c1 continuous stress recovery in finite element analysis abstract a penalized discrete least squares pdls variational principle is employed to recover c 1 continuous smooth stress fields from finite element stresses the error functional involves discrete least squares with a penalty constraint to enforce c 1 continuity of the recovered stresses the recovery procedure uses a smoothing element analysis sea with element based interpolation functions to minimize the error functional sea pdls recovers a superconvergent stress field of higher accuracy and continuity than the underlying consistent finite element stress field general and specialized formulations of the functional are given and an appropriate discretization strategy for the sea is discussed numerical results for both one and two dimensional stress fields are presented and compared with the corresponding solutions for the superconvergent patch recovery spr method of zienkiewicz and zhu the results demonstrate that in addition to achieving a higher degree of continuity sea pdls produces generally more accurate stresses than spr although an additional global analysis is required results indicate that two coarse mesh analyses finite element and smoothing produce solutions comparable to a single finite element analysis with a much greater degree of refinement and more computational effort the procedure is unique in that the recovered stress field is essentially c 1 continuous the results are shown to be insensitive to the value of the penalty parameter above a threshold and hence uncertainty in the choice of an appropriate penalty value is eliminated

a distributed spatio temporal eeg meg inverse solver we propose a novel l1l2 norm inverse solver for estimating the sources of eeg meg signals based on the standard l1 norm inverse solvers this sparse distributed inverse solver integrates the l1 norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and spiky reconstructed signals often produced by the currently used sparse solvers the joint spatio temporal model leads to a cost function with an l1l2 norm regularizer whose minimization can be reduced to a convex second order cone programming socp problem and efficiently solved using the interior point method the efficient computation of the socp problem allows us to implement permutation tests for estimating statistical significance of the inverse solution validation with simulated and human meg data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting but without the need to specify the number of dipole sources in advance furthermore the l1l2 norm solver achieves fewer false positives and a better representation of the source locations than the conventional l2 minimum norm estimates

positive filtering for continuous time positive systems under l 1 performance in this paper we address the positive filtering problem for positive continuous time systems under the l1 induced performance a pair of positive filters with error bounding feature is proposed to estimate the output of positive systems a novel characterisation is first obtained to ensure that the filtering error system is asymptotically stable with a prescribed l1 induced performance then necessary and sufficient conditions for the existence of required filters are presented and the obtained results are expressed in terms of linear programming problems which can be easily checked by standard software finally a numerical example is given to illustrate the effectiveness of the proposed design procedures

a general method for recovering equilibrating element tractions abstract a new geometrical presentation of a general method for recovering equilibrating element tractions is developed for 2d finite element models of problems in structural mechanics the data for the method consists of the prescribed loading and the stress fields resulting from a conventional linear elastic finite element analysis the geometrical presentation utilises the physical concepts of nodal forces and maxwell force diagrams based on nodal equilibrium only small problems have to be solved for each node this presentation complements the original algebraic approach of ladeveze and extends the method to cover the use of hierarchical p elements in regular meshes and general higher order elements in 1 irregular meshes as encountered in h p mesh refinement the same presentation is considered for the recovery of residual tractions as required in the solution of the local residual problem comparison is made with related methods for obtaining residual tractions in particular those proposed by bank and weiser and ainsworth et al detailed examples are included to illustrate the presentation this paper considers only the fundamental aspects of recovering equilibrating tractions the knowledge gained may be used in various applications such as error analysis limit analysis and structural design

absolute exponential l1 gain analysis and synthesis of switched nonlinear positive systems with time varying delay this paper investigates absolute exponential stability and stabilization with l1 gain performance of switched nonlinear positive systems with time varying delay nonlinear functions considered in the paper are located in a sector field and the time varying delay is unknown but bounded the notion of absolute exponential l1 stability of switched nonlinear positive systems is first introduced a nonlinear lyapunov krasovskii functional is constructed for the underlying systems by using the lyapunov krasovskii functional a sufficient condition for absolute exponential l1 stability of the systems is established in terms of linear programming then absolute exponential l1 control synthesis of the systems is addressed a feedback control law containing nonlinear functions and a state feedback control law are designed respectively by comparing with existing results it is shown that the present design is less conservative finally an illustrative example is provided to illustrate the effectiveness of the results

on l1 gain control of 2 d positive roesser systems with directional delays necessary and sufficient conditions abstract in this paper the problem of l 1 gain control is addressed for two dimensional 2 d positive roesser systems with directional delays a complete solution to the design problem is presented for the first time specifically by exploiting a new approach based on 2 d z transform an exact value of l 1 induced norm of the input output operator is obtained this analytical result is utilized to derive necessary and sufficient conditions under which a 2 d positive system with delays is asymptotically stable with a prescribed l 1 gain performance then by utilizing a vertex optimization approach necessary and sufficient conditions are established for the existence of a state feedback controller sfc that makes the closed loop system positive and stable subject to l 1 induced performance the proposed synthesis conditions are formulated in terms of linear programming lp which can be effectively solved by various convex algorithms to minimize the l 1 performance index

bayesian analysis of the neuromagnetic inverse problem with l p norm priors abstract magnetoencephalography meg allows millisecond scale non invasive measurement of magnetic fields generated by neural currents in the brain however localization of the underlying current sources is ambiguous due to the so called inverse problem the most widely used source localization methods i e minimum norm and minimum current estimates mne and mce and equivalent current dipole ecd fitting require ad hoc determination of the cortical current distribution l 2 l 1 norm priors and point sized dipolar respectively in this article we perform a bayesian analysis of the meg inverse problem with l p norm priors for the current sources this way we circumvent the arbitrary choice between l 1 and l 2 norm prior which is instead rendered automatically based on the data by obtaining numerical samples from the joint posterior probability distribution of the source current parameters and model hyperparameters such as the l p norm order p using markov chain monte carlo mcmc methods we calculated the spatial inverse estimates as expectation values of the source current parameters integrated over the hyperparameters real meg data and simulated known source currents with realistic mri based cortical geometry and 306 channel meg sensor array were used while the proposed model is sensitive to source space discretization size and computationally rather heavy it is mathematically straightforward thus allowing incorporation of for instance a priori functional magnetic resonance imaging fmri information

h_ infty positive filtering for positive linear discrete time systems an augmentation approach in this note we address the reduced order positive filtering problem of positive discrete time systems under the h performance commonly employed approaches such as linear transformation and elimination technique may not be applicable in general due to the positivity constraint of the filter to cope with the difficulty we first represent the filtering error system as a singular system by means of the system augmentation approach which will facilitate the consideration of the positivity constraint two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed h performance then a necessary and sufficient condition is proposed for the existence of the desired positive filters and an iterative linear matrix inequality lmi algorithm is presented to compute the filtering matrices which can be easily checked by standard software finally a numerical example to illustrate the effectiveness of the proposed design procedures is presented

internal positivity preserved model reduction this article studies model reduction of continuous time stable positive linear systems under the hankel norm h norm and h 2 norm performance the reduced order systems preserve the stability as well as the positivity of the original systems this is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the lyapunov matrices are decoupled with the system matrices in this way the positivity constraints in the reduced order model can be imposed in a natural way as the model reduction performances are expressed in linear matrix inequalities with equality constraints the desired reduced order positive models can be obtained by using the cone complementarity linearisation iterative algorithm a numerical example is presented to illustrate the effectiveness of the given methods

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

performance optimization over positive l cones abstract in this paper we study linear systems with positivity type of constraints first we consider the case where the input to a system is restricted to be in the positive cone of l denoted by l and seek to characterize the system s induced norm from l to l we obtain an exact characterization of this norm which is particularly easy to calculate in the case of lti systems furthermore we consider and solve the model matching problem and show that time varying linear or nonlinear control filtering does not improve the performance with respect to this norm for lti systems in the second part of the paper we consider the case when the output is forced to be in the positive l cone when the input is in this cone we show if internal positivity is sought a dynamic optimal controller offers no advantage over a static one also if the measurement matrix satisfies certain conditions synthesizing an optimal static output feedback controller reduces to a linear program

an asynchronous operation approach to event triggered control for fuzzy markovian jump systems with general switching policies this paper investigates the problem of event triggered control for a class of fuzzy markov jump systems with general switching policies a novel event triggered scheme is proposed to improve the transmission efficiency at each sampling instance each transition rate allows to be unknown known or only its uncertain domains value is known with the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller sufficient conditions for the resulting fuzzy markovian jump systems are established in terms of coupled linear matrix inequalities finally an example is given to illustrate the validity of the developed technique

a linear framework on the distributed model predictive control of positive systems abstract this paper investigates the distributed model predictive control dmpc for positive systems with interval and polytopic uncertainties respectively different from the traditional quadratic dmpc a new linear dmpc framework is established for positive systems first a linear cooperative cost function performance index function is introduced for the dmpc of positive systems accordingly some linear constraint conditions are imposed on the systems then a linear co positive lyapunov function is constructed using the linear lyapunov function the dmpc controllers are designed for interval positive systems and polytopic positive systems respectively the controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems linear programming based optimization algorithm is addressed to compute the controller parameters to guarantee the feasibility and stability of the systems a cone invariant set is proposed finally two case studies are provided to illustrate the effectiveness of the theoretical findings

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

static output feedback control of nonhomogeneous markovian jump systems with asynchronous time delays this paper investigates the problem of static output feedback control for a class of nonhomogeneous markovian jump system nmjs with asynchronous time delays atds since the atds subject to uncertain transition probabilities tps are taking into account in a practical phenomenon new approaches are introduced to deal with the atds characterized by nonhomogeneous markov processes it is assumed that the communication links are not perfect due to its detrimental effect on the performance of systems stochastic variables are presented to characterize the data transmission which are depending on operation modes and satisfying the bernoulli distribution sets of slack variables are adopted to decouple the product terms between system matrices and lyapunov matrices based on an extended lyapunov function combined with finsler inequality approach the robust static output feedback controller is designed for the closed loop nmjs finally a numerical example is provided to verify the design method

a comparison between hankel norms and induced system norms a general definition is formulated for the hankel norms as the induced norms of a strictly proper stable linear time invariant lti system mapping vector valued l sup p past inputs to vector valued l sup q future outputs some hankel norms are derived by the maximum principle and duality a property termed the system integral invariance is introduced by the derivation of those hankel norms furthermore the norm induced initial conditions and the comparison between the hankel norms and the induced system norms are also presented

on reachable sets for positive linear systems under constrained exogenous inputs this paper focuses on positive linear time invariant systems with constant coefficients and specific exogenous disturbance the problem of finding a hyper pyramid to bound the set of the states that are reachable from the origin in the euclidean space is addressed subject to inputs whose 1 1 norm or 1 norm is bounded by a prescribed constant the lyapunov approach is applied and a bounding hyper pyramid is obtained by solving a set of inequalities iterative procedures with an adjustable parameter for reducing the hyper volume of the bounding hyper pyramid for the reachable set are proposed

stability and l1 gain analysis of linear periodic piecewise positive systems this paper investigates the stability stabilization and l1 gain of linear periodic piecewise positive systems the monotonicity of linear periodic piecewise positive systems is first studied then a time varying co positive lyapunov function for periodic piecewise positive systems is employed and a sufficient condition for the asymptotic stability of the system is established based on the provided co positive lyapunov function and the sufficient stability condition a state feedback periodic piecewise controller to stabilize the system is formed and an upper bound of l1 gain of the system is given finally numerical examples are given to illustrate the theoretical results

l gain analysis for positive systems with distributed delays this paper addresses the l gain analysis problem of positive linear systems with distributed delays by virtue of the positivity and linearity of the system we first study the monotonic and asymptotic property of the system with distributed delays then by resorting to an auxiliary system without time delay an explicit expression of the l gain of positive systems with distributed delays is given in terms of system matrices moreover the results are extended to positive systems with distributed delays over a bounded time varying interval finally a necessary and sufficient condition on the l gain of an asymptotically stable positive system with distributed delays is presented via linear programming

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

constrained control of positive systems with delays this technical note addresses controller design for continuous time delayed linear systems the control is under positivity constraint which means that the resulting closed loop systems are not only stable but also positive bounded control is also considered further requiring that the trajectory of the closed loop system is bounded by a prescribed boundary if the initial condition is bounded by the same boundary the contribution lies in three aspects first some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint second a necessary and sufficient condition is established determining whether the trajectory of a positive system can be bounded by a prescribed boundary provided that the initial condition is bounded by the same boundary third a sufficient condition is presented for bounded control and it is shown to be also necessary if asymptotic stability is not required

positive filtering for positive takagi sugeno fuzzy systems under l 1 performance in this paper the positive filtering problem is addressed for positive takagi sugeno t s fuzzy systems under the 1 induced performance to estimate the output of positive t s fuzzy systems error bounding positive filters are constructed a new performance characterization is first established to guarantee the asymptotic stability of the filtering error system with the 1 induced performance moreover sufficient conditions expressed by linear programming problems are derived to design the required filters finally a numerical example is presented to show the effectiveness of the derived theoretical results

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties in this paper the problem of robust dynamic output feedback control for a class of discrete time nonlinear systems with parametric uncertainties is studied the parametric uncertainties are assumed to be of a linear fractional form first the takagi sugeno t s fuzzy model is employed to represent the nonlinear system then novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities lmis the proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods

on the existence of a positive realization the positive realization problem for linear systems is to find conditions for a given transfer function with nonnegative impulse response to have a realization such that the resulting system is a positive system recently it has been shown that under a mild assumption on the long term behaviour of the impulse response this problem is related to the maximum modulus poles only in this paper necessary and sufficient conditions for positive realizability of discrete time systems are given they show that also nondominant poles play a role in the most general case positive realizability conditions for the continuous time case are also given

bayesian electromagnetic spatio temporal imaging of extended sources with markov random field and temporal basis expansion estimating the locations and spatial extents of brain sources poses a long standing challenge for electroencephalography and magnetoencephalography e meg source imaging in the present work a novel source imaging method bayesian electromagnetic spatio temporal imaging of extended sources besties which is built upon a bayesian framework that determines the spatio temporal smoothness of source activities in a fully data driven fashion is proposed to address this challenge in particular a markov random field mrf which can precisely capture local cortical interactions is employed to characterize the spatial smoothness of source activities the temporal dynamics of which are modeled by a set of temporal basis functions tbfs crucially all of the unknowns in the mrf and tbf models are learned from the data to accomplish model inference efficiently on high resolution source spaces a scalable algorithm is developed to approximate the posterior distribution of the source activities which is based on the variational bayesian inference and convex analysis the performance of besties is assessed using both simulated and actual human e meg data compared with l2 norm constrained methods besties is superior in reconstructing extended sources with less spatial diffusion and less localization error by virtue of the mrf besties also overcomes the drawback of over focal estimates in sparse constrained methods

vector based spatial temporal minimum l1 norm solution for meg abstract minimum l1 norm solutions have been used by many investigators to analyze meg responses because they provide high spatial resolution images however conventional minimum l1 norm approaches suffer from instability in spatial construction and poor smoothness of the reconstructed source time courses activity commonly jumps from one grid point to usually the neighboring grid points equivalently the time course of one specific grid point can show substantial spiky looking discontinuity in the present study we present a new vector based spatial temporal analysis using a l1 minimum norm vestal this approach is based on a principle of meg physics the magnetic waveforms in sensor space are linear functions of the source time courses in the imaging space our computer simulations showed that vestal provides good reconstruction of the source amplitude and orientation with high stability and resolution in both the spatial and temporal domains spiky looking discontinuity was not observed in the source time courses importantly the simulations also showed that vestal can resolve sources that are 100 correlated we then examined the performance of vestal in the analysis of human median nerve meg responses the results demonstrated that this method easily distinguishes sources very spatially close to each other including individual primary somatosensory areas ba 1 2 3b primary motor area ba 4 and other regions in the somatosensory system e g ba 5 7 sii sma and temporal parietal junction with high temporal stability and resolution vestal s potential for obtaining information on source extent was also examined

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

stability analysis of linear delay systems with cone invariance this paper is concerned with the stability and input output gain analysis of linear delay systems with cone invariance based on the partial ordering over a cone the monotonicity of the trajectory of the cone preserving systems with constant delays is first studied then by comparing the trajectory of the constant delay systems and that of time varying delay systems we prove that a cone preserving system with interval time varying delays is asymptotically stable if and only if the corresponding delay free system is asymptotically stable this implies that the stability of a cone preserving system is insensitive to the magnitude of the delays moreover based on the cone induced norms an explicit characterization on the cone induced gain of an input output cone preserving system is given in terms of system matrices finally numerical examples are provided to illustrate the theoretical results

reachability properties of continuous time positive systems in this technical note reachability properties of continuous time positive systems are introduced and characterized specifically first it is shown that reachability and strong reachability are equivalent properties and thus the characterization of strong reachability derived in is extended to the weaker notion of reachability in the second part of the technical note essential reachability is introduced and necessary and sufficient conditions for this property to hold are provided

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

stochastic stability of positive markov jump linear systems abstract this paper investigates on the stability properties of positive markov jump linear systems pmjls s i e markov jump linear systems with nonnegative state variables specific features of these systems are highlighted in particular a new notion of stability exponential mean stability is introduced and is shown to be equivalent to the standard notion of 1 moment stability moreover various sufficient conditions for exponential almost sure stability are worked out with different levels of conservatism the implications among the different stability notions are discussed it is remarkable that thanks to the positivity assumption some conditions can be checked by solving linear programming feasibility problems

stochastic stability of ito differential equations with semi markovian jump parameters in this note the problem of stochastic stability for linear systems with jump parameters being semi markovian rather than full markovian is further investigated in particular the system under consideration is described by ito type nonlinear stochastic differential equations with phase type semi markovian jump parameters stochastic stability conditions are presented

dynamic output feedback control for continuous time interval positive systems under l1 performance this paper is concerned with the design of l1 induced dynamic output feedback controller for continuous time positive systems with interval uncertainties a necessary and sufficient condition for stability and l1 induced performance of positive linear systems is proposed in terms of linear inequalities based on this conditions for the existence of robust dynamic output feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions one illustrative example is provided to show the effectiveness and applicability of the theoretical results

finite time h static output control of markov jump systems with an auxiliary approach this paper considers the finite time h static output feedback control of markov jump systems with the help of introducing two new variables related to the original system state and output sufficient conditions for the closed loop system to be stochastic finite time boundedness with the prescribed h performance level are proposed in terms of linear matrix inequalities lmis meanwhile the static output control gains are solved explicitly by the proposed conditions it is shown that the proposed method is less or at least the same conservative than the existing result lastly a numerical example is given to demonstrate the effectiveness of the proposed method

controller design for time delay system with stochastic disturbance and actuator saturation via a new criterion abstract this paper deals with the problem of controller design for time delay system with stochastic disturbance and actuator saturation by use of more appropriate lyapunov krasovskii functional lkf and a new criterion for the domain of attraction less conservative conditions for stochastic stability are proposed then the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome these sufficient conditions are derived in terms of linear matrix inequality lmi finally two practical examples demonstrate the validity of the given results

stochastic stability and stabilization conditions of semi markovian jump systems with mode transition dependent sojourn time distributions this paper is concerned with the stochastic stability and stabilization problem for a class of continuous time semi markovian jump systems s mjss with mode transition dependent sojourn time distributions in contrast to other approaches this paper offers the possibility to explore more refined probability models on the sojourn time by considering the mode transition dependent sojourn time distributions instead of mode dependent ones here to construct a finite set of linear matrix inequalities lmis from sojourn time dependent matrix inequalities a less conservative relaxation method is proposed in such a way that all available constraints on time varying transition rates can be exploited simulation examples report the effectiveness of the proposed method

evaluation of cortical current density imaging methods using intracranial electrocorticograms and functional mri abstract objective eeg source imaging provides important information regarding the underlying neural activity from noninvasive electrophysiological measurements the aim of the present study was to evaluate source reconstruction techniques by means of the intracranial electrocorticograms ecogs and functional mri methods five source imaging algorithms including the minimum norm least square mnls loreta with l p norm p equal to 1 1 5 and 2 sloreta the minimum l p norm p equal to 1 and 1 5 when p 2 the mnls method is mathematically equivalent to the minimum l p norm and l 1 norm the linear programming methods were evaluated in a group of 10 human subjects in a paradigm with somatosensory stimulation cortical current density ccd distributions were estimated from the scalp somatosensory evoked potentials seps at approximately 30 ms following electrical stimulation of median nerve at the wrist realistic geometry boundary element head models were constructed from the mris of each subject and used in the ccd analysis functional mri results obtained from a motor task and sensory stimulation in all subjects were used to identify the central sulcus motor and sensory areas in three patients undergoing neurosurgical evaluation ecogs were recorded in response to the somatosensory stimulation and were used to help determine the central sulcus and the sensory cortex results the ccd distributions estimated by the l p norm and loreta l p methods were smoother when the p values were high the loreta based on the l 1 norm performed better than the loreta l 2 method for imaging well localized sources such as the p30 component of the sep the mean and standard deviation of the distance between the location of maximum ccd value and the central sulcus estimated by the minimum l p norm with p equal to 1 l 1 norm the linear programming and loreta l p with p equal to 1 methods were 4 7 7 mm and 3 4 2 mm respectively after converting into talairach coordinates the mean and standard deviation of the aforementioned distance estimated by the mnls loreta with l p norm p equal to 1 5 and 2 0 sloreta and the minimum l p norm p equal to 1 5 methods were over 11 mm and 6 mm respectively conclusions the present experimental study suggests that l 1 norm based algorithms provide better performance than l 2 and l 1 5 norm based algorithms in the context of ccd imaging of well localized sources induced by somatosensory electrical stimulation of median nerve at the wrist

functional magnetic resonance inverse imaging of human visuomotor systems using eigenspace linearly constrained minimum amplitude elcma beamformer recently proposed dynamic magnetic resonance mr inverse imaging ini is a novel parallel imaging reconstruction technique capable of improving the temporal resolution of blood oxygen level dependent bold contrast functional mri fmri to the order of milliseconds at the cost of moderate spatial resolution volumetric ini reconstructs spatial information from projection data by solving ill posed inverse problems using simultaneous acquisitions from a rf coil array previously a spatial filtering technique based on linearly constrained minimum variance lcmv beamformer was suggested to localize the hemodynamic changes of dynamic ini data with improved spatial resolution and sensitivity here we report an advancement of the spatial filtering method which combines the eigenspace projection of the measured data and the l1 norm minimization of the spatial filters output noise amplitude to further improve the detection power of bold contrast fmri data using numerical simulation and in vivo data we demonstrate that this eigenspace linearly constrained minimum amplitude elcma beamformer can reconstruct spatiotemporal hemodynamic signals with high statistical significance values and high spatial resolution in event related two choice reaction time visuomotor experiments

technical communique analysis and design of aimd congestion control algorithms in communication networks we present a model of a network of synchronised sources operating additive increase multiplicative decrease aimd congestion control algorithms we show i that networks of such devices in the presence of a drop tail bottleneck buffer may be modelled as a positive linear system ii that such networks possess a unique stationary point and iii that this stationary point is globally exponentially stable we use these results to establish conditions for the fair co existence of traffic in networks employing heterogeneous aimd algorithms and to design a new protocol for operation over high speed and long distance links

disturbance attenuation and rejection for stochastic markovian jump system with partially known transition probabilities in this paper the problem of disturbance attenuation and rejection is investigated for stochastic markovian jump system with multiple disturbances which include white noises and disturbances with partially known information a disturbance observer is designed to estimate the disturbances with partially known information based on the estimation value a disturbance observer based attenuation and rejection controller is constructed such that the closed loop system is asymptotically bounded in mean square or asymptotically stable in probability under different conditions finally a numerical example is given to illustrate the effectiveness of the proposed approach

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

stability analysis and control synthesis for positive semi markov jump systems with time varying delay abstract this paper deals with stability analysis and control synthesis for positive semi markov jump systems s mjss with time varying delay in which the stochastic semi markov process related to nonexponential distribution is considered the main motivation for this paper is that the positive condition sometimes needs to be considered in s mjss and the controller design methods in the existing have some conservation to deal with these problems the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition then some sufficient conditions for stochastic stability of positive s mjss are established by implying the linear lyapunov krasovskii functional depending on the bound of time varying delay furthermore an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed loop system is positive and stochastically stable in standard linear programming the advantages of the new framework lie in the following facts 1 the weak infinitesimal operator is derived for s mjss with time varying delay under the constraint of positive condition and 2 the less conservative stabilizing controller is designed to achieve the desired control performance finally three examples one of which is the virus mutation treatment model are given to demonstrate the validity of the main results

continuum and discrete models for structures including quasi inextensible elasticae with a view to the design and modeling of composite reinforcements abstract inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials some discrete models including quasi inextensible elasticae are considered a class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed some of these continuum models can be regarded as a special kind of second gradient elastic media in which the higher gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice the discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted the obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites the introduced discrete and continuum models are used to describe the so called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory however as discussed throughout the paper in the context of rigorous micro macro identification procedures there still remain many open problems to be solved especially when dealing with systems subjected to particular constraints such as inextensibility

space time event sparse penalization for magneto electroencephalography this article presents a new spatio temporal method for m eeg source reconstruction based on the assumption that only a small number of events localized in space and or time are responsible for the measured signal each space time event is represented using a basis function expansion which reflects the most relevant or measurable features of the signal this model of neural activity leads naturally to a bayesian likelihood function which balances the model fit to the data with the complexity of the model where the complexity is related to the number of included events a novel expectation maximization algorithm which maximizes the likelihood function is presented the new method is shown to be effective on several meg simulations of neurological activity as well as data from a self paced finger tapping experiment

on inter element forces in the fem displacement formulation and implications for stress recovery this paper describes a new technique for the determination of the inter element forces and tractions as well as stress state at nodes as a post processing step after the solution of standard fe displacement calculation the work is motivated in the context of a broader development of a procedure to simulate fracture processes using a discrete approach without the need of double noded interface elements the technique easily implementable is based on the double minimization of an objective function representing the error between the inter element stress tractions and the projection of the best fit stress tensor t along the planes of the interfaces converging at an element corner node the formulation is illustrated with some basic examples in which the resulting stress tensors and inter element forces are compared to theoretical solutions and to the results obtained by using a traditional stress average smoothing method

stability analysis and l1 gain characterization for switched positive systems under dwell time constraint abstract this paper deals with the problems of stability analysis and l 1 gain characterization for continuous time switched systems consisting of positive subsystems with the aid of a discretized copositive lyapunov function a sufficient condition ensuring the asymptotic stability of continuous time switched positive systems under dwell time constraint is obtained which can be checked via linear programming furthermore the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive lyapunov function is obtained the result is then extended to l 1 gain characterization for switched positive systems with a prescribed dwell time an unweighted l 1 gain can be computed via solving a linear programming problem a numerical example and a practical traffic example are given to illustrate our results

l induced output feedback controller synthesis for positive nonlinear systems via t s fuzzy model approach abstract this paper investigates the l induced output feedback controller synthesis problem for positive takagi sugeno t s fuzzy systems for positive t s fuzzy systems a sufficient condition for stability and l induced performance is first put forward using a group of linear inequalities then on the basis of these inequalities the conditions on which static output feedback controllers exist are set up and to solve these conditions a method of iterative convex optimization is provided moreover a complete solution to the synthesis problem of the controller is proposed based on linear programming for positive t s fuzzy systems with single output or input finally two examples are presented to illustrate and verify the effective and applicable methods derived in this paper

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

combining sparsity and rotational invariance in eeg meg source reconstruction we introduce focal vector field reconstruction fvr a novel technique for the inverse imaging of vector fields the method was designed to simultaneously achieve two goals a invariance with respect to the orientation of the coordinate system and b a preference for sparsity of the solutions and their spatial derivatives this was achieved by defining the regulating penalty function which renders the solutions unique as a global l 1 norm of local l 2 norms we show that the method can be successfully used for solving the eeg inverse problem in the joint localization of 2 3 simulated dipoles fvr always reliably recovers the true sources the competing methods have limitations in distinguishing close sources because their estimates are either too smooth loreta minimum l 1 norm or too scattered minimum l 2 norm in both noiseless and noisy simulations fvr has the smallest localization error according to the earth mover s distance emd which is introduced here as a meaningful measure to compare arbitrary source distributions we also apply the method to the simultaneous localization of left and right somatosensory n20 generators from real eeg recordings compared to its peers fvr was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge

new explicit microplane model for concrete theoretical aspects and numerical implementation abstract the microplane model is a powerful approach for the representation of the complex triaxial behavior of concrete and other similar materials however most efforts in previous formulations were devoted to the development of the model itself and to the experimental data fitting rather than to a comprehensive theoretical description or to attainment of a modular and computationally efficient implementation in a computer code in this paper these objectives are pursued the formulation of the model has been modified to rationalise the structure of the basic hypotheses simplify the equations and generalise the concepts whenever possible the result is a new formulation which while retaining the favorable properties achieved previously is also easier to understand and convenient for computer implementation and large scale calculations a computational scheme is presented with the unified structure of a general code serving the double purpose of lest specimen analysis and finite element analysis in practice this structure includes two different main programs which call the same set of constitutive subroutines a salient feature of the new version of the model is that the compulation of the stress corresponding to a prescribed strain increment of finite si e is fully explicit step by step numerical integration usually necessary for the practical use of constitutive models can be avoided consequently the complexity of the code and the cost of computations can be dramatically reduced some examples of applications used to verify the previous version of the model are also presented they demonstrate that this new formulation gives a much better numerical efficiency for code implementation while keeping the same desirable features and accuracy in experimental data fitting

linear copositive lyapunov functions for continuous time positive switched systems continuous time positive systems switching among p subsystems are introduced and a complete characterization for the existence of a common linear copositive lyapunov function for all the subsystems is provided when the subsystems are obtained by applying different feedback control laws to the same continuous time single input positive system the above characterization leads to a very easy checking procedure

dissipativity theory for nonnegative and compartmental dynamical systems with time delay nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous however in many engineering and life science systems transfers between compartments are not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments including some information of past system states in the system model leads to infinite dimensional delay nonnegative dynamical systems in this note we develop dissipativity theory for nonnegative dynamical systems with time delay using linear storage functionals with linear supply rates these results are then used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems with time delay

spatially sparse source cluster modeling by compressive neuromagnetic tomography magnetoencephalography enables non invasive detection of weak cerebral magnetic fields by utilizing super conducting quantum interference devices squids solving the meg inverse problem requires reconstructing the locations and orientations of the underlying neuronal current sources based on the extracranial measurements most inverse problem solvers explicitly favor either spatially more focal or diffuse current source patterns naturally in a situation where both focal and spatially extended sources are present such reconstruction methods may yield inaccurate estimates to address this problem we propose a novel compressive neuromagnetic tomography cent method based on the assumption that the current sources are compressible the compressibility is quantified by the joint sparsity of the source representation in the standard source space and in a transformed domain the purpose of the transformation sparsity constraint is to incorporate local spatial structure adaptively by exploiting the natural redundancy of the source configurations in the transform domain by combining these complementary constraints of standard and transformed domain sparsity we obtain source estimates which are not only locally smooth and regular but also form globally separable clusters in this work we use the l1 norm as a measure of sparsity and convex optimization to yield compressive estimates in a computationally tractable manner we study the laplacian matrix centl and spherical wavelets centw as alternatives for the transformation in the compression constraint in addition to the two prior constraints on the sources we control the discrepancy between the modeled and measured data by restricting the power of residual error below a specified value the results show that both centl and centw are capable of producing robust spatially regular source estimates with high computational efficiency for simulated sources of focal diffuse or combined types the cent method shows better accuracy on estimating the source locations and spatial extents than the minimum l1 norm or minimum l2 norm constrained inverse solutions different transformations yield different benefits by utilizing cent with the laplacian matrix it is possible to suppress physiologically atypical activations extending across two opposite banks of a deep sulcus with the spherical wavelet transform cent can improve the detection of two nearby yet not directly connected sources as demonstrated by simulations cent is capable of reflecting the spatial extent for both focal and spatially extended current sources the analysis of in vivo meg data by cent produces less physiologically inconsistent clutter current sources in somatosensory and auditory meg measurements overall the cent method is demonstrated to be a promising tool for adaptive modeling of distributed neuronal currents associated with cognitive tasks

l1 gain performance analysis and positive filter design for positive discrete time markov jump linear systems a linear programming approach abstract this paper is concerned with the l 1 gain performance analysis and positive filter design for a positive discrete time markov jump linear system mjls by using a linear programming lp approach first by constructing a linear stochastic lyapunov function and introducing an equivalent deterministic positive discrete time linear system necessary and sufficient conditions in the form of lp are derived for stochastic stability and l 1 gain performance of the positive discrete time mjls then a sufficient condition on the existence of the desired positive l 1 gain filter is provided the desired positive l 1 gain filter can be designed by solving a standard lp problem the pest s structured population dynamic model is employed to illustrate the effectiveness of the proposed method

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities

stability and l_1 gain analysis of boolean networks with markovian jump parameters this paper presents some results on stability and l 1 gain analysis of boolean networks with markovian jump parameters a necessary and sufficient condition for global stability of the concerned boolean networks is given in terms of linear programming by utilizing the semi tensor product of matrices and some properties of linear positive systems then the definition of lyapunov function for stochastic boolean networks is presented and lyapunov theorem is derived moreover an l 1 gain problem for stochastic boolean networks with external disturbances is formulated and solved by a sufficient condition examples are shown to illustrate the effectiveness of the obtained results

equilibria stability and reachability of leslie systems with nonnegative inputs leslie systems a particular class of positive systems used in population dynamics and control are defined and analyzed a simple property relating sign and stability of their equilibria and some geometric characteristics of their reachability set in cases of bounded and unbounded inputs are proved all the properties do not hold in general in other classes of positive systems it is shown that leslie systems have strictly positive equilibria if and only if they are asymptotically stable their reachability set in the case of unbounded inputs is the positive cone generated by the reachability vectors while in the case of bounded inputs it is a polyhedron whose vertices can be easily computed all of these properties follow from the nonpositiveness of the coefficients of the characteristic polynomial of the system

exponential stability and l1 gain analysis for positive time delay markovian jump systems with switching transition rates subject to average dwell time abstract the paper deals with the problems of exponential stability and l 1 gain analysis for positive time delay markovian jump systems mjss with switching transition rates another set of useful regime switching model is given which extends fixed transition rates to time varying transition rates by resorting to the linear co positive lyapunov function and average dwell time sufficient conditions for exponential stability are proposed in terms of standard linear programming based on the obtained results l 1 gain performance is analyzed finally an example is proposed to illustrate the validity of the main results