minimal strongly eventually positive realization for a class of externally positive systems the minimal positive realization of externally positive systems is still an open problem due to various restrictions caused by the nonnegativity constraint on the state space matrices in this paper the minimal strongly eventually positive realization which relaxes the nonnegativity constraint on the state space model and only requires that the state trajectory is nonnegative after a certain number of steps is proposed for an externally positive system it is shown that a discrete time transfer function with a simple strictly dominant root is externally positive if and only if it has a minimal strongly eventually positive realization a constructive proof is provided the continuous time counterpart is also addressed by transforming it into a corresponding discrete time case

stochastic controllability and minimum energy control of systems with multiple delays in control in recent years various controllability problems for different types of linear dynamical systems have been considered in many publications and monographs

a lower bound on the dimension of minimal positive realizations for discrete time systems abstract in some applications one is interested in having a state space realization with nonnegative matrices positive realization of a given transfer function and it is known that such a realization may have a dimension strictly larger than the order of the transfer function itself moreover in most cases it is desirable to have a realization with minimal dimension unfortunately it is not known to date how to determine in general the minimum dimension of a positive realization and only lower and upper bounds to it are available this letter provides an upper bound on the dimension of a minimal positive realization for transfer functions with simple poles this is a considerable improvement on an earlier upper bound in which only transfer functions with real poles were considered

on discrete time linear systems over cones abstract the subject of this paper is the theory of linear discrete time systems with input constrained to belong to a closed convex cone after discussing the generality of this class of systems a number of invariant cones of states are introduced in the last section these latter are shown to allow the extension of some classical results of the theory of linear unconstrained systems

on the reachability in any fixed time for positive continuous time linear systems this paper deals with the reachability of continuous time linear positive systems the reachability of such systems which we will call here the strong reachability amounts to the possibility of steering the state in any fixed time to any point of the positive orthant by using nonnegative control functions the main result of this paper essentially says that the only strongly reachable positive systems are those made of decoupled scalar subsystems moreover the strongly reachable set is also characterized

reachability observability and realizability of continuous time positive systems this paper discusses reachability observability and realizability of single input single output linear time invariant systems in which state variables and or input output functions are restricted to be nonnegative to reflect physical constraints frequently encountered in real systems we define a set reachable from the origin with nonnegative inputs and also a set observable with nonnegative outputs we investigate geometrical structures of the sets through convex analysis and a duality relation between them is established next we consider positive realization of a given transfer function using the reachable set and the observable set we give a necessary and sufficient condition for positive realizability an example is given to demonstrate that a positive realizable transfer function does not in general have a jointly controllable and observable positive realization

optimality of the cusum procedure in continuous time the optimality of cusum under a lorden type criterion setting is considered we demonstrate the optimality of the cusum test for ito processes in a sense similar to lorden s but with a criterion that replaces expected delays by the corresponding kullback leibler divergence

diagnosis of unknown parametric faults in non linear stochastic dynamical systems a new detection and isolation scheme for unknown parametric faults in non linear stochastic systems is presented that is particularly suited for small parametric changes the proposed residual is the moving angle between two stochastic processes the error derived from the reference model and the expected error in case a certain fault has occurred since the fault is unknown fault classes are defined most of the faults that belong to such a fault class can be detected and isolated by just testing one representative of this fault class as the moving angle itself is a stochastic process an estimator is designed and characterised conditions for the detectability and isolability of fault classes are given for this estimator based on hypotheses tests finally the theoretical results are confirmed by simulations and monte carlo tests

an example of how positivity may force realizations of large dimension abstract a standard result of linear system theory states that an siso proper rational transfer function of degree n always has a realization of dimension n in some applications one is interested in having a realization with nonnegative entries and it is known that when the dominant poles display a specific pattern forcing nonnegativity leads to a system which is not jointly reachable and observable in this paper we show that the minimal dimension of a positive realization may be large even in the case of a single dominant pole more precisely we provide a family of transfer functions each of which is of degree n 3 such that for any integer n 3 the corresponding member of the family admits a minimal positive realization of state space dimension not smaller than n

realization of continuous time positive linear systems positive linear systems are used in biomathematics economics and other research areas for discrete time positive linear systems part of the realization problem has been solved in this paper the solution of the corresponding problem for continuous time positive linear systems will be presented which can be deduced from that of the discrete time case by a transformation sufficient and necessary conditions for the existence of a positive realization are presented to solve the problem of minimality the solution of the factorization of positive matrices is needed

nonnegative realizations of matrix transfer functions abstract various aspects of the nonnegative finite dimensional realizability of time invariant discrete linear systems are considered a new proof of the basic result of the nonnegative realizability of a primitive scalar valued transfer function with nonnegative impulse response function is given an algorithm for establishing whether a scalar valued transfer function with nonnegative impulse response has a nonnegative realization is presented the main result characterizes the nonnegative realizability of a scalar valued transfer function with the help of primitive transfer functions and is extended to the general case of matrix valued transfer functions then conditions for the existence of some special nonnegative realizations of transfer functions are presented e g where the middle main matrix is irreducible strictly positive or primitive

positive output state maps and quasi positive realization of mimo discrete systems the positive realization of externally positive systems described by their transfer matrix g z is a complex problem whose analysis has been completed only recently for the siso case on the basis of algebraic and geometric approaches that underline the many constraints that condition its solution these constraints concern the minimal order of the obtained models the minimality of their parameterizations and even their existence this paper considers the new category of quasi positive state space models introduced in guidorzi 2014 that limit the assumptions on the nonnegativeness of the state space trajectories to the only trajectories that can be actually generated by the system under nonnegative controls it is shown that all externally positive systems admit a quasi positive minimally parameterized state space realization whose existence is not conditioned by restrictions on the signs of the parameters of the polynomials in g z

a mathematical framework for new fault detection schemes in nonlinear stochastic continuous time dynamical systems in this work a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous time dynamical systems is developed these schemes are based on a stochastic process called the residual which reflects the system behavior and whose changes are to be detected a quickest detection scheme for the residual is proposed which is based on the computed likelihood ratios for time varying statistical changes in the ornstein uhlenbeck process several expressions are provided depending on a priori knowledge of the fault which can be employed in a proposed cusum type approximated scheme this general setting gathers different existing fault detection schemes within a unifying framework and allows for the definition of new ones a comparative simulation example illustrates the behavior of the proposed schemes

necessary conditions for positive realizability of continuous time linear systems abstract this paper deals with the positive realization problem the problem is to find from a given transfer function a state equation in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative necessary conditions are investigated and a new one is given together with some related results

state space descriptor models and asymptotic behavior of continuous time positive control systems abstract this paper deals with new aspects of the theory of nonnegative matrices and their applications to some problems arising in the studies of continuous time control systems the criterion for asymptotic stability of linear state space control systems with positive state matrix a and respective initial conditions is established and proven it states that the system is asymptotically stable if and only if the state variables are linearly dependent moreover the case of dynamical systems in descriptor forms with positive leading and state matrices is studied the asymptotic stability of descriptor systems characterized by positive leading and state matrices is expressed in terms of the geometric relations between matrices of a proper part of the corresponding regular matrix pencil inverse and the initial conditions several illustrating examples are also included

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

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

geometrical conditions for the reachability and realizability of positive periodic discrete systems reachability and realizability of discrete time linear systems in which the state variable and the input are constrained to lie in the positive orthant r are studied more precisely a characterization of positive reachability is given in terms of certain geometrical conditions on the reachability cones further it is shown that the existence of certain polyhedral cones is equivalent to positive periodic realizations the connection between the above two kinds of cones is established elsevier science inc 1997

positive nonlinear realizations of response maps abstract the problem of realization of a positive response map as a positive initialized system on a finite dimensional euclidean state space is investigated the dynamical part of the system is described by a delta differential equation on an arbitrary time scale this incorporates continuous and discrete time systems the main result states necessary and sufficient conditions for existence of positive realization of a particular class the criterion is expressed in the language of skew differential global universes

canonical forms for positive discrete time linear control systems abstract in this paper the properties of reachability controllability and essential reachability of positive discrete time linear control systems are studied these properties are characterized in terms of the directed graph of the state matrix from these characterizations canonical forms of those properties are deduced

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

brief identification of positive linear systems with poisson output transformation positive systems are systems in which the input state output variables are always positive since they represent quantities we propose an identification procedure for a class of positive linear systems

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

positive realizations of nonlinear input output discrete time systems abstract the problem of realization of a positive nonlinear input output discrete time system as a positive state space system is investigated the input output system is given by a difference equation of a higher order a necessary and sufficient condition for existence of positive and regularly positively observable realization is provided the state space variables of the realization are found as independent generators of some positive universe associated to the input output system only the single input single output case is studied and all functions describing the systems and their properties are assumed to be continuous

new statistical investigations of the ornstein uhlenbeck process an asymptotic analysis is presented for estimation in the three parameter ornstein uhlenbeck process where the parameters are the local mean the drift and the variance we are interested in the case when the damping parameter or t is nearly zero the asymptotic sufficient statistics can be related to noncentral 12 distribution the maximum likelihood estimate of the parameter vector is a solution of a rather complicated system of equations we describe the methods for solving maximum likelihood equations classical and robust estimators are determined for parameters it is shown that the lower confidence limit of the drift or damping parameter is equal to zero with positive probability when it is near to zero

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

positive realizations of linear systems abstract this paper deals with the realization problem of linear systems in which a sign pattern is imposed on the realization a b c t this problem arises in the context of positive linear systems i e systems in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative using a unitary framework for continuous time and discrete time systems we derive necessary and sufficient conditions for positive realizability by means of convex analysis moreover the complete solution in the case of a transfer function of mcmillan degree n 3 is obtained

on level crossing excursions of gaussian low pass random processes level crossing problems have been the subject of much study for centuries practical applications can be found in many fields of engineering e g predicting flood levels random mechanical stress analysis electrical excursions that overload equipment and disruptive effects in signal processing in this paper we focus on stationary gaussian low pass random processes and in particular of the discrete time first order markov type we derive new results for discrete time processes and links to known results for continuous time processes to arrive at a general understanding of the excursion statistics expressions are derived for the crossing rate shape of large excursions peak distribution and sojourn probability simulation results are compared with the various theoretical formulations along the way we obtain a new continuous time sojourn density approximation that extends the useful range of rice s formula to longer intervals

positive and compartmental systems when dealing with compartmental systems an important question is given an experiment i e an input output sequence and supposing there is no error in the data is the sequence compatible with the compartmental assumption if the process under analysis is linear then the previous question is obviously equivalent to asking whether a given transfer function is that of a compartmental system in this note we provide an answer to the latter question giving necessary and sufficient conditions for a transfer function to be that of a compartmental system of some finite order i e number of compartments another problem tackled in this note originates from the observation that in many cases one wants to determine the number of compartments involved in the process in this note we report a step toward the solution of this fundamental problem by proving necessary and sufficient conditions for a given third order transfer function with real poles to be that of a compartmental system with three compartments

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

existence and iterative approximations of solutions for mixed quasi variational like inequalities in banach spaces abstract in this paper we introduce and investigate a new class of mixed quasi variational like inequalities in reflexive banach spaces by applying a minimax inequality due to ding tan and a lemma due to chang we establish some existence and uniqueness results of solution for the mixed quasi variational like inequality next by using a kkm theorem due to fan and an auxiliary principle technique due to cohen we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms our results extend improve and unify several known results in the literature

realization of positive linear systems abstract positive linear systems are frequently used as mathematical models in research areas like biology and economics the problem of classifying all minimal realizations of these systems is treated in this paper extensive use is made of the theory of polyhedral cones sufficient and necessary conditions for the existence of a positive realization are given but the problem of minimality leads to the factorization problem for positive matrices ideas and results are given to come towards a solution of this factorization problem

quickest detection of abrupt changes for a class of random processes we consider the problem of quickest detection of abrupt changes for processes that are not necessarily independent and identically distributed i i d before and after the change by making a very simple observation that applies to most well known optimum stopping times developed for this problem in particular cusum and shiryayev roberts 1963 stopping rule we show that their optimality can be easily extended to more general processes than the usual i i d case

minimal eventually positive realizations of externally positive systems it is a well known fact that externally positive linear systems may fail to have a minimal positive realization in order to investigate these cases we introduce the notion of minimal eventually positive realization for which the state update matrix becomes positive after a certain power eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive but only transiently as a consequence we show that in discrete time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of markov coefficients of the impulse response in continuous time instead if the sampling time is chosen sufficiently long a minimal eventually positive realization leads always to a sampled realization which is minimal and positive

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

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

lyapunov functions and duality for convex processes the paper studies convex lyapunov functions for differential and difference inclusions with right hand sides given by convex processes that is by set valued mappings the graphs of which are convex cones convex conjugacy between weak lyapunov functions for such inclusions and lyapunov functions for adjoint inclusions is established asymptotic stability concepts are compared and the existence of convex lyapunov functions for classes of convex processes is shown the relevance of the results for the study of asymptotic controllability or stabilizability and of detectability for linear control systems with conical control and state constraints is underlined

rates of convergence of approximate maximum likelihood estimators in the ornstein uhlenbeck process berry esseen bounds with random and nonrandom normings and large deviation probability bounds for two approximate maximum likelihood estimators of the drift parameter in the ornstein uhlenbeck process are obtained when the process is observed at equally spaced dense time points also obtained are the rates at which these estimators converge to the maximum likelihood estimator based on continuous observation

two strategies in the problem of change detection and isolation the comparison between optimal sequential and nonsequential fixed size sample strategies in the problem of abrupt change detection and isolation is discussed in particular we show that sometimes a simple fixed size sample algorithm is almost as efficient as an optimal sequential algorithm which leads to a burdensome number of arithmetical operations

fault detection schemes for continuous time stochastic dynamical systems in this paper the fault detection fd task in stochastic continuous time dynamical systems is addressed a new family of fd approaches is presented which is based on the application of hypothesis testing on continuous time estimators the given fd schemes are widely analyzed in the framework of their characteristics such as fault detectability false alarms and missed detection a collection of sufficient detectability conditions are given for a class of faults referred here as generic characterizing the faults which can be detected with certain formalized guarantee by the given fd schemes and providing also an upper bound for the detection time in a probabilistic sense the application and comparative performance of these fd approaches is illustrated for different faults in a simulation example

fault detection for discrete time linear systems based on descriptor observer approach this paper investigates the problem of actuator fault detection filter design for discrete time linear systems with output disturbance by using the descriptor observer method an h fault detection filter is designed to guarantee the residual system is admissible and satisfies the h performance by utilizing lyapunov function approach a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality lmi the desired fault detection filter can be designed by solving a set of lmis finally a numerical example is proposed to illustrate the effectiveness of the developed method

on the reachable set for third order linear discrete time systems with positive control the case of complex eigenvalues abstract in this paper we study the geometrical properties of the set of reachable states of a single input third order discrete time linear system with positive controls this set is a cone and we give a complete geometrical characterization of this set when the system has a complex conjugate pair of eigenvalues more in detail we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations

on the positive invariance of polyhedral sets for discrete time systems abstract in this note necessary and sufficient conditions for a polyhedral set to be a positively invariant set of a linear discrete time system are established

analysis of systems with slope restricted nonlinearities using externally positive zames falb multipliers this paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope restricted nonlinearity and the other element is a linear system the approach is based on the use of zames falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive noncausal transfer function by restricting attention to a subset of these multipliers a set of pure linear matrix inequality conditions is obtained which requires no initial parameterization by the user a useful byproduct of using externally positive systems is that the results are applicable to nonodd slope restricted nonlinearities which is not the case for all classes of zames falb multipliers

stability and dissipativity theory for discrete time non negative and compartmental dynamical systems non negative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are non negative these models are widespread in engineering biomedicine and ecology in this paper we develop several results on stability dissipativity and stability of feedback interconnections of discrete time linear and non linear non negative dynamical systems specifically using linear lyapunov functions we first develop necessary and sufficient conditions for lyapunov stability and asymptotic stability for non negative systems in addition using linear and non linear storage functions with linear supply rates we develop new notions of dissipativity theory for non negative dynamical systems finally these results are used to develop general stability criteria for feedback interconnections of non negative dynamical systems

structural properties of discrete time linear positive periodic systems abstract we study reachability and controllability properties for discrete time positive periodic systems the equivalence between n periodic systems with n states and m inputs and invariant systems with n states and nm inputs preserves the positivity of such systems and in addition closely relates their reachability cones this equivalence permits us to show that the complete contrallability reachability of a positive n periodic system is equivalent to the complete contrallability reachability of n associated positive invariant systems

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

a note on ritov s bayes approach to the minimax property of the cusum procedure 1 introduction page 1954 proposed the cusum procedures as a solu tion to the problem of sequential detection of a change in distribution lorden 1971 introduced a notion of minimax optimality for change point models andshowed that the cusum procedures are asymptotically optimal in his sense moustakides 1986 then showed the minimax optimality of the cusum pro cedures when the initial and nal distribution are both known ritov 1990 used a bayes approach and gave an interesting argument for moustakides result similar to that of lehmann 1959 on the optimality of the sequentialprobability ratio test we transfer his approach to a continuous time modeland discuss the structure of the bayes risk let be an arbitrary but known constant we will consider a process wwithw

positive input reachability and controllability of positive systems abstract we study controllability and reachability for discrete linear control systems x k 1 ax k bu k in which the state vector x k the control vector u k the n n matrix a and the n m matrix b have nonnegative entries for an unconstrained system controllability is equivalent to reachability from the zero state in n steps furthermore a b is controllable if and only if the matrix c n b ab a 2 b a n 1 b has rank n we show that these properties are not equivalent for positive systems this has important implications for control strategy the timing of control inputs and the size and structure of the control matrix b are much more critical the zero nonzero pattern of c n plays a crucial role we illustrate these fundamental differences with models of a two species reversible chemical reaction and with two pharmacokinetic models of drug distribution in the human body

on the reachable set for third order linear discrete time systems with positive control abstract in this paper we study the geometrical properties of the set of reachable states of a single input third order discrete time linear system with positive controls this set is a cone and we give a complete geometrical characterization of this set when the system has all real eigenvalues more in detail we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations moreover we provide necessary and sufficient conditions for finite time reachability of every reachable state and characterize the minimum number of steps needed to reach every state in terms of eigenvalue locations

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

controllability and reachability criteria for discrete time positive systems discrete time positive systems have been the object of widespread interest in the literature in the last decade particular attention has been devoted to the analysis and characterization of the different notions of reachability and controllability which in this context make their appearance in this paper the properties of ordinary and essential controllability and reachability are analysed based on a graph theoretic approach we provide practical criteria to verify whether a given positive system f g is endowed with these properties together with canonical forms for describing reachable controllable pairs

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

null controllability of discrete time positive control systems abstract the discrete time linear positive and quasilinear monotone systems are considered the set of initial points is restricted to be the cone of non negative vectors the input belongs to the cone of non positive vectors the necessary and sufficient conditions of null controllability for linear systems are obtained the conditions are sufficient for quasilinear systems