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

exponential stability of discrete time switched linear positive systems with time delay abstract this paper addresses the exponential stability problem for a class of discrete time switched linear positive systems dslpss with time delay firstly an exponential stability criterion for a non switched delay positive system is proposed then by constructing a suitable co positive type lyapunov krasovskii functional an exponential stability criterion for switched delay positive systems is derived via the average dwell time approach and a stability criterion for switched positive systems with multiple delays is stated and its proof is sketched finally a numerical example is given to illustrate the obtained results

stochastic stability and l1 gain analysis for positive nonlinear semi markov jump systems with time varying delay via t s fuzzy model approach abstract this paper treats the issues of stochastic stability and l 1 gain analysis for continuous time positive fuzzy semi markov jump systems pfsmjss with time varying delay the system under consideration involves semi markov stochastic process related to weibull distribution the practical systems such as lotka volterra population model described by pfsmjss always need to consider the sudden change in the operating process to deal with these problems a sufficient condition for stochastic stability of pfsmjss is established which is dependent of the bound of time varying delay then based on the obtained results l 1 gain performance is analyzed in standard linear programming lp finally lotka volterra population model shows the validity of the conclusions

decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology this paper considers synchronization problem of a complex dynamical network with randomly switching topology which means that the topology of a complex network probabilistically switches for this problem a decentralized guaranteed cost dynamic feedback controller is designed to achieve the synchronization of the network based on lyapunov stability theory and linear matrix inequality framework the existence condition for feasible controllers is derived in terms of linear matrix inequalities finally the proposed method is applied to two numerical examples in order to show the effectiveness of our result

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

codimension 2 hopf bifurcation of a two degree of freedom vibro impact system abstract codimension 2 hopf bifurcation problem of a two degree of freedom system vibrating against a rigid surface is investigated in this paper the four dimensional poincare map of the vibro impact system is reduced to a two dimensional normal form by virtue of a center manifold reduction and a normal form technique then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of codimension 2 hopf bifurcation of the vibro impact system the quasi periodic response of the system by theoretical analysis is well supported by numerical simulations it is shown that there exists codimension 2 hopf bifurcation in multi degree of freedom vibro impact systems the codimension 2 tori doubling phenomenon and the routes of quasi periodic impacts to chaos are reported briefly

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

a note on discrete time positive realizations abstract a discrete time positive linear system has the property that any nonnegative initial state and any nonnegative input produces a nonnegative trajectory in the state space and output for all time such systems are r n reachable if every state of the nonnegative orthant r n is reachable from origin with a nonnegative input function in a finite time interval a simple necessary and sufficient condition for r n realizability i e for the existence of a nonnegative realization that is also r n reachable is stated the realization procedure is straightforward

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

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

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

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

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

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

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

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

brief paper feedback control of limit cycle amplitudes from a frequency domain approach in this paper a problem in feedback control of limit cycle amplitudes is studied a graphical approach for this bifurcation control problem is developed by means of higher order harmonic balance approximations for both amplitude and frequency of the system oscillatory outputs the approach starts with the familiar hopf bifurcation mechanism and employs the second fourth and sixth order harmonic balance approximations to generate a sequence of graphical tests for convergence analysis of the system oscillatory outputs this sequential graphical testing leads to accurate approximations of limit cycles of small amplitudes in the system outputs degenerate hopf bifurcation theory is used to formulate an appropriate control objective of capturing small amplitude limit cycles which can avoid reaching unstable equilibria or other undesirable limit sets a rich cubic planar model is presented for illustration of the proposed control method

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

guaranteed cost synchronization of a complex dynamical network via dynamic feedback control abstract in this paper the problem of guaranteed cost synchronization for a complex network is investigated in order to achieve the synchronization two types of guaranteed cost dynamic feedback controller are designed based on lyapunov stability theory a linear matrix inequality lmi convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function finally a numerical example is given to illustrate the proposed method

modulation equation and spdes on unbounded domains we consider the approximation via modulation equations for nonlinear spdes on unbounded domains with additive space time white noise close to a bifurcation an infinite band of eigenvalues changes stability and we study the impact of small space time white noise on the dynamics close to this bifurcation as a first example we study the stochastic swift hohenberg equation on the whole real line here due to the weak regularity of solutions the standard methods for modulation equations fail and we need to develop new tools to treat the approximation as an additional result we sketch the proof for local existence and uniqueness of solutions for the stochastic swift hohenberg and the complex ginzburg landau equations on the whole real line in weighted spaces that allow for unboundedness at infinity of solutions which is natural for translation invariant noise like space time white noise we use energy estimates to show that solutions of the ginzburg landau equation are holder continuous and have moments in those functions spaces this gives just enough regularity to proceed with the error estimates of the approximation result

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

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

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

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

approximation and attractivity properties of the degenerated ginzburg landau equation abstract we are interested in spatially extended pattern forming systems close to the threshold of the first instability in case when the so called degenerated ginzburg landau equation takes the role of the classical ginzburg landau equation as the amplitude equation of the system this is the case when the relevant nonlinear terms vanish at the bifurcation point here we prove that in this situation every small solution of the pattern forming system develops in such a way that after a certain time it can be approximated by the solutions of the degenerated ginzburg landau equation in this paper we restrict ourselves to a swift hohenberg kuramoto shivashinsky equation as a model for such a pattern forming system

nonlinear stability of taylor vortices in infinite cylinders we consider the taylor couette problem in an infinitely extended cylindrical domain in the case when couette flow is weakly unstable and a family of spatially periodic equilibria called the taylor vortices has bifurcated from this trivial ground state we show that those taylor vortices which are not linearly unstable in the sense of eckhaus are in fact nonlinearly stable with respect to small spatially localized perturbations the main difficulty in showing this result stems from the fact that on unbounded cylindrical domains the taylor vortices are only linearly marginally stable with continuous spectrum up to the imaginary axis bloch wave representations of the solutions and renormalization theory allow us to show that the nonlinear problem behaves asymptotically like the linearized one which is under a diffusive regime

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

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

hopf bifurcation of a two degree of freedom vibro impact system abstract the bifurcation problem of a two degree of freedom system vibrating against a rigid surface is studied in this paper it is shown that there exist hopf bifurcations in the vibro impact systems with two or more degrees of freedom under suitable system parameters in the paper a centre manifold theorem technique is applied to reduce the poincare map of the vibro impact system to a two dimensional one and then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of hopf bifurcation of the vibro impact system the theoretical solutions are verified by numerical computations the quasi periodic response of the system represented by invariant circles in the projected poincare sections is obtained by numerical simulations and routes of quasi periodic impacts to chaos are stated briefly

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

more relaxed stability analysis and positivity analysis for positive polynomial fuzzy systems via membership functions dependent method abstract in this paper the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy model based ppfmb control system are studied also in order to improve the flexibility of controller design a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed in the existing literatures it is proved that the lclf can reduce the conservatism of stability results however the lclf generally results in non convex conditions which is still a conservatism source to handle the non convex conditions the sector nonlinear concept is applied to handle non convex terms in stability conditions and the obstacles caused by mismatched membership functions can be eliminated by plmf dependent method in addition to relax the conservatism caused by the lack of membership functions information the plmf dependent positivity analysis are performed for the first time meanwhile plmf dependent method is extended to stability conditions to obtained more relaxed conditions finally a simulation example is presented to verify the feasibility of this method

stability analysis of positive switched linear systems with delays this technical note addresses the stability problem of delayed positive switched linear systems whose subsystems are all positive both discrete time systems and continuous time systems are studied in our analysis the delays in systems can be unbounded under certain conditions several stability results are established by constructing a sequence of functions that are positive monotonically decreasing and convergent to zero as time tends to infinity additionally continuous for continuous time systems it turns out that these functions can serve as an upper bound of the systems trajectories starting from a particular region finally a numerical example is presented to illustrate the obtained results

anti controlling quasi periodic impact motion of an inertial impact shaker system in this paper anti controlling quasi periodic impact motion of an inertial impact shaker system is addressed there exist two aspects of difficulty in the anti control design one is from the implicit poincare map of the system itself and the other from the limitation of the classical critical criterion of hopf bifurcation described by the properties of eigenvalues through using linear feedback control method in the original differential system and applying an explicit criterion of hopf bifurcation without using eigenvalues to the poincare map of the close loop system the two difficulties above can be overcome and the control design for creation of the quasi periodic impact motion at a specified system parameter location is achieved numerical simulation shows that the stable quasi periodic impact motion of the system is created at a desired parameter location by adjusting control parameter appropriately

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

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

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

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

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

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

positivity exponential stability and disturbance attenuation performance for singular switched positive systems with time varying distributed delays abstract this article analyzes the singular switched positive systems with time varying distributed delays from the perspective of positivity exponential stability and disturbance attenuation performance referring to both l1 gain and l gain for the system a sufficient and necessary positivity condition is firstly developed by using the singular value decomposition technique then a sufficient condition of exponential stability which makes the considered system exponentially stable is proposed on the basis of co positive lyapunov krasovskii functional and average dwell time techniques and the obtained exponential decay rate can be adjusted in the light of various actual situations furthermore the article analyzes the disturbance attenuation performance referring to both l1 gain and l gain and through the convex optimization approach the optimal l1 gain and l gain performance level could be established respectively three examples are finally presented to show the feasibility and effectiveness of the obtained results

stability analysis and synthesis for switched takagi sugeno fuzzy positive systems described by the roesser model abstract this article focuses on stability analysis and controller synthesis of a class of roesser type switched takagi sugeno fuzzy systems with delays first sufficient conditions derived by use of the co positive lyapunov function and the average dwell time method are presented to guarantee the proposed system is positive and exponentially stable then via a state feedback fuzzy controller criteria are also given under which not only the resulting closed loop system is positive and exponentially stable but also the desired controller gain matrices can be designed by solving a set of coupled matrix inequalities finally two illustrative examples are provided to show the effectiveness of the approach outlined in this article

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

stabilization of period doubling bifurcations and implications for control of chaos abstract the stabilization of period doubling bifurcations for discrete time nonlinear systems is investigated it is shown that generically such bifurcations can be stabilized using smooth feedback even if the linearized system is uncontrollable at criticality in the course of the analysis expressions are derived for bifurcation stability coefficients of general n dimensional systems undergoing period doubling bifurcation a connection is determined between control of the amplitude of a period doubled orbit and the elimination of a period doubling cascade to chaos for illustration the results are applied to the henon attractor

amplitude equation for lattice maps a renormalization group approach we consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps under some generic hypotheses we derive an amplitude equation which is the space time continuous ginzburg landau equation using dynamical renormalization group methods we control the accuracy of this approximation in a large ball of its basin of attraction

lmi approach to linear positive system analysis and synthesis abstract this paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities lmis we first show that the celebrated perron frobenius theorem can be proved concisely by a duality based argument again by duality we next clarify a necessary and sufficient condition under which a hurwitz stable metzler matrix admits a diagonal lyapunov matrix with some identical diagonal entries as the solution of the lyapunov inequality this new result leads to an alternative proof of the recent result by tanaka and langbort on the existence of a diagonal lyapunov matrix for the lmi characterizing the h performance of continuous time positive systems in addition we further derive a new lmi for the h performance analysis where the variable corresponding to the lyapunov matrix is allowed to be non symmetric we readily extend these results to discrete time positive systems and derive new lmis for the h performance analysis and synthesis we finally illustrate their effectiveness by numerical examples on robust state feedback h controller synthesis for discrete time positive systems affected by parametric uncertainties

design of polynomial fuzzy observer controller with membership functions using unmeasurable premise variables for nonlinear systems in this paper the stability of polynomial fuzzy model based pfmb observer control system is investigated via lyapunov stability theory the polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states then the estimated system states are used for the state feedback control of nonlinear systems although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy model based fmb control strategy it leads to non convex stability conditions therefore the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares sos with less manually designed parameters in addition the membership functions of the polynomial observer controller are optimized by the improved gradient descent method which outperforms the widely applied parallel distributed compensation pdc approach according to a general performance index simulation examples are provided to verify the proposed design and optimization scheme

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

pre specified performance based model reduction for time varying delay systems in fuzzy framework this paper attempts to provide a new solution to the model approximation problem for dynamic systems with time varying delays under the fuzzy framework for a given high order system our focus is on the construction of a reduced order model which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system based on the reciprocally convex technique a less conservative stability condition is established for the dynamic error system with a given error performance index furthermore the reduced order model is eventually obtained by applying the projection approach which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm finally two numerical examples are provided to illustrate the effectiveness of the proposed method

bifurcations and chaos in a system with impacts abstract a vibro impact system is considered a body bounces on a flat horizontal surface of the vibro bench hopf bifurcations of the vibro impact system in two kinds of strong resonance cases 03 1 and 04 1 are investigated a poincare map of the system is established the period 1 single impact motion of the system and its stability are studied by analytical methods and hopf bifurcation values and intersecting conditions of the system in strong resonance cases are determined a center manifold theorem technique is applied to reduce the poincare map to a two dimensional one which is put into normal form by theory of normal forms by the theory of hopf and subharmonic bifurcations of fixed points in r 2 strong resonance dynamic behavior of the vibro impact system near points of resonance is analyzed in the resonance case of 03 1 the system generally exhibits unstable period 3 three impact motion in the resonance case of 04 1 the system can exhibit stable period 4 four impact motion and quasi periodic motion the theoretical analyses are verified by numerical solutions routes to chaos in two kinds of strong resonance cases considered are obtained by numerical simulations quasi periodic impacts in non resonance and weak resonance cases doubling periodic bifurcations and chaotic motions are also stated briefly by numerical analyses

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

diffusive stability of spatial periodic solutions of the swift hohenberg equation we are interested in the nonlinear stability of the eckhaus stable equilibria of the swift hohenberg equation on the infinite line with respect to small integrable perturbations the difficulty in showing stability for these stationary solutions comes from the fact that their linearizations possess continuous spectrum up to zero the nonlinear stability problem is treated with renormalization theory which allows us to show that the nonlinear terms are irrelevant i e that the fully nonlinear problem behaves asymptotically as the linearized one which is under a diffusive regime

interaction of hopf and period doubling bifurcations of a vibro impact system abstract an inertial shaker as a vibratory system with impact is considered by means of differential equations periodicity and matching conditions the theoretical solution of periodic n 1 impacting motion can be obtained and the poincare map is established dynamics of the system are studied with special attention to interaction of hopf and period doubling bifurcations corresponding to a codimension 2 one when a pair of complex conjugate eigenvalues crosses the unit circle and the other eigenvalue crosses 1 simultaneously for the jacobi matrix the four dimensional map can be reduced to a three dimensional normal form by the center manifold theorem and the theory of normal forms the two parameter unfoldings of local dynamical behavior are put forward and the singularity is investigated it is proved that there exist curve doubling bifurcation a torus doubling bifurcation hopf bifurcation of 2 2 fixed points as well as period doubling bifurcation and hopf bifurcation of 1 1 fixed points near the critical point numerical results indicate that the vibro impact system presents complicated and interesting curve doubling bifurcation and hopf bifurcation as the two controlling parameters vary

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

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

attractivity of the ginzburg landau mode distribution for a pattern forming system with marginally stable long modes abstract the mathematical theory of the description of pattern forming systems close to the first instability via the ginzburg landau equation is based on approximation and attractivity results this theory allowed to prove global existence results and upper semicontinuity of attractors for classical hydrodynamical stability problems such as the couette taylor problem recently approximation results for the ginzburg landau approximation for pattern forming systems with marginally stable long modes such as the benard marangoni system have been shown it is the purpose of this paper to prove the second fundamental property namely the attractivity of the ginzburg landau mode distribution for such systems

local feedback stabilization and bifurcation control i hopf bifurcation abstract local bifurcation control problems are defined and employed in the study of the local feedback stabilization problem for nonlinear systems in critical cases sufficient conditions are obtained for the local stabilizability of general nonlinear systems whose linearizations have a pair of simple nonzero imaginary eigenvalues the conditions show in particular that generically these nonlinear critical systems can be stabilized locally even if the critical modes are uncontrollable the analysis also yields a direct method for computing stabilizing feedback controls use is made of bifurcation formulae which require only a series expansion of the vector field

delay dependent and decay rate dependent conditions for exponential mean stability and non fragile controller design of positive markov jump linear systems with time delay abstract this paper proposes some new sufficient conditions and necessary conditions for exponential mean stability with prescribed decay rate and sufficient conditions for non fragile controller design of both continuous time and discrete time positive markov jump linear systems with time delay first sufficient stability conditions are derived by constructing novel linear stochastic co positive lyapunov krasovskii functionals second the corresponding necessary conditions are established by applying a model transformation technique and analyzing the relationship between stochastic stability of the transformed systems and exponential mean stability with given decay rate of the original systems compared with the existing conditions the proposed stability conditions are not only delay dependent but also decay rate dependent and the sufficient conditions plus the necessary conditions can be used to judge the system stability more precisely third based on the new sufficient conditions non fragile controllers are designed by solving linear programming problems such that the closed loop systems are positive and exponentially mean stable with an expected decay rate finally by numerical examples the effects of both time delay and decay rate on exponential mean stability are exploited and the validity of the non fragile controller design conditions is demonstrated

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

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

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

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

stability and stabilization for positive systems with semi markov switching abstract in this article the problems of mean stability analysis and control synthesis are studied for stochastic switching systems subject to positive constraint such a switching is governed by a semi markov process subject to a special non exponential distribution considering a linear lyapunov krasovskii function lkf necessary and sufficient conditions are proposed to realize mean stability for the open loop system based on this the solvability conditions for the desired stabilizing controller can be determined under a linear programming lp framework finally the theoretical findings are illustrated by the virus mutation treatment model

criterion to identify hopf bifurcations in maps of arbitrary dimension the classical hopf bifurcation criterion is stated in terms of the properties of eigenvalues in this paper a criterion without using eigenvalues is proposed for maps of arbitrary dimension the parameter mechanism of hopf bifurcation may be explicitly formulated on the basis of the criterion a numerical example demonstrates that the proposed criterion is preferable to the classical hopf bifurcation criterion in theoretical analysis and practical applications

analyticity of ginzburg landau modes ginzburg landau formalism applies for dissipative systems defined on cylindrical domains which are close to the threshold of instability and for which the unstable fourier modes belong to non zero wave numbers in these situations the real part of the curve of critical eigenvalues as function drawn over the wave numbers k is positive of height o 2 and of width o here it is shown that the set of solutions which can be described by the ginzburg landau formalism is attractive to do this we demonstrate that in fourier space peaks appear at integer multiples of the critical wave number kc these peaks called ginzburg landau modes concentrate in time like e k mkc t for 0 t o 1 2 and m z the inverse fourier transform of such a ginzburg landau mode is an analytic function in a strip of width t this result extends a former work of w eckhaus

dynamic output feedback control for positive roesser system under the switched and t s fuzzy rules abstract this paper is concerned with the dynamic output feedback controller design for the positive roesser type nonlinear system which is intrinsically characterized by the switched mechanism and subtly decomposed into the linear form under the takagi sugeno fuzzy rules firstly based on the co positive lyapunov function and the average dwell time method sufficient conditions are presented under which the resulting closed loop system is exponentially stable and has l 1 gain bound then explicit expressions are also given to derive the expected controller gain matrices with desired l 1 gain bound finally effectiveness of the proposed results is illustrated by two numerical examples

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

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