on the decay rates of homogeneous positive systems of any degree with time varying delays this technical note studies the stability problem of homogeneous positive systems of any degree with time varying delays delay independent conditions are derived for asymptotic and finite time stability estimates on the decay rates which reveal how the system delays affect the rates of convergence are obtained more precisely this technical note features three contributions first we derive a necessary and sufficient condition for global polynomial stability of continuous time homogeneous cooperative systems with time varying delays when the degree of homogeneity is greater than one second we characterize finite time stability of continuous time homogeneous cooperative delay free systems of degree smaller than one finally for discrete time positive systems with time varying delays a local exponential stability criterion is established when the vector fields are order preserving and homogeneous of degree greater than one an illustrative example is given to show the effectiveness of our results

nonlinear control of feedforward systems with bounded signals the stabilization problem for a class of nonlinear feedforward systems is solved using bounded control it is shown that when the lower subsystem of the cascade is input to state stable and the upper subsystem not exponentially unstable global asymptotic stability can be achieved via a simple static feedback having bounded amplitude that requires knowledge of the upper part of the state only this is made possible by invoking the bounded real lemma and a generalization of the small gain theorem thus stabilization is achieved with typical saturation functions saturations of constant sign or quantized control moreover the problem of asymptotic stabilization of a stable linear system with bounded outputs is solved by means of dynamic feedback finally a new class of stabilizing control laws for a chain of integrators with input saturation is proposed some robustness issues are also addressed and the theory is illustrated with examples on the stabilization of physical systems

stability and performance of continuous time power control in wireless networks this paper develops a comprehensive stability analysis framework for general classes of continuous time power control algorithms under heterogeneous time varying delays our first set of results establish global asymptotic stability of power control laws involving two sided scalable interference functions and include earlier work on standard interference functions as a special case we then consider contractive interference functions and demonstrate that the associated continuous time power control laws always have unique fixed points which are exponentially stable even under bounded heterogeneous time varying delays for this class of interference functions we present explicit bounds on the decay rate that allow us to quantify the impact of delays on the convergence time of the algorithm when interference functions are linear we also prove that contractivity is necessary and sufficient for exponential stability of continuous time power control algorithms with time varying delays finally numerical simulations illustrate the validity of our theoretical results

on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

static output feedback stabilization with optimal l 1 gain for positive linear systems this paper is concerned with the static output feedback stabilization with optimal l1l1 gain for positive linear systems we aim to construct a static output feedback controller such that the closed loop system is positive asymptotically stable and the l1l1 gain from the exogenous input to the regulated output is minimized we show that when the control input or the measured output is a scalar this problem can be directly solved via linear programming by adding a one dimensional search moreover it is pointed out that the results can be extended to solve the l l optimal controller synthesis problem finally several illustrative examples are given to show the effectiveness of the theoretical results

stability analysis for continuous time positive systems with time varying delays this note addresses the stability problem of continuous time positive systems with time varying delays it is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a hurwitz matrix the result is a time varying version of the widely known asymptotic stability criterion for constant delay positive systems a numerical example illustrates the correctness of our result

brief paper unconditional stability of the foschini miljanic algorithm in this note we prove the unconditional stability of the foschini miljanic algorithm our results show that the foschini miljanic algorithm is unconditionally stable convergent even in the presence of bounded time varying communication delays and in the presence of topology changes the implication of our results may be important for the design of code division multiple access cdma based wireless networks

structure in asynchronous cellular automata abstract the properties of synchronous cellular automata are compared with two types of cellular automata which iterate asynchronously either at random or with clocks of slightly different periods it is shown that some of the apparent self organization of cellular automata is an artifact of the synchronization of the clocks the structure which does exist in asynchronous cellular automata is compared with that found in the synchronous case and some apparently new forms of self organization which appear are studied

stability of continuous time positive switched linear systems a weak common copositive lyapunov functions approach in this paper we study the problem of asymptotic stability of continuous time positive switched linear systems under both arbitrary and restricted switchings it is well known that asymptotic stability under arbitrary switching can be implied by several classes of strong common copositive lyapunov functions clfs i e functions whose derivative along the nontrivial system trajectories is negative however asymptotically stable positive switched systems may not admit strong common clfs the main contribution of this paper is to study the stability problem by requiring only weak common clfs firstly necessary and sufficient conditions are established for asymptotic stability under arbitrary switching among them an easily verifiable graphical stability criterion based on the connectivity of the digraphs associated with the subsystem matrices is proposed secondly we further relax the obtained graphical condition to derive a relaxed weak excitation condition for asymptotic stability under dwell time switching finally two examples are provided to illustrate the effectiveness of our theoretical results

pattern generation using likelihood inference for cellular automata cellular automata are discrete dynamical systems which evolve on a discrete grid recent studies have shown that cellular automata with relatively simple rules can produce highly complex patterns we develop likelihood based methods for estimating rules of cellular automata aimed at the re generation of observed regular patterns under noisy data our approach is equivalent to estimating the local map of a stochastic cellular automaton direct computations of the maximum likelihood estimates are possible for regular binary patterns the likelihood formulation of the problem is congenial with the use of the minimum description length principle as a model selection tool we illustrate our method with a series of examples using binary images

asymptotic swarm stability of fractional order swarm systems in the presence of uniform time delays abstractin this paper asymptotic swarm stability of fractional order swarm systems in the presence of uniform time delays is studied by using a frequency domain approach the necessary and sufficient condition on the values of time delay is derived to guarantee the asymptotic swarm stability under a directed undirected interaction graph numerical examples are given to confirm the obtained analytical results

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

exponential stability of homogeneous positive systems of degree one with time varying delays while the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated the theory for nonlinear positive systems is considerably less well developed this technical note presents a set of conditions for establishing delay independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case specifically when the time delays have a known upper bound we derive necessary and sufficient conditions for exponential stability of a continuous time positive systems whose vector fields are homogeneous and cooperative and b discrete time positive systems whose vector fields are homogeneous and order preserving we then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization finally we extend the results to general linear systems with time varying delays

on the stabilizability and consensus of positive homogeneous multi agent dynamical systems in this note we consider a supervisory control scheme that achieves either asymptotic stability or consensus for a group of homogenous agents described by a positive state space model each agent is modeled by means of the same siso positive state space model and the supervisory controller representing the information exchange among the agents is implemented via a static output feedback necessary and sufficient conditions for the asymptotic stability or the consensus of all agents are derived under the positivity constraint

analysis and synthesis of interconnected positive systems this paper is concerned with the analysis and synthesis of interconnected systems constructed from heterogeneous positive subsystems and a nonnegative interconnection matrix we first show that admissibility to be defined in this paper is an essential requirement in constructing such interconnected systems then we clarify that the interconnected system is admissible and stable if and only if a metzler matrix which is built from the coefficient matrices of positive subsystems and the nonnegative interconnection matrix is hurwitz stable by means of this key result we further provide several results that characterize the admissibility and stability of the interconnected system in terms of the frobenius eigenvalue of the interconnection matrix and the weighted l1 induced norm of the positive subsystems again to be defined in this paper moreover in the case where every subsystem is siso we provide explicit conditions under which the interconnected system has the property of persistence i e its state converges to a unique strictly positive vector that is known in advance up to a strictly positive constant multiplicative factor for any nonnegative and nonzero initial state as an important consequence of this property we show that the output of the interconnected system converges to a scalar multiple of the right eigenvector of a nonnegative matrix associated with its frobenius eigenvalue where the nonnegative matrix is nothing but the interconnection matrix scaled by the steady stage gains of the positive subsystems this result is then naturally and effectively applied to formation control of multiagent systems with positive dynamics this result can be seen as a generalization of a well known consensus algorithm that has been basically applied to interconnected systems constructed from integrators

observer based discrete time nonnegative edge synchronization of networked systems this paper studies the multi input and multi output discrete time nonnegative edge synchronization of networked systems based on neighbors output information the communication relationship among the edges of networked systems is modeled by well known line graph two observer based edge synchronization algorithms are designed for which some necessary and sufficient synchronization conditions are derived moreover some computable sufficient synchronization conditions are obtained in which the feedback matrix and the observer matrix are computed by solving the linear programming problems we finally design several simulation examples to demonstrate the validity of the given nonnegative edge synchronization algorithms

fully asynchronous behavior of double quiescent elementary cellular automata in this paper we propose a probabilistic analysis of the fully asynchronous behavior i e two cells are never simultaneously updated as in a continuous time process of elementary finite cellular automata i e 0 1 states radius 1 and unidimensional for which both states are quiescent i e 0 0 0 0 and 1 1 1 1 it has been experimentally shown in previous works that introducing asynchronism in the global function of a cellular automata was perturbing its behavior but as far as we know only few theoretical work exists on the subject the cellular automata we consider live on a ring of size n and asynchronism is introduced as follows at each time step one cell is selected uniformly at random and the transition is made on this cell while the others stay in the same state among the 64 cellular automata belonging to the class we consider we show that 9 of them diverge on all non trivial configurations while the 55 other converge almost surely to a random fixed point we show that the exact convergence time of these 55 automata can only take the following values either 0 n ln n n2 n3 or n2n furthermore the global behavior of each of these cellular automata is fully determined by reading its code

h_2 analysis of lti systems via conversion to externally positive systems motivated by recent advances in the study of linear time invariant lti positive systems we explore analysis techniques of general not necessarily positive lti systems using positive system theory even though a positive system is characterized by its peculiar property that its impulse response is nonnegative we often deal with nonnegative impulse responses even in general lti system analysis a typical example is the computation of the h 2 norm where we focus on squared impulse responses to deal with such products of impulse responses in a systematic fashion in this paper we first establish a construction technique of an lti system whose impulse response is given by the product of impulse responses of two different lti systems then as the main result we reduce the h 2 norm computation problem of a general lti system into the l infty induced norm computation problem or l 1 problem in short of a positive system by which we can derive various formulas for the h 2 norm computation

robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties this paper studies the static output feedback sof control problem of continuous time linear systems with polytopic uncertainties novel lmi conditions with a line search over a scalar variable for designing robust sof controllers are proposed where the uncertain output matrix of the considered system is allowed to be not of full row rank in particular it is shown that the new method can give less or at least the same conservative results than those methods by inserting a matrix equality constraint between system output matrix and lyapunov matrix furthermore the result is extended to the case of h control numerical examples are given to illustrate the effectiveness of the proposed method

spatial pattern formation in asynchronous cellular automata with mass conservation abstract this paper proposes a class of two dimensional asynchronous cellular automata with conservation of mass for the formation of patterns in groups and describes the merits given by this methodology a cellular automaton rule causing a specified kind of pattern was designed manually thanks to this realistic modeling method reflecting nature the mechanism of pattern formation was found to be similar to real chemical processes because of the conservation of mass some boring cellular automata which evolve for instance into homogeneity are automatically excluded in this scheme this is greatly advantageous for searching automatically for pattern forming cellular automata a search technique using genetic algorithm is proposed and it successfully find a few types of pattern spontaneously that is without giving a priori information on the type of pattern this technique is expected to be applied to a wide range of potential studies related to self organization

the multivariable servomechanism problem for positive lti systems in this technical note we study the servomechanism problem for positive open loop stable lti systems under constant tracking signals and constant disturbances in particular we show that in general the mimo servomechanism problem for positive systems is not solvable but is solvable for various classes of mimo systems and for the class of siso systems in which the disturbances are small compared to the tracking signal in particular we give existence results as to what subclass of reference and disturbance signals can be considered for the case when either the mathematical model of the plant is known or unknown and we provide the controller structure that solves the problem for the case of measurable or unmeasurable disturbance signals

lqg optimal scalar static output feedback an eigenproblem based technique is given for computing the stabilizing scalar static output feedback gain that minimizes the standard linear quadratic performance index in the presence of a gaussian white noise disturbance the method adapts recent work on eigenproblem based computation of h norms

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 on linear co positive lyapunov functions for sets of linear positive systems in this paper we derive necessary and sufficient conditions for the existence of a common linear co positive lyapunov function for a finite set of linear positive systems both the state dependent and arbitrary switching cases are considered our results reveal an interesting characterisation of linear stability for the arbitrary switching case namely the existence of such a linear lyapunov function can be related to the requirement that a number of extreme systems are metzler and hurwitz stable examples are given to illustrate the implications of our results

stability analysis and delay control for switched positive linear systems in this paper the problems of stability analysis and delay control for switched positive linear systems splss are studied by using average dwell time adt switching by developing a new class of multiple piecewise continuous linear copositive lyapunov function mplclf approach an improved stability condition for splss is obtained which can obtain a tighter bound on the adt guaranteeing the stability the obtained stability condition covers the existing results on stability analysis for splss since the multiple linear copositive lyapunov function used in the literature can be viewed as a special case of our proposed mplclf and our result can obtain a tighter bound of the adt then a more efficient controller design method over the existing ones is also established for splss with switching delay to guarantee the underlying system to be exponentially stable to illustrate the advantages of our proposed results two numerical examples are finally given

progresses in the analysis of stochastic 2d cellular automata a study of asynchronous 2d minority cellular automata are often used to model systems in physics social sciences biology that are inherently asynchronous over the past 20 years studies have demonstrated that the behavior of cellular automata drastically changes under asynchronous updates still the few mathematical analyses of asynchronism focus on 1d probabilistic cellular automata either on single examples or on specific classes as for other classic dynamical systems in physics extending known methods from 1d to 2d systems is a long lasting challenging problem in this paper we address the problem of analyzing an apparently simple 2d asynchronous cellular automaton 2d minority where each cell when fired updates to the minority state of its neighborhood our simulations reveal that in spite of its simplicity the minority rule exhibits a quite complex response to asynchronism by focusing on the fully asynchronous regime we are however able to describe completely the asymptotic behavior of this dynamics as long as the initial configuration satisfies some natural constraints besides these technical results we have strong reasons to believe that our techniques relying on defining an energy function from the transition table of the automaton may be extended to the wider class of threshold automata

brief paper stability of switched positive linear systems with average dwell time switching in this paper the stability analysis problem for a class of switched positive linear systems splss with average dwell time switching is investigated a multiple linear copositive lyapunov function mlclf is first introduced by which the sufficient stability criteria in terms of a set of linear matrix inequalities are given for the underlying systems in both continuous time and discrete time contexts the stability results for the splss under arbitrary switching which have been previously studied in the literature can be easily obtained by reducing mlclf to the common linear copositive lyapunov function used for the system under arbitrary switching those systems finally a numerical example is given to show the effectiveness and advantages of the proposed techniques

differentially positive systems the paper introduces and studies differentially positive systems that is systems whose linearization along an arbitrary trajectory is positive a generalization of perron frobenius theory is developed in this differential framework to show that the property induces a conal order that strongly constrains the asymptotic behavior of solutions the results illustrate that behaviors constrained by local order properties extend beyond the well studied class of linear positive systems and monotone systems which both require a constant cone field and a linear state space

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

stability analysis of positive descriptor systems abstract in this paper we discuss stability properties of positive descriptor systems in the continuous time as well as in the discrete time case we present characterisations of positivity and establish generalised stability criteria for the case of positive descriptor systems we show that if the spectral projector onto the finite deflating subspace of the matrix pair e a is nonnegative then all stability criteria for standard positive systems take a comparably simple form in the positive descriptor case furthermore we provide sufficient conditions that guarantee entry wise nonnegativity along with positive semidefiniteness of solutions of generalised projected lyapunov equations as an application of the framework established throughout this paper we exemplarily generalise two criteria for the stability of two switched standard positive systems under arbitrary switching to the descriptor case

observers for linear positive systems observer synthesis for linear positive systems is treated the concept of observability of a linear positive system is defined and a characterization of observability is provided an observable canonical form is proposed for a linear positive system with respect to an equivalent relation defined by permutations of the state and of the output set observer synthesis is carried out for linear observers which are either globally asymptotically stable or whose error dynamics is assignable an algorithm for the construction of a linear observer is stated which is based on the observable canonical form

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

solvability of static output feedback stabilization for lti positive systems abstract this paper addresses the stabilization problem of positive linear systems which have nonnegative states whenever the initial conditions are nonnegative the synthesis of static output feedback controllers that ensure the positivity and asymptotic stability of the closed loop system is investigated it is shown that this important problem is completely solved for single input and single output positive systems the proposed approach can be applied to multi input positive systems with controllers having one rank gains all the provided conditions are necessary and sufficient and can be solved in terms of linear programming

l l gain analysis for positive linear systems with unbounded time varying delays this technical note addresses the l gain respectively l gain analysis problem for discrete time respectively continuous time positive linear systems with unbounded time varying delays for the discrete time case by virtue of the monotonicity of an auxiliary system and the corresponding delay free system it is shown that the l gain of discrete time positive systems with unbounded delays is insensitive of the magnitude of delays for the continuous time case we first construct a sampled data positive system and analyze its monotonicity and asymptotic behavior then by comparing the delayed positive system with the proposed sampled data positive system and the corresponding delay free system it is further proved that the l gain of continuous time positive systems with unbounded delays is also independent of the delays and fully determined by the system matrices the application of the results is illustrated by a sampled data system with unbounded sampling intervals

pole placement via static output feedback is np hard this note proves that the problem of pole placement via static output feedback for linear time invariant systems is np hard

dc dominant property of cone preserving transfer functions abstract we consider a class of square mimo transfer functions that map a proper cone in the space of l 2 input signals to the same cone in the space of output signals transfer functions in this class have the dc dominant property the maximum radius of the operator spectrum is attained by a dc input signal and hence the dynamic stability of the feedback interconnection of such transfer functions is guaranteed solely by static gain analysis using this property we prove that cone preserving linear delay differential equations are robustly stable against arbitrary constant delay values this provides an alternative proof of the delay independent mean square stability of a multi dimensional geometric brownian motion

parameterization of positively stabilizing feedbacks for single input positive systems abstract this paper provides parameterizations of all positively stabilizing feedbacks for a particular class of finite dimensional single input positive systems a method to yield these parameterizations by means of tools of linear programming and a convergence analysis which allows to extend the results to a particular infinite dimensional system described by a parabolic partial differential equation it also provides an academic standard example the pure diffusion equation to support the theoretical results

state unilateral tracking control of positive switched systems via designing a switching law abstractthis paper focuses on the model reference state unilateral tracking control problem of positive switched systems the state unilateral tracking means that the state always keeps in the same direction of the reference objective either above or below this feature makes unilateral tracking play a role of avoiding the overshoot via the dual design of both the controller and the switching signal the state unilateral tracking control problem with l1 gain performance for positive switched systems is solved through adopting multiple linear co positive lyapunov functions technique the design method is applicable to the case that the unilateral tracking control problem is unsolvable for any subsystem of a positive switched system moreover two techniques are presented in order to deal with the state unilateral tracking problem finally a practical example demonstrates the validity of the presented result

cellular automata as a paradigm for ecological modeling we review cellular automata as a modeling formalism and discuss how it can be used for modeling spatial ecological processes the implications of this modeling paradigm for ecological observation are stressed finally we discuss some shortcomings of the cellular automaton formalism and mention some extensions and generalizations which may remedy these shortcomings

np hardness of some linear control design problems we show that some basic linear control design problems are np hard implying that unless p np they cannot be solved by polynomial time algorithms the problems that we consider include simultaneous stabilization by output feedback stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix and decentralized control these results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is np hard

on the algebraic riccati inequality arising in cone preserving time delay systems abstract this paper studies the problem of riccati stability of a pair of matrices for a matrix pair a b it was recently shown that if its corresponding time delay system is internally positive meaning that a is metzler and b is nonnegative then the pair a b is diagonally riccati stable if and only if a b is hurwitz we extend this to the case when the pair a b corresponds to a time delay system with a more general cone preserving property we show that if the time delay system relating to the pair a b is invariant on a symmetric cone the corresponding algebraic riccati inequality admits positive definite solutions which can be constructed via the scaling transformation on the euclidean jordan algebra associated with the symmetric cone for the special case when the symmetric cone is the positive semi definite cone an application to a class of stochastic systems is discussed

sign properties of metzler matrices with applications abstract several results about sign properties of metzler matrices are obtained it is first established that checking the sign stability of a metzler sign matrix can be either characterized in terms of the hurwitz stability of the unit sign matrix in the corresponding qualitative class or in terms the negativity of the diagonal elements of the metzler sign matrix and the acyclicity of the associated directed graph similar results are obtained for the case of metzler block matrices and metzler mixed matrices the latter being a class of metzler matrices containing both sign and real type entries the problem of assessing the sign stability of the convex hull of a finite and summable family of metzler matrices is also solved and a necessary and sufficient condition for the existence of common lyapunov functions for all the matrices in the convex hull is obtained the concept of sign stability is then generalized to the concept of ker b sign stability a problem that arises in the analysis of certain jump markov processes a sufficient condition for the ker b sign stability of metzler sign matrices is obtained and formulated using inverses of sign matrices and the concept of l matrices several applications of the results are discussed in the last section

on the generalized spectral subradius in this note we study the concepts of generalized spectral subradius and joint spectral subradius of a family of matrices we show that both these numbers are equal and we present two different formulas for them we also explain the relation between them and maximal lyapunov exponent of discrete linear time varying system finally we show that the spectral subradius is less than one if and only if a discrete linear inclusion is stable in a certain sense

stability of discrete time positive switched linear systems with stable and marginally stable subsystems abstract in this paper we investigate the stability of discrete time positive switched linear systems the highlight of this work is that each subsystem is only assumed to be stable or marginally stable some sufficient conditions imposed on the subsystem matrices and switching signals are established to guarantee exponential stability of the considered positive switched linear systems an extension to the case of time varying and unbounded delay is also given compared with the continuous time counterparts in the literature our discrete time case is much more complicated involving the transitive connectivity between the subsystems specified by the switching signals

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

an improved ilmi method for static output feedback control with application to multivariable pid control an improved iterative linear matrix inequality ilmi algorithm for static output feedback sof stabilization problem without introducing any additional variables is proposed in this note the proposed ilmi algorithm is also extended to solve the sof hinfin controller design problem they are applied to the multivariable pid controllers numerical examples show that the proposed algorithms yield better results and faster convergence than the existing ones

deducing local rules for solving global tasks with random boolean networks abstract it has been shown that uniform as well as non uniform cellular automata ca can be evolved to perform certain computational tasks random boolean networks are a generalization of two state cellular automata where the interconnection topology and the cell s rules are specified at random here we present a novel analytical approach to find the local rules of random boolean networks rbns to solve the global density classification and the synchronization task from any initial configuration we quantitatively and qualitatively compare our results with previously published work on cellular automata and show that randomly interconnected automata are computationally more efficient in solving these two global tasks our approach also provides convergence and quality estimates and allows the networks to be randomly rewired during operation without affecting the global performance finally we show that rbns outperform small world topologies on the density classification task and that they perform equally well on the synchronization task our novel approach and the results may have applications in designing robust complex networks and locally interacting distributed computing systems for solving global tasks

asymptotic stability and decay rates of homogeneous positive systems with bounded and unbounded delays there are several results on the stability of nonlinear positive systems in the presence of time delays however most of them assume that the delays are constant this paper considers time varying possibly unbounded delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case specifically we present a necessary and sufficient condition for delay independent stability of continuous time positive systems whose vector fields are cooperative and homogeneous we show that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays for various classes of time delays we are able to derive explicit expressions that quantify the decay rates of positive systems we also provide the corresponding counterparts for discrete time positive systems whose vector fields are nondecreasing and homogeneous

input output gain analysis for linear systems on cones abstract this paper is concerned with the input output gain analysis for dynamic systems that are defined on cones for such monotone systems we characterize their input output gain induced by the so called cone linear absolute norm in terms of generalized inequalities it is further shown that for a linear time invariant system represented by a convolution operator that maps one proper cone to another in the l 1 space its operator norm is governed by the static gain of the system as a byproduct the spectral radius of a cone preserving convolution operator turns out to be the same as that of the static gain matrix moreover dual results based on the cone max norm are presented finally the theoretical results are illustrated via linear systems over polyhedral cones or second order cones as well as a class of stochastic systems

stability and stabilizability of continuous time linear compartmental switched systems in this paper we introduce continuous time linear compartmental switched systems and investigate their stability and stabilizability properties by their nature these systems are always stable necessary and sufficient conditions for asymptotic stability for arbitrary switching functions and sufficient conditions for asymptotic stability under certain dwell time conditions on the switching functions are proposed finally stabilizability is thoroughly investigated and proved to be equivalent to the existence of a hurwitz convex combination of the subsystem matrices a condition that for positive switched systems is only sufficient for stabilizability

discrete time positive periodic systems with state and control constraints the aim of this technical note is to provide an efficient control design technique for discrete time positive periodic systems in particular stability positivity and periodic invariance of such systems are studied moreover the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability it is shown how such concept can be used for deriving a stabilizing state feedback control that maintains the positivity of the closed loop system and respects states and control signals constraints in addition all the proposed results can be efficiently solved in terms of linear programming

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

some extensions on the bounded real lemma for positive systems recent advances have shown that the l 2 gain of positive systems is fully determined by the static gain matrix and hence the linear matrix inequality lmi characterizing their h infty performance admits a diagonal lyapunov matrix variable in this technical note we aim to extend this property for systems with input state and output defined on general cones although it is known that the l 2 gain is no longer governed by the static gain matrix for systems defined on general proper cones we show that this property is still valid when the cone in the state space is symmetric and the cones in the input and output spaces are self dual meanwhile it is proved that the lyapunov matrix appearing in the lmi characterization for the h infty performance can be constructed by the quadratic representation of the jordan algebra asso ciated with the symmetric cone in the state space finally the established results are illustrated via a linear system defined on second order cones

stabilization of positive linear systems we consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant the existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane this allows to transform the problem to the stabilization problem of compartmental systems which is known and for which a solution has been proposed already we provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback a class of stabilizing feedbacks is given explicitly

a convex characterization of robust stability for positive and positively dominated linear systems we provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems in particular we show that the structured singular value is always equal to its convex upper bound for nonnegative matrices and we use this result to derive necessary and sufficient linear matrix inequality lmi conditions for robust stability that involve only the system s static gain we show how this approach can be applied to test the robust stability of the foschini miljanic algorithm for power control in wireless networks in presence of uncertain interference

generalized goodman harpe jones construction of subfactors ii we build some exceptional representations of birman wenzl algebras from the data of certain conformal embeddings as a result we construct new finite depth subfactors whose principal graphs are completely determined

orbifold construction in subfactors we use the lattice models to determine the obstructions to the flatness of the orbifold connections in some finite depth subsfactors

stability and l 1 l1 to l 1 l1 performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays abstractsolutions to the interval observation problem for delayed impulsive and switched systems with l1 performance are provided the approach is based on first obtaining stability and l1 l1 to l1

positivity preserving balanced truncation for descriptor systems we propose a model reduction method for positive systems that ensures the positivity of the reduced order model in the standard as well as in the descriptor case for continuous time and discrete time systems our approach is based on constructing diagonal solutions of lyapunov inequalities these are linear matrix inequalities lmis which are shown to be feasible positivity and stability are preserved and an error bound in the mathcal h infty norm is provided

asynchronous game of life abstract this paper proposes the 8 state asynchronous equivalence of the well known game of life gl our cellular automaton called asynchronous game of life simulates exactly the behavior of the gl such as universal computation and self organization no matter whether the update of cells is simultaneous or independent according to some updating scheme like a step driven or time driven method see biosystems 51 1999 123 we employ the updating scheme of blok and bergersen phys rev e 59 1999 3876 such that at every time step each cell has a certain probability to be updated and investigate the statistical properties of our model through power spectral analyses

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

convergence time and phase transition in a non monotonic family of probabilistic cellular automata in dynamical systems some of the most important questions are related to phase transitions and convergence time we consider a one dimensional probabilistic cellular automaton where their components assume two possible states zero and one and interact with their two nearest neighbors at each time step under the local interaction if the component is in the same state as its two neighbors it does not change its state in the other cases a component in state zero turns into a one with probability alpha and a component in state one turns into a zero with probability 1 beta for certain values of alpha and beta we show that the process will always converge weakly to delta 0 the measure concentrated on the configuration where all the components are zeros moreover the mean time of this convergence is finite and we describe an upper bound in this case which is a linear function of the initial distribution we also demonstrate an application of our results to the percolation pca finally we use mean field approximation and monte carlo simulations to show coexistence of three distinct behaviours for some values of parameters alpha and beta

positive linear observers for linear compartmental systems linear compartmental systems are mathematical systems that are frequently used in biology and mathematics the inputs states and outputs of such systems are positive because they denote amounts or concentrations of material for linear dynamic systems the observer problem has been solved the purpose of the observer problem is to determine a linear observer such that the state can be approximated the difference between the state and its estimate should converge to zero the interpretation in terms of a physical system requires that an estimate of the state be positive like the state itself in this paper conditions on the system matrices are presented that guarantee that there exists a positive linear observer such that both the error converges to zero and the estimate is positive

necessary and sufficient conditions for stabilizability of positive lti systems this paper obtains necessary and sufficient conditions for the stabilization of positive lti systems using a vertex algorithmic approach the results of this paper also encompass positive direct output feedback control the topic of the sequential separation principle and a particularly efficient algorithm for a class of positive systems

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

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

asymptotic tracking for constrained monotone systems this note addresses tracking control of nonlinear discrete time monotone systems subject to input and state constraints forcing saturation on a previously designed controller may in general lead to destabilization or at least result in constraint violation and performance losses hereby it is shown that for a certain class of nonlinear monotone systems it is possible to design a static nonlinear output feedback which saturated among suitable state dependent bounds is able to guarantee constraint satisfaction and asymptotic tracking of piecewise constant references with a moderate online computational burden simulation experiments concerning the synthesis of a protein demonstrate the effectiveness of the proposed control strategy