explicit solution to the singular discrete time stationary linear filtering problem a closed form solution to the stationary discrete time linear filtering problem is obtained explicitly in terms of the system state space matrices in the limiting singular case where the measurement noise tends to zero simple expressions in closed form are obtained for the kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the kalman filter closed loop matrix is derived the minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure and a remarkably different behavior of the solution in the minimum and nonminimum phase cases is found

solution to the inverse regulator problem for discrete time systems a complete solution is given for the inverse problem of lq optimal regulators for the discrete time multi input case the kalman equation for discrete time systems is derived to characterize the optimal regulators it is then shown that this equation holds for some quadratic weighting if and only if the feedback satisfies a condition corresponding to the circle criterion for continuous time systems the optimality criterion given here consists of this condition and an additional condition to ensure detectability an example is given to illustrate the results

an influence of unilateral sources and sinks in reaction diffusion systems exhibiting turing s instability on bifurcation and pattern formation abstract we consider a general reaction diffusion system exhibiting turing s diffusion driven instability in the first part of the paper we supplement the activator equation by unilateral integral sources and sinks of the type k u x k d k and k u x k d k these terms measure an average of the concentration over the set k and are active only when this average decreases below or increases above the value of the reference spatially homogeneous steady state which is shifted to the origin we show that the set of diffusion parameters in which spatially heterogeneous stationary solutions can bifurcate from the reference state is smaller than in the classical case without any unilateral integral terms this problem is studied for the case of mixed pure neumann and periodic boundary conditions in the second part of the paper we investigate the effect of both unilateral terms of the type u u and unilateral integral terms on the pattern formation using numerical experiments on the system with well known schnakenberg kinetics

some new results in the theory of negative imaginary systems with symmetric transfer matrix function abstract this note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of analyticity along the same lines of the classic definition of positive real systems under the standing assumption of symmetric transfer functions we then derive a necessary and sufficient condition that characterises negative imaginary transfer functions in terms of a matrix sign condition restricted to the imaginary axis once again following the same line of argument of the standard positive real case using this definition even transfer functions with a pole at the origin with double multiplicity as well as with a possibly negative relative degree can be negative imaginary

on the robustness of lq regulators it is shown that in spite of its large gain and phase margins the linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system may lead to fast unstable closed loop modes

unilateral sources and sinks of an activator in reaction diffusion systems exhibiting diffusion driven instability abstract a reaction diffusion system exhibiting turing s diffusion driven instability is considered the equation for an activator is supplemented by unilateral terms of the type s x u s x u describing sources and sinks active only if the concentration decreases below and increases above respectively the value of the basic spatially constant solution which is shifted to zero we show that the domain of diffusion parameters in which spatially non homogeneous stationary solutions can bifurcate from that constant solution is smaller than in the classical case without unilateral terms it is a dual information to previous results stating that analogous terms in the equation for an inhibitor imply the existence of bifurcation points even in diffusion parameters for which bifurcation is excluded without unilateral sources the case of mixed dirichlet neumann boundary conditions as well as that of pure neumann conditions is described

stochastic turing patterns in the brusselator model a stochastic version of the brusselator model is proposed and studied via the system size expansion the mean field equations are derived and shown to yield to organized turing patterns within a specific parameters region when determining the turing condition for instability we pay particular attention to the role of cross diffusive terms often neglected in the heuristic derivation of reaction diffusion schemes stochastic fluctuations are shown to give rise to spatially ordered solutions sharing the same quantitative characteristic of the mean field based turing scenario in term of excited wavelengths interestingly the region of parameter yielding to the stochastic self organization is wider than that determined via the conventional turing approach suggesting that the condition for spatial order to appear can be less stringent than customarily believed

stability robustness of lq optimal regulators for the performance index with cross product terms suggested are the guaranteed stability margins of lq optimal regulators for the performance index with cross product terms using modified return difference equality sufficient conditions to guarantee the required stability margins are presented as well as the conditions to guarantee the stability margins of standard lq optimal regulators an example for lq optimal control of a dc motor system is given to demonstrate how the weighting matrices can be chosen to guarantee the required stability margins

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

gelation in coagulating systems abstract a review of recent achievements in the theory of sol gel transitions is given this paper outlines the basic ideas of a stochastic approach and describes its possible application as a basis for a theory of gelation in coagulating systems the kinetics of coagulation is described in terms of the probability w to find in the system a given set of monomers dimers etc at time t this approach allows for a consideration of finite coagulating systems i e those containing a finite number of monomeric units the evolution equation for the generating functional of w is formulated and solved exactly for the coagulation kernel proportional to the product of masses of coagulating particles for which the traditional smoluchowski s scheme leads to a paradox related to the loss of the total mass of the coagulating particles this paradox is resolved within the scheme described in this paper it is shown that a single giant object a gel invisible in the thermodynamic limit arises after a critical time and begins to consume the mass of smaller but higher populated fraction the sol this approach is then applied for considering the time evolution of random graphs the distribution of the linked components of a random graph over their orders and numbers of edges is found exactly the paper is concluded with a short consideration of the sol gel transition in systems with instantaneous sinks at large particle mass it is demonstrated how the sol gel transition manifests itself in such systems

bifurcation for a reaction diffusion system with unilateral and neumann boundary conditions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability if supplemented by pure neumann boundary conditions we show by a degree theoretic approach that an obstacle e g a unilateral membrane modeled in terms of inequalities introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable moreover this parameter domain is rather different from the known case when also dirichlet conditions are assumed in particular bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know

analysis of stationary droplets in a generic turing reaction diffusion system solitonlike structures called droplets are found to exist within a paradigm reaction diffusion model that can be used to describe patterning in a number of biological systems for example on the skin of various fish species they have also been found in many other systems that can be modeled with a complex ginzburg landau system these droplets can be analyzed in the biological paradigm model because the system has two nonzero stable steady states that are symmetric however the asymmetric case is more challenging we first review the properties of the paradigm system and then extend a recently developed perturbation technique d gomila et al j opt b quantum semiclassical opt 6 s265 2004 to investigate the weakly asymmetric case we compare the results of our mathematical analysis with numerical simulations and show good agreement in the region where the assumptions hold

brief paper on lossless negative imaginary systems the paper is concerned with the notion of lossless negative imaginary systems and their stabilization using strictly negative imaginary controllers through positive feedback firstly the concept of lossless negative imaginary transfer functions is introduced and some properties of such transfer functions are studied secondly a lossless negative imaginary lemma is given which establishes conditions on matrices appearing in a minimal state space realization that are necessary and sufficient for a transfer function to be lossless negative imaginary thirdly a necessary and sufficient condition is provided for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller finally a flexible structure example is presented to illustrate the theory

three dimensional dissipative structures in reaction diffusion systems abstract we study analytically and numerically the tridimensional pattern selection problem for reaction diffusion systems qualitative agreement is found with the recent experimental results

output feedback negative imaginary synthesis under structural constraints the negative imaginary property is a property that many practical systems exhibit this paper is concerned with the negative imaginary synthesis problem for linear time invariant systems by output feedback control sufficient conditions are developed for the design of static output feedback controllers dynamic output feedback controllers and observer based feedback controllers based on the design conditions a numerical algorithm is suggested to find the desired controllers structural constraints can be imposed on the controllers to reflect the practical system constraints also the separation principle is shown to be valid for the observer based design finally three numerical examples are presented to illustrate the efficiency of the developed theory

on α and d negative imaginary systems this paper is concerned with and d negative imaginary systems the definition of negative imaginary transfer functions is firstly introduced then the relationship between negative imaginary and negative imaginary transfer functions is studied by means of the generalised inverse an negative imaginary lemma is proposed to test the negative imaginary property of transfer functions also a necessary and sufficient condition is provided for the stability of interconnection of negative imaginary systems a state feedback controller design condition is established such that the resulting system is negative imaginary moreover the concept of negative imaginary transfer functions is extended to that of d negative imaginary transfer functions finally the developed results are illustrated by numerical examples

stability robustness of a feedback interconnection of systems with negative imaginary frequency response a necessary and sufficient condition expressed simply as the dc loop gain i e the loop gain at zero frequency being less than unity is given in this note to guarantee the internal stability of a feedback interconnection of linear time invariant lti multiple input multiple output systems with negative imaginary frequency response systems with negative imaginary frequency response arise for example when considering transfer functions from force actuators to colocated position sensors and are commonly important in for example lightly damped structures the key result presented here has similar application to the small gain theorem which refers to the stability of feedback interconnections of contractive gain systems and the passivity theorem which refers to the stability of feedback interconnections of positive real or passive systems a complete state space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided

power spectra methods for a stochastic description of diffusion on deterministically growing domains a central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity generally the mathematical treatments of biological systems have used continuum mean field hypotheses for their constituent parts which ignores any sources of intrinsic stochastic effects in this paper we consider a stochastic space jump process as a description of diffusion i e particles are able to undergo a random walk on a discretized domain by developing analytical fourier methods we are able to probe this probabilistic framework which gives us insight into the patterning potential of diffusive systems further an alternative description of domain growth is introduced with which we are able to rigorously link the mean field and stochastic descriptions finally through combining these ideas it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean field steady state

cyclization in bipartite random graphs in this paper the time evolution of a finite bipartite graph initially comprising two sorts of isolated vertices is considered the graph is assumed to evolve by adding edges one at a time each new edge connects either two linked components and forms a new component of a larger order coalescence of graphs or increases by one the number of edges in a given linked component cycling any state of the graph is thus characterized by the set of occupation numbers the numbers of linked components comprising a given numbers of vertexes of the both sorts and a given number of edges once the rate of appearance of an extra edge in the graph being known the master equation governing the time evolution of the probability to find the random graph in a given state is reformulated in terms of the functional generating the probability to find the evolving graph in a given state the exact solution of the evolution equation for the generating functional applies for analyzing the average population numbers of linked components in the limit of large order of the graph the distribution factorizes into two multipliers one of which is just the spectrum of linked components in the infinite bipartite graph the second multiplier includes the dependence on the total size of the graph both these multipliers contain information on the emergence of the giant component that forms at a critical time

polymers and random graphs asymptotic equivalence to branching processes in 1974 falk and thomas did a computer simulation of flory s equireactive raf polymer model rings forbidden and rings allowed asymptotically the rings forbidden model tended to stockmayer s raf distribution in which the sol distribution sticks after gelation while the rings allowed model tended to the flory version of the raf distribution in 1965 whittle introduced the tree and pseudomultigraph models we show that these random graphs generalize the falk and thomas models by incorporating first shell substitution effects moreover asymptotically the tree model displays postgelation sticking hence this phenomenon results from the absence of rings and occurs independently of equireactivity we also show that the pseudomultigraph model is asymptotically identical to the branching process model introduced by gordon in 1962 this provides a possible basis for the branching process model in standard statistical mechanics

technical communique absolute stability criteria with prescribed decay rate for finite dimensional and delay systems we provide here an extension of popov criterion permitting to check exponential stability with prescribed decay rate otherwise called a stability of nonlinear delay systems with sector bounded nonlinearities as for the celebrated result the main hypothesis is expressed under a frequency form for the delay free case the latter is equivalent to a linear matrix inequality whose solution may be found by widespread algorithms

time evolution of a random graph an initially empty no edges graph of the order of m is assumed to evolve by adding one edge at a time this edge can connect either two linked components and form a new component of a larger order coalescence of graphs or increase by one the number of edges in a given linked component the evolution equation for the generating functional of the probability to find in the system a given set of occupation numbers the numbers of graphs of the order of g having exactly edges at time t is formulated and solved exactly the expression for the graph composition spectrum is derived and analysed in the limit of large m

turing patterns in three dimensions we investigate three dimensional turing patterns in two component reaction diffusion systems the fitzhugh nagumo equation the brusselator and the gray scott model are solved numerically in three dimensions several interconnected structures of domains as well as lamellar hexagonal and spherical domains are obtained as stable motionless equilibrium patterns the relative stability of these structures is studied analytically based on the reduction approximation the relation with the microphase separated structures in block copolymers is also discussed

d stability of polynomial matrices necessary and sufficient conditions are formulated for the zeros of an arbitrary polynomial matrix to belong to a given region d of the complex plane the conditions stem from a general optimization methodology mixing quadratic and semidefinite programming lfrs and rank one lmis they are expressed as an lmi feasibility problem that can be tackled with widespread powerful interior point methods most importantly the d stability conditions can be combined with other lmi conditions arising in robust stability analysis

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

bounds on the solution of the algebraic riccati equation under perturbations in the coefficients abstract this paper is concerned with bounds on symmetric solutions of the continuous algebraic matrix riccati equation under perturbations on its coefficients special emphasis is given to the question of estimating the size of the perturbations on the stabilizing solution of the riccati equation when one or all its coefficients are subject to small perturbations upper bounds on the norm of the perturbations on the stabilizing solution are presented moreover it is shown that these perturbations can be determined as a single valued continuous function of the perturbations on the coefficient of the riccati equation

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

kinetic theory of random graphs from paths to cycles the structural properties of evolving random graphs are investigated treating linking as a dynamic aggregation process rate equations for the distribution of node to node distances paths and of cycles are formulated and solved analytically at the gelation point the typical length of paths and cycles l scales with the component size k as l approximately k 1 2 dynamic and finite size scaling laws for the behavior at and near the gelation point are obtained finite size scaling laws are verified using numerical simulations

comment regarding on delay independant stability of large scale systems with time delays this paper comments the result of a recent paper by xu ibid vol 40 p 930 3 1995 the commenter points out that these results have already been published in a more general framework by him int j contr vol 45 no 6 1987 and the following points are also clarified the state which has to be considered and a connection with the passivity theorem

exponential estimates for retarded time delay systems an lmi approach exponential estimates and sufficient conditions for the exponential stability of linear time delay systems are given the proof make use of lyapunov krasovskii functionals and the conditions are expressed in terms of linear matrix inequalities

unicyclic components in random graphs the distribution of unicyclic components in a random graph is obtained analytically the number of unicyclic components of a given size approaches a self similar form in the vicinity of the gelation transition at the gelation point this distribution decays algebraically uk 4k 1 for k 1 as a result the total number of unicyclic components grows logarithmically with the system size

stochastic turing patterns on a network the process of stochastic turing instability on a scale free network is discussed for a specific case study the stochastic brusselator model the system is shown to spontaneously differentiate into activator rich and activator poor nodes outside the region of parameters classically deputed to the deterministic turing instability this phenomenon as revealed by direct stochastic simulations is explained analytically and eventually traced back to the finite size corrections stemming from the inherent graininess of the scrutinized medium

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

robust d stabilization of a polytope of matrices the problem of stabilization of a polytope of matrices in a subregion d r of the complex plane is revisited a new sufficient condition of robust d r stabilization is given it implies the solution of an lmi involving matrix variables constrained by a non linear algebraic relation some lmi relaxations are first proposed then it is shown that a cone complementarity formulation of this condition allows us to associate an efficient iterative numerical procedure which leads to a low computational burden this algorithm is tested on different numerical examples for which existing approaches in control literature fail

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

pattern fluid interpretation of chemical turbulence the spontaneous formation of heterogeneous patterns is a hallmark of many nonlinear systems from biological tissue to evolutionary population dynamics the standard model for pattern formation in general and for turing patterns in chemical reaction diffusion systems in particular are deterministic nonlinear partial differential equations where an unstable homogeneous solution gives way to a stable heterogeneous pattern however these models fail to fully explain the experimental observation of turbulent patterns with spatio temporal disorder in chemical systems here we introduce a pattern fluid model as a general concept where turbulence is interpreted as a weakly interacting ensemble obtained by random superposition of stationary solutions to the underlying reaction diffusion system the transition from turbulent to stationary patterns is then interpreted as a condensation phenomenon where the nonlinearity forces one single mode to dominate the ensemble this model leads to better reproduction of the experimental concentration profiles for the stationary phases and reproduces the turbulent chemical patterns observed by q ouyang and h l swinney chaos 1 411 1991

influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport however self organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity as illustrated by the behavior of the french flag model in response to intrinsic noise and turing s model when subjected to fluctuations in initial conditions domain growth is known to be a stabilizing factor for the latter though the interaction of intrinsic noise and domain growth is underexplored even in the simplest of biophysical settings previously we developed analytical fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems in this paper we extend our analysis to encompass stochastically growing domains this form of growth can be used only to link the meso and macroscopic domains as the box splitting form of growth on the microscopic scale has an ill defined thermodynamic limit the extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain while stochastically controlling the length of each discretized compartment due to the dependence of diffusion on the domain discretization we find that the description of diffusion cannot be uniquely derived we apply these analytical methods to two justified descriptions where it is shown that under certain conditions diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium without additional kinetics finally a logistically growing domain is considered not only does this show that we can deal with nonmonotonic descriptions of stochastic growth but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary on average

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

finite frequency negative imaginary systems this technical note is concerned with finite frequency negative imaginary ffni systems firstly the concept of ffni transfer function matrices is introduced and the relationship between the ffni property and the finite frequency positive real property of transfer function matrices is studied then the technical note establishes an ffni lemma which gives a necessary and sufficient condition on matrices appearing in a minimal state space realization for a transfer function to be ffni also a time domain interpretation of the ffni property is provided in terms of the system input output and state finally an example is presented to illustrate the ffni concept and the ffni lemma

nonlinear effects on turing patterns time oscillations and chaos we show that a model reaction diffusion system with two species in a monostable regime and over a large region of parameter space produces turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis as a consequence the patterns oscillate in time when varying a single parameter a series of bifurcations leads to period doubling quasiperiodic and chaotic oscillations without modifying the underlying turing pattern a ruelle takens newhouse route to chaos is identified we also examine the turing conditions for obtaining a diffusion driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients these results demonstrate the limitations of the linear analysis for reaction diffusion systems

stochastic reaction and diffusion on growing domains understanding the breakdown of robust pattern formation many biological patterns from population densities to animal coat markings can be thought of as heterogeneous spatiotemporal distributions of mobile agents many mathematical models have been proposed to account for the emergence of this complexity but in general they have consisted of deterministic systems of differential equations which do not take into account the stochastic nature of population interactions one particular pertinent criticism of these deterministic systems is that the exhibited patterns can often be highly sensitive to changes in initial conditions domain geometry parameter values etc due to this sensitivity we seek to understand the effects of stochasticity and growth on paradigm biological patterning models in this paper we extend spatial fourier analysis and growing domain mapping techniques to encompass stochastic turing systems through this we find that the stochastic systems are able to realize much richer dynamics than their deterministic counterparts in that patterns are able to exist outside the standard turing parameter range further it is seen that the inherent stochasticity in the reactions appears to be more important than the noise generated by growth when considering which wave modes are excited finally although growth is able to generate robust pattern sequences in the deterministic case we see that stochastic effects destroy this mechanism for conferring robustness however through fourier analysis we are able to suggest a reason behind this lack of robustness and identify possible mechanisms by which to reclaim it

robust control of linear discrete time systems abstract given a linear discrete time system with additive disturbances a general methodology for designing a stable control algorithm is shown the approach is lyapunov based with certain liberty of tailoring the candidate function for a given problem comparison to the existing solutions based on a variable structure approach is given

on positive realness negative imaginariness and h control of state space symmetric systems this paper studies positive realness and negative imaginariness of state space symmetric systems first a necessary and sufficient condition is provided for a state space symmetric system to be respectively positive real and negative imaginary then an explicit formulation for the infimum of h norm under a mixed h and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem finally three examples are provided to illustrate the main results of the paper

a negative imaginary lemma without minimality assumptions and robust state feedback synthesis for uncertain negative imaginary systems abstract negative imaginary systems have important engineering applications for example in lightly damped flexible structures with collocated position sensors and force actuators this paper proposes a new negative imaginary lemma for generalized negative imaginary systems where the minimality assumption is relaxed the proposed lemma facilitates both analysis and synthesis for negative imaginary systems invoking this result a systematic robust static state feedback synthesis method is proposed in an lmi framework for systems with strictly negative imaginary uncertainty e g unmodeled spill over dynamics in a lightly damped flexible structure assuming all states are available for state feedback two numerical examples are given to show the usefulness of the proposed results

guaranteed stability margins for the discrete time linear quadratic optimal regulator the stability properties of the linear quadratic deterministic optimal regulator are investigated in the discrete time case guaranteed phase and gain margins are obtained for the regulator in terms of the singular values of the matrices of the regulator state space description these margins are compared to their continuous time counterparts and their implication on the regulator robustness is discussed

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

pattern production through a chiral chasing mechanism recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families specifically two of these cell families have been shown to interact through a nonlocal chasing mechanism which has previously been modeled using integro differential equations we extend this framework to include the experimentally observed fact that the cells often exhibit chiral movement in that the cells chase and run away at angles different to the line connecting their centers this framework is simplified through the use of multiple small limits leading to a coupled set of partial differential equations which are amenable to fourier analysis this analysis results in the production of dispersion relations and necessary conditions for a patterning instability to occur beyond the theoretical development and the production of new pattern planiforms we are able to corroborate the experimental hypothesis that the global pigmentation patterns can be dependent on the chirality of the chromatophores

h sub spl infin memoryless control with an spl alpha stability constraint for time delay systems an lmi approach focuses on the design of h sub spl infin memoryless state feedback controllers satisfying some spl alpha stability constraints on the closed loop poles for a class of linear systems with delayed state subject to disturbance inputs a sufficient condition for feasibility is derived in terms of linear matrix inequalities furthermore we also consider a particular optimization problem the maximal bound allowed on time delay such that the prescribed level on disturbance attenuation and the spl alpha stability constraints are still preserved this problem is converted into a linear matrix inequality lmi optimization problem and we give a suboptimal bound on the delay

α stability and robustness of large scale interconnected systems abstract the a stability or the stability with degree of large scale interconnected systems is studied a general stability theorem is established that applies even when the subsystems are governed by a functional differential equation rather than by an o d e this theorem is then applied to robustness the result obtained is a generalization of the well known properties of lq regulators an algorithm enabling the design of a robust controller for a large scale interconnected system is indicated

discrete time loop transfer recovery for systems with nonminimum phase zeros and time delays abstract the purpose of this paper is to study what happens when the discrete time loop transfer recovery ltr procedure is applied to plants with nonminimum phase zeros and with uniform time delay in all channels explicit expressions are given for the asymptotic behavior of the resulting sensitivity function and loop transfer function these results yield a better understanding of the mechanism of the discrete time loop transfer recovery procedure and the design limitations due to nonminimum phase zeros and time delays

robust stability bounds for a class of discrete time regulators with computation delays abstract robust stability of discrete time regulators which utilize state predictors to compensate computation delays is considered novel expressions for the return difference matrices and the complementary sensitivity matrices at the input and the output of the regulator are found to obtain simple bounds for unstructured perturbations robust stability for perturbations of the system matrix and or the gain matrix is also considered under certain restrictions on the nominal system simple bounds for the perturbations are obtained directly from the characteristic equation it is shown that as far as the effect of the computation delays is concerned these bounds are explicitly related to those for the unstructured perturbations

periodic aperiodic and transient patterns in vibrated granular layers abstract experiments on vertically vibrated granular layers in evacuated containers reveal a variety of patterns for acceleration amplitudes above a critical value 2 5 g stripes squares hexagons spirals triangles and targets as well as particle like localized excitations oscillons and fronts kinks between regions with different vibrational phase are observed as the layer depth and the container oscillation frequency and amplitude are varied a zig zag instability unstable hexagons phase disordered patterns and two phase squares are also observed with a few noteworthy exceptions the patterns are essentially independent of the lateral boundary conditions

robust state derivative pole placement lmi based designs for linear systems in some practical problems for instance in the control systems for the suppression of vibration in mechanical systems the state derivative signals are easier to obtain than the state signals necessary and sufficient lmi based conditions for pole placement of linear systems using state derivative feedback are proposed sufficient conditions for pole placement for a class of uncertain systems or systems subject to structural failures are also presented the simulation of practical applications illustrates the efficiency of the proposed methods

a note on tests for positive real functions this technical note presents a modified test for positive realness of scalar real rational functions which avoids the need to test residue conditions necessary and sufficient conditions for the positive realness of some classes of low order real rational functions are given by making use of the modified test

unilateral regulation breaks regularity of turing patterns we consider a reaction diffusion system undergoing turing instability and augment it by an additional unilateral source term we investigate its influence on the turing instability and on the character of resulting patterns the nonsmooth positively homogeneous unilateral term v has favorable properties but the standard linear stability analysis cannot be performed we illustrate the importance of the nonsmoothness by a numerical case study which shows that the turing instability can considerably change if we replace this term by its arbitrarily precise smooth approximation however the nonsmooth unilateral term and all its approximations yield qualitatively similar patterns although not necessarily developing from small disturbances of the spatially homogeneous steady state further we show that the unilateral source breaks the approximate symmetry and regularity of the classical patterns and yields asymmetric and irregular patterns moreover a given system with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same system without any unilateral term

reduced order dynamic compensator design for stability robustness of linear discrete time systems a reduced order dynamic compensator design is presented with stability robustness for linear discrete systems by including a stability robustness component in addition to the standard quadratic state and control terms in the performance criterion the robustness component is based on an unstructured perturbation stability bound for time varying perturbations the controller design is developed by the parameter optimization technique and involves the solution of five algebraic matrix equations four of which are discrete time lyapunov matrix equations

enforcing negative imaginary dynamics on mathematical system models flexible structures with collocated force actuators and position sensors lead to negative imaginary dynamics however in some cases the mathematical models obtained for these systems for example using system identification methods may not yield a negative imaginary system this paper provides two methods for enforcing negative imaginary dynamics on such mathematical models given that it is known that the underlying dynamics ought to belong to this system class the first method is based on a study of the spectral properties of hamiltonian matrices a test for checking the negativity of the imaginary part of a corresponding transfer function matrix is first developed if an associated hamiltonian matrix has pure imaginary axis eigenvalues the mathematical model loses the negative imaginary property in some frequency bands in such cases a first order perturbation method is proposed for iteratively collapsing the frequency bands whose negative imaginary property is violated and finally displacing the

morphological characterization of patterns in reaction diffusion systems received 24 october 1995 morphological measures for spatial patterns occuring as dissipative structures in systems driven far from equilibrium are introduced they characterize the geometry and topology of the patterns and are capable to distinguish irregular structures with respect to the morphology in particular we analyze turbulent and regular patterns turing patterns in chemical reaction diffusion systems observed in a two dimensional open gel reactor with a chlorite iodide malonic acid reaction introducing the concept of level contours the measures turn out to be polynomials of low order cubic and fourth degree in the grey scale level of the images thus the dependence on the experimental conditions is reflected only in a finite number of coefficients which can be used as order parameters for the morphology of patterns we observe a symmetry breaking of the polynomials when the type of the pattern changes from hexagons to turbulence or stripes therefore it is possible to describe the pattern transitions quantitatively and it may be possible to classify them in a similar way like thermodynamic phase transitions

exact kinetics of sol gel transition in a coagulating mixture the formation of a gel in a two component disperse system wherein binary coagulation governs the temporal changes to particle composition spectra is studied under the assumption that the coagulation kernel is proportional to m 1 n 2 m 2 n 1 with m n being the numbers of monomers of the first and the second component in the coalescing pair of particles this model is shown to reveal the sol gel transition i e the formation of one giant cluster with the mass comparable to the total mass of the whole system this paper reports on the exact solution of this model within the marcus lushnikov stochastic scheme the evolution equation for the generating functional of the probability to find in the system a given set of occupation numbers the numbers of particles containing m and n monomers of each component at time t is formulated and solved exactly the expression for the particle composition spectrum is derived and analyzed in the thermodynamic limit it is shown that after a critical time a giant single particle the gel appears the time evolution of its composition is found special attention is given to the transition point where the gel is appearing the time dependencies of the gel composition the number concentration and the second moments of the particle composition spectrum are found

a new dimension to turing patterns abstract it is well known that simple reaction diffusion systems can display very rich pattern formation behaviour here we have studied two examples of such systems in three dimensions first we investigate the morphology and stability of a generic turing system in three dimensions and then the well known gray scott model in the latter case we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources our results raise the question of whether turing patterning can produce an inductive signalling mechanism for neuronal growth