inequalities between the chern numbers of a singular fiber in a family of algebraic curves chern numbers of a singular fiber in a family of curves are the local contributions of the fiber to the global chern numbers of the total space our first purpose of this paper is to find the best inequalities between the chern numbers of a singular fiber our second purpose is to try to give a new approach to the classification of singular fibers of genus g we know that when g is big there are too many singular fibers of genus g to classify completely see 5 7 8 16 in order to get the local global relations between the invariants one possible way is to classify singular fibers according to their contributions to the global invariants to explain this approach we will classify singular fibers with big or small chern numbers and give some applications see the survey 2 for the background of the study on the local global properties for families of curves a family of curves of genus g over c is a fibration f x c whose general fibers f are smooth curves of genus g where x is a complex smooth projective surface the family is called semistable if all of the singular fibers are reduced nodal curves if x f c and f is just the second projection to c then we call f a trivial family if all of the smooth fibers of f are isomorphic to each other equivalently f becomes trivial under a finite base change c c then f is called isotrivial we always assume that f is relatively minimal i e there is no 1 curve in any singular fiber when g 1 kodaira 6 found the global invariants from the singular fibers the first chern number c1 x is always zero the second chern number c2 x is equal to 12 ox by noether s formula and

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

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

t s fuzzy control of positive markov jump nonlinear systems the positive stochastic stabilization issue is investigated for markov jump nonlinear systems the nonlinear systems in the absence and presence of uncertainties are considered and modeled into markov jump fuzzy systems with known and partially known membership functions respectively for the former the parallel distributed compensator pdc controllers are designed to realize the positive stochastic stabilization besides an additional criterion is derived to reduce the number of linear inequalities for the latter namely some elements of membership functions are unavailable and the pdc strategy is infeasible then a switching controller whose structure is parallel to that of fuzzy model is constructed to achieve the corresponding positivity and stability all the conditions are transformed to standard form of linear programming problem which is solved with the help of linprog toolbox finally the feasibility of the obtained results is illustrated by a pest s structured population model

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 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

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

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

clustering with evolution strategies tbe applicability of evolution strategies ess population based stochastic optimization techniques to optimize clustering objective functions is explored clustering objective functions are categorized into centroid and non centroid type of functions optimization of the centroid type of objective functions is accomplished by formulating them as functions of real valued parameters using ess both hard and fuzzy clustering objective functions are considered in this study applicability of ess to discrete optimization problems is extended to optimize the non centroid type of objective functions as ess are amenable to parallelization a parallel model master slave model is described in the context of the clustering problem results obtained for selected data sets substantiate the utility of ess in clustering

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

fibered algebraic surfaces with low slope the background of this paper is the following conjecture on complex surfaces of general type let s be a smooth projective minimal surface of general type over ti with c 2 throughout the paper

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

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

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

comparison of linear and classical velocity update rules in particle swarm optimization notes on diversity in this study we investigate the significance of diversity in the particle swarm optimization pso algorithm to do so we study two different implementations of the pso being the so called linear and classical pso formulations while the behaviour of these two implementations is markedly different they only differ in the formulation of the velocity update rule in fact the differences are merely due to subtle differences in the introduction of randomness into the algorithm in this paper we show that in algorithms employing the linear pso velocity update rule particle trajectories collapse to line searches in n dimensional space the classical formulation does not suffer this drawback instead directional diverse stochastic search trajectories are retained which in turn helps to alleviate premature convergence the performance of the classical implementation is therefore superior for all test problems considered due to the presence of adequate diversity copyright 2006 john wiley sons ltd

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

modified fuzzy c means for ordinal valued attributes with particle swarm for optimization there are well established methods for fuzzy clustering especially for the cases where the feature values are numerical of ratio or interval scale not so well established are methods to be applied when the feature values are ordinal or nominal in that case there is no satisfactory method it seems this paper discusses a modified fuzzy c means clustering method where an ordinal to numeric mapping for the ordinal features is obtained as part of the clustering process part of minimizing the objective function for the clustering is to find this ordinal to numeric mapping having this mapping allows standard methods of fuzzy c means clustering to be used since then if there are no categorical features all the features are numeric the mapping is not of interest in itself and to obtain it is only a subsidiary objective of the clustering process the mapping allows for the degrees of freedom that is characteristic of the data the method involves solving a rather challenging optimization problem since the objective function has many local minima this makes the use of a global optimization method such as particle swarm optimization pso attractive for determining the membership matrix for the clustering to minimize computational effort a bayesian stopping criterion may be used in combination with a multi start strategy for the pso other clustering methods generally find local optimum of their objective function through simulations and experiments with real and artificial data the method proposed here is shown to be quite effective

genetic algorithm based clustering technique abstract a genetic algorithm based clustering technique called ga clustering is proposed in this article the searching capability of genetic algorithms is exploited in order to search for appropriate cluster centres in the feature space such that a similarity metric of the resulting clusters is optimized the chromosomes which are represented as strings of real numbers encode the centres of a fixed number of clusters the superiority of the ga clustering algorithm over the commonly used k means algorithm is extensively demonstrated for four artificial and three real life data sets

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

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

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

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

on the gonality and the slope of a fibered surface abstract let f x b be a locally non trivial relatively minimal fibration of curves of genus g 2 we obtain a lower bound of the slope f increasing with the gonality of the general fiber of f in particular we show that f 4 provided that f is non hyperelliptic and g 16

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

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

a fuzzy k modes algorithm for clustering categorical data this correspondence describes extensions to the fuzzy k means algorithm for clustering categorical data by using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters a new approach is developed which allows the use of the k means paradigm to efficiently cluster large categorical data sets a fuzzy k modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results

frequency limited mmb h _ infty model reduction for positive systems in this paper the problem of frequency limited mmb h infty model reduction for positive linear time invariant systems is investigated specifically our goal is to find a stable positive reduced order model for a given positive system such that the mmb h infty norm of the error system is bounded over a frequency interval of interest a new condition in terms of matrix inequality is developed for characterizing the frequency limited mmb h infty performance then an equivalent parametrization of a positive reduced order model is derived based on which an iterative algorithm is constructed for optimizing the reduced order model the algorithm utilizes coarse reduced order models resulting from generalized balanced truncation as the initial value both continuous and discrete time systems are considered in the same framework numerical examples clearly show the effectiveness and advantages of the proposed model reduction method

l1 gain analysis and model reduction problem for boolean control networks in this paper the weighted l1 gain analysis and l1 model reduction problem for boolean control networks are proposed and investigated via semi tensor product method first the input energy and output energy are described by pseudo boolean functions based on which the definition of the weighted l1 gain is introduced by constructing a co positive lyapunov function a sufficient condition is established to ensure that a boolean control network is not only internally asymptotically stable but also has an l1 gain no more than a given scalar along this line by virtue of the properties of semi tensor product the l1 model reduction problem of a boolean control network is defined and converted to the l1 gain problem of another boolean control network with more nodes a sufficient condition for the l1 model reduction problem is then derived immediately and an algorithm is presented to compute the matrices in the reduced order model finally two examples including the boolean model for biochemical oscillators in the cell cycle are displayed to show the feasibility of the theoretical results

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

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