequences are provided and comparisons with other methods are made

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

probability one homotopy algorithms for solving the coupled lyapunov equations arising in reduced order h2 h modeling estimation and control optimal reduced order modeling estimation and control with respect to combined h 2 h criteria give rise to coupled lyapunov and riccati equations to develop reliable numerical algorithms for these problems this paper focuses on the coupled lyapunov equations which appear as a subset of the synthesis equations in particular this paper systematically examines the requirements of probability one homotopy algorithms to guarantee global convergence homotopy algorithms for nonlinear systems of equations construct a continuous family of systems and solve the given system by tracking the continuous curve of solutions to the family the main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the coupled lyapunov equations and variations based upon canonical forms these results are essential to the probability one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms

a function space approach to sampled data control systems and tracking problems this paper presents a new framework for hybrid sampled data control systems instead of considering the state only at sampling instants this paper introduces a function piece during the sampling period as the state and gives an infinite dimensional model with such a state space this gives the advantage that sampled data systems with built in intersample behavior can be regarded as linear time invariant discrete time systems as a result the approach makes it possible to introduce such time invariant concepts as transfer functions poles and zeros to the sampled data systems even with the presence of the intersample behavior in particular tracking problems can be studied in this setting in a simple and unified way and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions this leads to the internal model principle for sampled data systems

relating h 2 and h bounds for finite dimensional systems for a linear time invariant system the infinity norm of the transfer function can be used as a measure of the gain of the system this notion of system gain is ideally suited to the frequency domain design techniques such as h infinity optimal control another measure of the gain of a system is the h 2 norm which is often associated with the lqg optimal control problem the only known connection between these two norms is that for discrete time transfer functions the h 2 norm is bounded by the h infinity norm it is shown in this paper that given precise or certain partial knowledge of the poles of the transfer function it is possible to obtain an upper bound of the h infinity norm as a function of the h 2 norm both in the continuous and discrete time cases it is also shown that in continuous time the h 2 norm can be bounded by a function of the h infinity norm and the bandwidth of the system

sampled data control of continuous time systems with an h optimality criterion abstract the synthesis of sampled data controllers for continuous time systems is studied in the context of h control theory the sampled data h optimal control problem consists of finding a sampled data controller which minimizes the l2 induced norm from the continuous time disturbance to the continuous time output the problem is here solved via a discrete system representation this is achieved by describing the closed loop system as a discrete system with finite state dimension and with a representation of the disturbance and the output signals of the discrete system as sequences of elements of certain infinite dimensional spaces via finite rank approximations of a compact integral operator associated with the system the sampled data h control problem can be solved to any degree of accuracy from the structure of the problem it follows that irrespective of the order of the approximation a feasible sampled data controller can be found which has the same order as the system

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

global asymptotic stability of steady states in a chemotaxis growth system with singular sensitivity abstract this paper deals with a fully parabolic chemotaxis growth system with singular sensitivity u t u u ln v r u u 2 x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r 2 where the parameters 0 and r r global existence and boundedness of solutions to the above system were established under some suitable conditions by zhao and zheng 2017 the main aim of this paper is further to show the large time behavior of global solutions which cannot be derived in the previous work

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

blow up prevention by logistic sources in a parabolic elliptic keller segel system with singular sensitivity abstract this paper is concerned with the parabolic elliptic keller segel system with singular sensitivity and logistic source u t u u v v r u u 2 x t 0 0 v v u x t 0 under homogeneous neumann boundary conditions in a smoothly bounded domain r 2 where 0 r r 0 with nonnegative initial data 0 u 0 c 0 it is shown that in this two dimensional setting the absorptive character of the logistic kinetics is sufficient to enforce global existence of classical solutions even for arbitrarily large 0 and any 0 and r r it is moreover shown that if in addition r 0 is sufficiently large then all these solutions are uniformly bounded a main step in the derivation of these results consists of establishing appropriate positive a priori bounds from below for the mass functional u which due to the presence of logistic kinetics is not preserved these in turn provide pointwise lower bounds for v which then allow for the choice of p 1 explicitly depending inter alia on inf v such that u p x t d x can be suitably bounded from above

nonlinear motion estimation using the supercoupling approach this paper presents the application of a very efficient multiresolution transformation which is related to the renormalization group approach of physics to the problem of motion segmentation the approach proposed is much faster and yields much better results than the full resolution approach the problem is formulated as one of global optimization where a cost function is constructed to combine the information obtained by various processors as well as the constraints we impose to the problem the cost function is optimized using the supercoupling multiresolution approach

global boundedness in a quasilinear chemotaxis system with general density signal governed sensitivity abstract in this paper we study the global boundedness of solutions to the quasilinear parabolic chemotaxis system u t d u u s u v 0 v v u subject to homogeneous neumann boundary conditions and the initial data u 0 in a bounded and smooth domain r n n 2 where the diffusivity d u is supposed to satisfy d u a 0 u 1 with a 0 0 and r while the density signal governed sensitivity fulfills 0 s u b 0 u 1 and 0 v v k for b 0 0 and k r it is shown that the solution is globally bounded if 1 2 n k 2 n with n 3 and k 1 or 1 for k 1 this implies that the large k benefits the global boundedness of solutions due to the weaker chemotactic migration of the signal dependent sensitivity at high signal concentrations moreover when arrives at the critical value we establish the global boundedness of solutions for the coefficient properly small it should be emphasized that the smallness of under k 1 is positively related to the total cellular mass u 0 d x which is attributed to the stronger singularity of v at v 0 for k 1 and the fact that v can be estimated from below by a multiple of u 0 d x in addition distinctive phenomena concerning this model are observed by comparison with the known results

formulation and solution of structured total least norm problems for parameter estimation the total least squares tls method is a generalization of the least squares ls method for solving overdetermined sets of linear equations ax spl ap b the tls method minimizes spl par e r spl par sub f where r b a e x so that b r spl isin range a e given a spl isin c sup m spl times n with m spl ges n and b spl isin c sup m spl times 1 the most common tls algorithm is based on the singular value decomposition svd of a b however the svd based methods may not be appropriate when the matrix a has a special structure since they do not preserve the structure previously a new problem formulation known as structured total least norm stln and the algorithm for computing the stln solution have been developed the stln method preserves the special structure of a or a b and can minimize the error in the discrete l sub p norm where p 1 2 or spl infin in this paper the stln problem formulation is generalized for computing the solution of stln problems with multiple right hand sides ax spl ap b it is shown that these problems can be converted to ordinary stln problems with one right hand side in addition the method is shown to converge to the optimal solution in certain model reduction problems furthermore the application of the stln method to various parameter estimation problems is studied in which the computed correction matrix applied to a or a b keeps the same toeplitz structure as the data matrix a of a b respectively in particular the l sub 2 norm stln method is compared with the ls and tls methods in deconvolution transfer function modeling and linear prediction problems

model reduction of large scale systems by least squares abstract in this paper we introduce an approximation method for model reduction of large scale dynamical systems this is a projection which combines aspects of the svd and krylov based reduction methods this projection can be efficiently computed using tools from numerical analysis namely the rational krylov method for the krylov side of the projection and a low rank smith type iteration to solve a lyapunov equation for the svd side of the projection for discrete time systems the proposed approach is based on the least squares fit of the r 1 th column of a hankel matrix to the preceding r columns where r is the order of the reduced system the reduced system is asymptotically stable matches the first r markov parameters of the full order model and minimizes a weighted h 2 error the method is also generalized for moment matching at arbitrary interpolation points application to continuous time systems is achieved via the bilinear transformation numerical examples prove the effectiveness of the approach the proposed method is significant because it combines guaranteed stability and moment matching together with an optimization criterion

h sub spl infin type problem for sampled data control systems a solution via minimum energy characterization this paper aims at deriving a solution for h sub spl infin type problem for sampled data control systems the solution is given in terms of an equivalent discrete time h sub spl infin problem the reduction procedure is viewed and characterized from the viewpoint of minimum energy principle and j unitary transformations

sub logistic source can prevent blow up in the 2d minimal keller segel chemotaxis system it is well known that the neumann initial boundary value problem for the minimal keller segel chemotaxis system in a 2d bounded smooth domain has no blow ups for any presence of logistic source of cell kinetics here for a large class of cell kinetics including sub logistic sources we find an explicit condition involving the chemotactic strength the asymptotic damping rate and the initial mass of cells to ensure the uniform in time boundedness for the corresponding 2d neumann initial boundary value problem our finding in particular shows that sub logistic source can prevent blow up in 2d indicating that logistic damping is not the weakest damping to guarantee boundedness for the 2d keller segel minimal chemotaxis model

boundedness in a fully parabolic chemotaxis system with singular sensitivity abstract this paper deals with a fully parabolic chemotaxis system u t u u v v v t v v u with singular sensitivity v 0 on a bounded domain r n n 2 the main result solves the open problem of uniform in time boundedness of solutions for 2 n which was conjectured by winkler 16

frequency response of sampled data systems this paper develops a frequency domain theory that provides a method to analyze and design sampled data control systems including their intersample behaviors the key idea is to consider the signal space x x t x t n x xn exp j t jn st n x xn 2 where s is the sampling angular frequency it is shown that a stable sampled data system equipped with a strictly proper pre filter before the sampler maps x into x l2 in the steady state that mapping is denoted by q j and is referred to as an fr operator it is proved that the norm of the sampled data system as an operator from l2 to l2 is given by max q j 2 2 where 12 s 12 s a set of equations relating outputs of a closed loop system to its inputs in the frequency domain is derived and their solution is given in an explicit form based on that solution the sensitivity fr operator y j and the complementary sensitivity fr operator t j are defined for feedback control systems and it is shown that y j gives the improvement of the sensitivity of the transfer characteristics from the reference to the controlled output and also represents the ability of rejecting disturbances and that t j represents the degree of robust stability and at the same time gives the effect of detection noises it is also shown that y j t j i and thus a frequency domain paradigm for the design of sampled data control systems which is exactly parallel to the continuous time case is established

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

on a parabolic elliptic system with chemotaxis and logistic type growth we consider a nonlinear pdes system of two equations of parabolic elliptic type with chemotactic terms the system models the movement of a biological population u towards a higher concentration of a chemical agent w in a bounded and regular domain rn for arbitrary n n after normalization the system is as follows ut u div um w u 1 u in t 0 t w w u in t for some positive constants m and with positive initial datum u0 and neumann boundary conditions we study the range of parameters and constrains for which the solution exists globally in time if either m 1 or m 1 and n 22 m 1 n the solution exists globally in time moreover if m 1 and 2 and there exist positive constants u 0 and u 0 such that 0 u 0 u0 u 0 we have that u 1 l w 1 l 0 as t

a lyapunov theory for linear time delay systems some relationships between a lyapunov based stability test and linear control system models with time delays are explored the main result is a generalization of the result that if a b is a reachable pair of matrices then square a is a stability matrix if and only if there is a positive definite matrix k such that ak ka bb

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

a new approach to the discretization of continuous time controllers a new method for discretizing continuous time controllers is derived using principles of controller approximation it focuses on the closed loop use of the discrete time controller the resulting approximation criterion is a measure for stability of the control system provides an upper bound on the sampling time for which stability can be guaranteed and because it is based on continuous time controller approximation it indicates the cost of discretization in terms of performance degradation the discrete time controller is obtained through minimization of this criterion which can be performed with standard software used in h sub infinity controller design

spatio temporal chaos in a chemotaxis model abstract in this paper we explore the dynamics of a one dimensional keller segel type model for chemotaxis incorporating a logistic cell growth term we demonstrate the capacity of the model to self organise into multiple cellular aggregations which according to position in parameter space either form a stationary pattern or undergo a sustained spatio temporal sequence of merging two aggregations coalesce and emerging a new aggregation appears this spatio temporal patterning can be further subdivided into either a time periodic or time irregular fashion numerical explorations into the latter indicate a positive lyapunov exponent sensitive dependence to initial conditions together with a rich bifurcation structure in particular we find stationary patterns that bifurcate onto a path of periodic patterns which prior to the onset of spatio temporal irregularity undergo a periodic doubling sequence based on these results and comparisons with other systems we argue that the spatio temporal irregularity observed here describes a form of spatio temporal chaos we discuss briefly our results in the context of previous applications of chemotaxis models including tumour invasion embryonic development and ecology

brief paper on the stability of a reduced order filter based on dominant singular value decomposition of the system dynamics the stability of a reduced order filter rof the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics is examined a definition of s detectability is introduced it is found that the observability of all unstable and neutral singular vectors s detectability is a sufficient condition for the existence of a stable filter

hankel norm approximation for well posed linear systems the sub optimal hankel norm approximation problem is solved for a well posed linear system with generating operators a b c and transfer function g satisfying some mild assumptions in the special case of the sub optimal nehari problem an explicit parameterization of all solutions is obtained in terms of the system parameters a b c and g 0

asymptotic behavior of solutions to two dimensional chemotaxis system with logistic source and singular sensitivity abstract in this paper we study the asymptotic behavior of solutions to the parabolic elliptic chemotaxis system with singular sensitivity and logistic source u t u u v v r u u 2 0 v v u subject to homogeneous neumann boundary conditions in a bounded domain r 2 with smooth boundary where 0 and r r it is proved that for any nonnegative initial date u 0 c such that u 0 1 16 2 2 with the constant relying on the solution u t v t converges asymptotically to the constant equilibrium r r in the l norm as t if r 2 1 1 2 2 16

model reduction for state space symmetric systems in this paper the model reduction problem for state space symmetric systems is investigated first it is shown that several model reduction methods such as balanced truncation balanced truncation which preserves the dc gain optimal and suboptimal hankel norm approximations inherit the state space symmetric property furthermore for single input and single output siso state space symmetric systems we prove that the h norm of its transfer functions can be calculated via two simple formulas moreover the siso state space symmetric systems are equivalent to systems with zeros interlacing the poles zip under mild conditions

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

a stable state space realization in the formulation of h norm computation in the two block hinftyoptimization problem usually we are given the state space realizations of the proper rational matrices r 1 s and r 2 s whose poles are all the open right half plane two problems are studied in the note the first is the evaluation of phi s r 1 s at s s k k 1 2 n where phi s is an inner function whose zeros s k k 1 2 n are the poles of r 1 s this evaluation is essential if chang and pearson s method is used for computing the optimal hinftynorm the problem is solved in state space via the solutions of lyapunov equations neither polynomial matrix manipulations nor numerical pole zero cancellations are involved in the evaluation the second problem is to find a stable state space realization of s s u s r 2 s where u s is an inner matrix this problem arises in the spectral factorization of gamma 2 r 2 ast r 2 doyle and chu had a method for constructing stable s s based on a minimal realization of r 2 s an alternate method is proposed the alternate method does not require a minimal realization of r 2 s and only a lyapunov equation is involved

a general framework for linear periodic systems with applications to h sup infinity sampled data control the authors present a framework for dealing with continuous time periodic systems the main tool is a lifting technique which provides a strong correspondence between continuous time periodic systems and certain types of discrete time time invariant systems with infinite dimensional input and output spaces despite the infinite dimensionality of the input and output spaces a lifted system has a finite dimensional state space if the original system does this fact permits rather constructive methods for analyzing these systems as a demonstration of the utility of this framework the authors use it to describe the continuous time i e intersample behavior of sampled data systems and to obtain a complete solution to the problem of parameterizing all controllers that constrain the l sup 2 induced norm of a sampled data system to within a certain bound

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

directional interpolation approach to h optimization and robust stabilization it is shown that under a mild condition h infty optimization and robust stabilization are equivalent to a directional interpolation problem which is a matrix extension of the classical pick nevanlinna interpolation problem a classical iterative method which is an extension of the schur nevanlinna algorithm is given for solving the problem this method does not require the inner outer factorization nor the balanced realization of the original plant a circuit theoretical parameterization of all solutions is derived that is expected to enhance the physical insight to the h infty optimal control and robust stabilization this parameterization has the degree much less than the one obtained previously

brief paper balanced truncation model reduction for systems with inhomogeneous initial conditions we present a rigorous approach to extend balanced truncation model reduction btmr to systems with inhomogeneous initial conditions we provide an estimate for the error between the input output maps of the original and of the reduced initial value system and we illustrate numerically the superiority of our approach over the naive application of btmr when btmr is applied to linear time invariant systems with inhomogeneous initial conditions it is crucial that the initial data are well represented by the subspaces generated by btmr this requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero to ensure that the initial data are well represented by the btmr subspaces we add auxiliary inputs determined by the initial data

convolution and hankel operator norms for linear systems some norms are derived for convolution and hankel operators associated with linear time invariant systems in certain cases these norms are shown to be identical the tightest possible bound has been obtained for the absolute magnitude of the euclidean 2 or infinity norm of the time domain response of a multioutput system to certain classes of input disturbance

h sub 2 optimal sampled data control the h sub 2 optimal control of continuous time linear time invariant systems by sampled data controllers is discussed two different solutions state space and operator theoretic are given in both cases the h sub 2 sampled data problem is shown to be equivalent to a certain discrete time h sub 2 problem other topics discussed include input output stability of sampled data systems performance recovery in digital implementation of analog controllers and sampled data control of systems with the possibility of multiple time delays

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

h sub 2 optimal linear robust sampled data filtering design using polynomial approach a new frequency domain approach to robust multi input multi output mimo linear filter design for sampled data systems is presented the system and noise models are assumed to be represented by polynomial forms that are not perfectly known except that they belong to a certain set the optimal design guarantees that the error variance is kept below an upper bound that is minimized for all admissible uncertainties the design problem is cast in the context of h sub 2 via the polynomial matrix representation of systems with norm bounded unstructured uncertainties the sampled data mix of continuous and discrete time systems is handled by means of a lifting technique however it does not increase the dimensionality or alter the computational cost of the solution the setup adopted allows dealing with several filtering problems a simple deconvolution example illustrates the procedure

global existence and asymptotic stability of solutions to a two species chemotaxis system with any chemical diffusion abstract this paper deals with the two species chemotaxis system u t u u 1 w w 1 u 1 u in 0 v t v v 2 w w 2 v 1 v in 0 w t d w h u v w in 0 where is a bounded domain in r n with smooth boundary n n h i are functions satisfying some conditions negreanu tello 2014 2015 12 13 proved global existence and asymptotic behavior of solutions to the above system when 0 d 1 the main purpose of the present paper is to remove the restriction of 0 d 1

eventual smoothness of generalized solutions to a singular chemotaxis stokes system in 2d abstract we study the chemotaxis fluid system n t u n n n c c x t 0 c t u c c n c x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous neumann boundary conditions for n and c and homogeneous dirichlet boundary conditions for u where r 2 is a bounded domain with smooth boundary and c 2 from recent results it is known that for suitable regular initial data the corresponding initial boundary value problem possesses a global generalized solution we will show that for small initial mass n 0 these generalized solutions will eventually become classical solutions of the system and obey certain asymptotic properties moreover from the analysis of certain energy type inequalities arising during the investigation of the eventual regularity we will also derive a result on global existence of classical solutions under assumption of certain smallness conditions on the size of n 0 in l 1 and in l log l u 0 in l 4 and of c 0 in l 2

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