controllability of linear single input positive discrete time systems linear positive systems are utilized in various scientific areas such as economic modelling behavioural science stochastic processes etc a recent study has focused on some sufficient conditions for the controllability of these systems a full characterization is provided of the controllability for discrete time single input positive systems necessary and sufficient conditions are derived using a digraph theoretic approach the main results show that strong constraints are to be imposed on the digraph associated with the pair a b to ensure the controllability of the system

structural properties of positive linear time invariant difference algebraic equations in this paper we analyze positive difference algebraic equations conditions regarding some of the matrices involved in the solution of this kind of systems are described geometrical conditions are used to characterize positive structural properties

dynamics of a single degree of freedom structure with quadratic cubic and quartic non linearities to a harmonic resonance the solution of a non linear equation having often encountered in the study of structural dynamically and in which both parametric and external excitations are present have been obtained analytically and numerically the only considered case is when both the parametric and external excitations have the same frequency the method of multiple time scale is applied to determine the equations that describe up to and including the second order both the modulation of the amplitude and phase these equations are used to determine the fixed points and their stability frequency response curves are presented graphically discussion of the results is given numerical solutions are presented for the effects of the different equation parameters on system stability response and chaos different cases of resonance are investigated and reported

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

stability and stabilization analysis of positive polynomial fuzzy systems with time delay considering piecewise membership functions this paper is concerned with the stability analysis of positive polynomial fuzzy model based control systems with time delay each of the polynomial fuzzy model and the polynomial fuzzy controller is allowed to have its own set of premise membership functions which can improve the design and realization flexibility conditions showing the positivity of the system are first obtained then to deal with the difficulty resulting from the mismatched premise membership functions to the stability stabilization analysis approximated membership functions representing the original ones are constructed and the information of membership functions is brought into the stability conditions this way the stability conditions can be relaxed since the extra knowledge on the system is considered stability conditions are obtained by using the sum of squares approach based on the lyapunov stability theory a simulation example is provided to verify the effectiveness of this method

looking for nonnegative solutions of a leontief dynamic model let a be an n n nonnegative real matrix we know that a is monotone if it has a nonnegative inverse moreover if a has an appropriate generalized inverse then we can obtain nonnegative solutions for the linear system ax b where b 0 in this paper using properties about nonnegatives matrices we present sufficient conditions in order that the leontief price model i f p k 1 1 r k fp k gp0 k 1 a0 where f i at 1bt and g i at 1 have nonnegative solutions

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

non stationary parametric oscillations the response of a single degree of freedom system with cubic non linearity to a non stationary principal parametric excitation is investigated the method of multiple scales is used to derive two first order ordinary differential equations for the evolution of the amplitude and phase of the response the evolution equations are numerically integrated for various sweeping rates of the amplitude and frequency of the excitation the results show that the non stationary response penetrates the instability regions and the higher the sweeping rate is the deeper the penetration is

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

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

model based control and stability analysis of discrete time polynomial fuzzy systems with time delay and positivity constraints this paper proposes a novel lyapunov stabilization analysis of discrete time polynomial fuzzy model based control systems with time delay under positivity constraint the polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete time system with time delay a model based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the positivity constraints the lyapunov stability and positivity conditions are formulated as sum of squares to relax the conservativeness of the obtained stability results two main methods are proposed in this paper first the piecewise linear membership functions plmfs are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis and second introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information a numerical example is given to demonstrate the effectiveness of the proposed approach

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

stable internally positive representations of continuous time systems an internally positive representation ipr of a non positive system is a positive system that under suitable input state and output transformations exactly replicates the behavior of the original system any construction method of an ipr necessarily introduces additional natural modes which in some cases are unstable in a previous paper the authors have presented a method that provides a stable ipr if and only if the eigenvalues of the original system lie in a specific sector of the open left half complex plane in this technical note a new technique is proposed that overcomes such a limitation and provides a stable ipr for any stable system although in some cases the dimension of the ipr must be large in order to guarantee its stability although for simplicity the method is only illustrated for single input single output systems with distinct eigenvalues it also applies to multi input multi output systems with multiple eigenvalues

advances on the reachability index of positive 2 d systems this work was supported by dgi grant mtm2010 18228 recommended by associate editor z wang

stability and bifurcations of hysteretic systems subjected to principal parametric excitation dynamic behavior of smooth hysteretic systems subjected to harmonic parametric excitation is investigated wen s differential equation model for hysteresis which can describe a large class of hysteretic systems is used employing the piecewise power series expression for hysteresis proposed in the previous paper the method of multiple scales is applied for the case of principal parametric resonance to obtain the second order approximate solutions and their stability it is shown that the hysteretic systems are unstable inside the principal resonance region but the responses are bounded having symmetric periodic solutions it is also shown that the systems are stable outside the region even if viscous damping does not exist because of hopf bifurcation numerical integrations are also performed to illustrate the nonlinear resonant characteristics of the systems and confirmed that trivial stationary solutions and stable symmetric periodic solutions in principal resonance region bifurcate to produce a pair of non symmetric periodic solutions stability regions with regard to excitation parameters are also illustrated the theoretical and numerical results are compared to examine the validity of the present analysis

the response of two degree of freedom systems with quadratic non linearities to a combination parametric resonance abstract the response of two degree of freedom systems with quadratic non linearities to a combination parametric resonance in the presence of two to one internal resonances is investigated the method of multiple scales is used to construct a first order uniform expansion yielding four first order non linear ordinary differential equations governing the modulation of the amplitudes and the phases of the two modes steady state responses and their stability are computed for selected values of the system parameters the effects of detuning the internal resonance detuning the parametric resonance the phase and magnitude of the second mode parametric excitation and the initial conditions are investigated the first order perturbation solution predicts qualitatively the trivial and non trivial stable steady state solutions and illustrates both the quenching and saturation phenomena in addition to the steady state solutions other periodic solutions are predicted by the perturbation amplitude and phase modulation equations these equations predict a transition from constant steady state non trivial responses to limit cycle responses hopf bifurcation some limit cycles are also shown to experience period doubling bifurcations the perturbation solutions are verified by numerically integrating the governing differential equations

homology of the zero set of a nilpotent vector field on a flag manifold 0 1 let x be a linear transformation of a finite dimensional vector space v the configuration of flags in v which are fixed by x has rather remarkable properties when x is unipotent though this case is especially interesting the proper generality in which to study such configurations is in the theory of reductive algebraic groups where their definition can be reformulated in the language of borel subalgebras as follows let g be a connected reductive group over c with lie algebra g and let n e g be a nilpotent element let q be the variety of all borel subalgebras of g and let

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

indeterminate sub critical bifurcations in parametric resonance in this paper we show that an indeterminate sub critical bifurcation with an unpredictable outcome arises in typical parametrically excited systems this occurs when the trivial solution is located on a fractal boundary as it loses its stability at a sub critical bifurcation here in the presence of even infinitesimal noise the outcome is indeterminate in the sense that we cannot predict on to which co existing attractor the system will settle

parametric vibrations of a restrained beam with an end mass under displacement excitation this paper is concerned with the stability and the steady state response of the main parametric resonance vibrations of a simply supported vertical beam the beam carries a concentrated mass and is restrained at one end and subjected to a periodic axial displacement excitation at the other end this system can be looked upon as a dynamic model of the vibrations of an engine valve mechanism non linear terms arising from moderately large curvatures longitudinal inertia of the beam elements and concentrated mass are included in the equation of motion by using the one mode approximation and applying galerkin s method the governing partial differential equation is reduced to a non linear ordinary differential equation with a periodic coefficient the boundaries of the main parametric instability region of the linearized equation are obtained the harmonic balance method is applied to solve the equation and an analytical expression for the dynamic response in the vicinity of the main parametric resonance is derived the effects of various parameters on the boundaries of the instability region and the dynamic response are investigated

interaction of fundamental parametric resonances with subharmonic resonances of order one half abstract the interaction of fundamental parametric resonances with subharmonic resonances of order one half in a single degree of freedom system with quadratic and cubic nonlinearities is investigated the method of multiple scales is used to derive two first order ordinary differential equations that describe the modulation of the amplitude and the phase of the response with the non linearity and both resonances these equations are used to determine the steady state solutions and their stability conditions are derived for the quenching or enhancement of a parametric resonance by the addition of a subharmonic resonance of order one half the degree of quenching or enhancement depends on the relative amplitudes and phases of the excitations the analytical results are verified by numerically integrating the original governing differential equation

a simple graph theoretic characterization of reachability for positive linear systems in this paper we consider discrete time linear positive systems that is systems defined by a pair a b of non negative matrices we study the reachability of such systems which in this case amounts to the freedom of steering the state in the positive orthant by using non negative control sequences this problem was solved recently canonical forms for positive discrete time linear control systems linear algebra appl 310 2000 49 however we derive here necessary and sufficient conditions for reachability in a simpler and more compact form these conditions are expressed in terms of particular paths in the graph which is naturally associated with the system

bifurcations of approximate harmonic balance solutions and transition to chaos in an oscillator with inertial and elastic symmetric nonlinearities abstract the local stability of approximate periodic solutions and period doubling bifurcations in a harmonically forced non linear oscillator with symmetric elastic and inertia non linearities are studied analytically and numerically approximate principal resonance solutions are first obtained using a two term harmonic balance and then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict zones of symmetry breaking leading to period doubling bifurcation and chaos the results of the present work which follows the analysis approach presented by szemplinska stupnika 1986 international journal of nonlinear mechanics 23 257 277 1987 journal of sound and vibration 113 155 172 are verified for selected system parameters by numerical simulations using methods of qualitative theory and good agreement was obtained between the analytical and numerical results finally a criterion for the period doubling bifurcation is proposed analytically for this type of oscillator and compared with computer simulation results that predict the true period doubling bifurcation and chaos boundaries

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

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

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

the response of a single degree of freedom system with quadratic and cubic non linearities to a fundamental parametric resonance abstract the response of a one degree of freedom system with quadratic and cubic non linearities to a principal parametric resonance is investigated the method of multiple scales is used to determine the equations that describe to second order the modulation of the amplitude and phase with time about one of the foci these equations are used to determine the fixed points and their stability the perturbation results are verified by integrating the governing equation with use of a digital computer and an analogue computer for small excitation amplitudes the analytical results are in excellent agreement with the numerical solutions the large amplitude responses are investigated by using both a digital and an analogue computer the cases of single and double well potentials are investigated systems with double well potentials exhibit complicated dynamic behaviors including period multiplying and demultiplying bifurcations and chaos in some cases a bifurcated response coexists with another periodic attractor and a chaotic attractor coexists with a periodic attractor long time histories phase planes poincare maps fractal basin maps and spectra of the response are presented a bifurcation diagram of many solutions in the excitation amplitude excitation frequency plane is also presented

non linear structural vibrations under combined parametric and external excitations abstract a set of second order equations with weak quadratic and cubic non linearities is considered simultaneous parametric and external forcing excitations are included the frequency of the parametric excitation is near a natural frequency of the system and three cases are analyzed i the external excitation is absent ii the external excitation is present but is not involved in a resonance and iii the external frequency is the same as the parametric frequency results are obtained by the method of multiple scales frequency response curves are presented for various combinations of excitation amplitudes damping coefficients and phase shift between the excitations it is found that stable multi modal responses may exist in the first order asymptotic solution even though only one mode is involved in the resonance and no internal resonance condition is present

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

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

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

about nonnegative realizations we will state sufficient conditions such that a discrete time time invariant finite dimensional system with a nonnegative impulse response has a nonnegative finite dimensional realization the conditions are in terms of the minimal polynomial

some comments on positive orthant controllability of bilinear systems consider the bilinear system dot x a ub x x in r n and u unrestricted the system has the property that any solution x t with x 0 geqq 0 i e all components of x nonnegative will remain in the positive orthant r n x in r n x geqq 0 for 0 leqq t 0 and detailed results are presented for the case n 2

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

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

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

observations on the stability properties of cooperative systems we extend two fundamental properties of positive linear time invariant lti systems to homogeneous cooperative systems specifically we demonstrate that such systems are d stable meaning that global asymptotic stability is preserved under diagonal scaling we also show that a delayed homogeneous cooperative system is globally asymptotically stable gas for all non negative delays if and only if the system is gas for zero delay

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

numerical integration of positive linear differential algebraic systems in the simulation of dynamical processes in economy social sciences biology or chemistry the analyzed values often represent non negative quantities like the amount of goods or individuals or the density of a chemical or biological species such systems are typically described by positive ordinary differential equations odes that have a non negative solution for every non negative initial value besides positivity these processes often are subject to algebraic constraints that result from conservation laws limitation of resources or balance conditions and thus the models are differential algebraic equations daes in this work we present conditions under which both these properties the positivity as well as the algebraic constraints are preserved in the numerical simulation by runge kutta or multistep discretization methods using a decomposition approach we separate the dynamic and the algebraic equations of a given linear positive dae to give positivity preserving conditions for each part separately for the dynamic part we generalize the results for positive odes to daes using the solution representation via drazin inverses for the algebraic part we use the consistency conditions of the discretization method to derive conditions under which this part of the approximation overestimates the exact solution and thus is non negative we analyze these conditions for some common runge kutta and multistep methods and observe that for index 1 systems and stiffly accurate runge kutta methods positivity is conditionally preserved under similar conditions as for odes for higher index problems however none of the common methods is suitable

reachability properties of single input continuous time positive switched systems in this paper two reachability properties for single input positive switched systems are introduced monomial reachability and reachability monomial reachability which represents a necessary but not sufficient condition for reachability is fully characterized necessary and sufficient conditions for reachability are provided for the class of n dimensional systems switching among n subsystems several necessary or sufficient conditions are also provided moreover the definition of k switching reachability set is given and an equivalent condition for the existence of an upper bound on the number of switchings required to reach any reachable vector is given finally it is shown that for reachable systems of low dimension n 2 or n 3 each vector of the positive orthant can be reached by resorting to a switching sequence which switches no more than n 1 times

thermal vibrational analysis for simply supported beam and clamped beam the presented paper shows how the temperature field in beams has impact on vibrations of beams due to the relatively high possible temperature variations in beams we have developed the mathematical model where fundamental thermomechanical properties of state are functions of temperature such as modulus of elasticity poisson number linear expansion coefficient shear modulus and some other important thermodynamic properties of state the detailed analysis shows that also small changes of temperature cause significant changes of natural frequencies for beams the comparison between our analytical model and experimental data shows good agreement in the presented paper it is possible to find for the first time in scientific literature the application of the combination of statistical thermodynamics and the theory of vibration at the same time

tuneable non degenerated nonlinear parametrically excited amplifier abstract the proposed parametric amplifier scheme can be tuned to amplify a wide range of input frequencies by altering the parametric excitation with no need to physically modify the oscillator parametric amplifiers had been studied extensively although most of the work focused on amplifiers that are parametrically excited at a frequency twice the amplifier s natural frequency these amplifiers are confined to amplifying predetermined frequencies the proposed parametric amplifier s bandwidth is indeed tuneable to nearly any input frequency not bound to be an integer multiple of a natural frequency in order to tune the stiffness and induce a variable frequency parametric excitation a digitally controlled electromechanical element must be incorporated in the realization we introduce a novel parametric amplifier with nonlinearity duffing type hardening that bounds the otherwise unlimited amplitude moreover we present a multi degree of freedom system in which a utilization of the proposed method enables the projection of low frequency vector forces on any eigenvector and corresponding natural frequency of the system and thus to transform external excitations to a frequency band where signal levels are considerably higher using the method of multiple scales analytical expressions for the responses have been retrieved and verified numerically parametric studies of the amplifiers gain sensitivities and spatial projection of the excitation on the system eigenvectors were carried out analytically the results demonstrate the advantage of the proposed approach over existing schemes practical applications envisaged for the proposed method will be outlined

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

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

on the zero pattern properties and asymptotic behavior of continuous time positive system trajectories abstract in this paper the zero pattern properties and the asymptotic evolution of the trajectories of a continuous time positive system are investigated to this end we need to introduce some new tools and to derive some new results within the broad research area of nonnegative matrix theory which enable use to explore the zero pattern and the elementary modes of the exponential of a metzler matrix specifically a normal form for the exponential of a metzler matrix is provided and the concept of echelon basis consisting of eigenvectors and generalized eigenvectors of the metzler matrix is introduced by making use of these two ingredients a detailed result about the dominant mode of each single block appearing in the normal form of the exponential matrix is provided this allows to obtain a modal decomposition of the exponential matrix emphasizing the column dominant modes as a result the zero pattern as well as the asymptotic behavior of every free state evolution depending on the zero pattern of the initial state can be easily determined

monomial reachability and zero controllability of discrete time positive switched systems in this paper monomial reachability and zero controllability properties of discrete time positive switched systems are investigated necessary and sufficient conditions for these properties to hold together with some interesting examples and some testing algorithms are provided

internally positive representation of a class of continuous time systems the problem of realizing arbitrary transfer functions as combinations of positive filters or more in general of representing arbitrary systems by means of internally positive representations iprs has been widely investigated in the discrete time framework an ipr is a positive state space representation endowed with input state and output transformations that realizes arbitrary input state output dynamics this technical note investigates the problem of the ipr construction for continuous time systems and proposes a technique that provides stable iprs for a particular class of systems

a method for the numerical computation of hopf bifurcation this paper deals with the computation of hopf bifurcations in parameter dependent ordinary differential equations an algorithm based on an indirect method is presented while the conventional method approaches the hopf bifurcation point from the stationary solution the proposed method detects the hopf bifurcation points from the dynamic solution a computation using the proposed algorithm is implemented for finding the hopf bifurcation point of several cases and the comparison with the results obtained by other methods is given the proposed method is applicable for both autonomous and non autonomous systems

bifurcations and chaos of an immersed cantilever beam in a fluid and carrying an intermediate mass abstract the concern of this work is the local stability and period doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass the unimodal form of the non linear dynamic model describing the beam mass in plane large amplitude flexural vibration which accounts for axial inertia non linear curvature and inextensibility condition developed in al qaisia et al 2000 shock and vibration 7 179 194 is analyzed and studied for the resonance responses of the first three modes of vibration using two term harmonic balance method then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period doubling bifurcation and chaos on the resonance response curves the results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory and good agreement was obtained between the analytical and numerical results also analytical prediction of the period doubling bifurcation and chaos boundaries obtained using a period doubling bifurcation criterion proposed in al qaisia and hamdan 2001 journal of sound and vibration 244 453 479 are compared with those of computer simulations in addition results of the effect of fluid density fluid depth mass ratio mass position and damping on the period doubling bifurcation diagrams are studies and presented

controllability of positive linear discrete time systems the class of positive linear discrete time systems is considered reachability sets of such systems denned on cones are studied and some of their properties established reachability null controllability and controllability criteria are obtained in forms that are easier to implement than the corresponding criteria for linear discrete time systems of general type some classes of positive linear discrete time systems are investigated and their controllability properties are established

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

multiplicity matrices for the affine graded hecke algebra in this paper we are looking at the problem of determining the composition factors for the affine graded hecke algebra via the computation of kazhdan lusztig type polynomials we review the algorithms of g lusztig study of perverse sheaves arising from graded lie algebras adv math 112 1995 147 217 g lusztig graded lie algebras and intersection cohomology preprint and use them in particular to compute at every real central character which admits tempered modules the geometric parameterization the kazhdan lusztig polynomials the composition series and the iwahori matsumoto involution for the representations with iwahori fixed vectors of the split p adic groups of type g2 and f4 and by the nature of the algorithms for their levi subgroups

controllability of multi input positive discrete time systems linear discrete time positive systems arise in various fields of science such as economic modelling behavioural science stochastic processes etc recently some authors have examined the problem of the controllability of such systems for the single input case this paper provides necessary and sufficient conditions for characterizing the controllability properties of multi input systems the results here developed show that only a narrow class of these systems enjoys the properties of reachability and controllability

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