parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

stochastic stabilization and destabilization of nonlinear differential equations abstract this paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations which more precisely further develops the general theory of stochastic stabilization and destabilization that was studied by mao 1994 4 and appleby et al 2008 1 the proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems which is also verified with examples of application to mass action systems

analysis of the fuzzy controllability property and stabilization for a class of t s fuzzy models in this paper the controllability property for a class of takagi sugeno t s fuzzy models is analyzed while a fully nonlinear stabilizer is designed in a practical way it is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach the existence of such controllers depends on the fuzzy controllability conditions which are derived in a straightforward way the main advantage of the proposed approach is that the convergence of the closed loop system can be imposed arbitrarily some examples are given in order to illustrate the validity of the method finally the proposed controller is applied on an underactuated system known as pendubot and the results are compared with an stabilizer designed on the basis of lmis

intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators a theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit cycle oscillators with distributed native frequencies in particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above this peculiar feature is demonstrated by numerical simulations mainly through finite size scaling analyses in the course of exploring its origin we encounter a new concept termed a correlation frequency which provides a natural interpretation of the finite size scaling laws a comment is given on a recent theory by kuramoto and nishikawa to clarify why it contradicts our results

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

adaptive fuzzy backstepping tracking control for strict feedback systems with input delay this paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict feedback systems with input delay and output constraint input delay is handled based on the information of pade approximation and output constraint problem is solved by barrier lypaunov function some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub vectors a novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed loop systems are semiglobally uniformly ultimately bounded and the tracking error can be adjusted around the origin with a small neighborhood the stability of the closed loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach

adaptive fuzzy control for a class of nonlinear discrete time systems with backlash an adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper the considered systems are of the discrete time form in a triangular structure and include the backlash and the external disturbance by using the prediction function of future states the systems are transformed into an n step ahead predictor the fuzzy logic systems flss are used to approximate the unknown functions unknown backlash and backlash inversion respectively a discrete time tuning algorithm is developed to estimate the optimal fuzzy parameters compared with the previous works for the discrete time systems with backlash the main contributions of the paper are that 1 the rigorous restriction for the functional estimation error is removed and 2 the external disturbance is bounded but the bound is not required to be known a novel controller and the adaptation laws are constructed by using the discrete taylor series expansion and the difference lyapunov analysis and thus those limitations in the previous works are overcome it is proven that all the signals in the closed loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set a simulation example is provided to illustrate the effectiveness of the proposed approach

adaptive fuzzy identification and control for a class of nonlinear pure feedback mimo systems with unknown dead zones the adaptive fuzzy identification and control problems are considered for a class of multi input multi output nonlinear systems with unknown functions and unknown dead zone inputs the main characteristics of the considered systems are that 1 they are composed of n subsystems and each subsystem is in nested lower triangular form 2 dead zone inputs are in nonsymmetric nonlinear form and 3 dead zone inputs appear nonlinearly in the systems and their parameters are not required to be known the controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions the couplings among the nested subsystems and the dead zone inputs in the controller design the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead zone inputs to compensate for dead zone inputs the compensative terms are designed in the controllers the stability of the closed loop system is proved via the lyapunov stability theorem a simulation example is provided to validate the feasibility of the approach

two dimensional dissipative control and filtering for roesser model this paper investigates the problems of two dimensional 2 d dissipative control and filtering for a linear discrete time roesser model first a novel sufficient condition is proposed such that the discrete time roesser system is asymptotically stable and 2 d q s r hbox alpha dissipative special cases such as 2 d passivity performance and 2 d h infty performance and feedback interconnected systems are also discussed based on this condition new 2 d q s r hbox alpha dissipative state feedback and output feedback control problems are defined and solved for a discrete time roesser model the design problems of 2 d q s r hbox alpha dissipative filters of observer form and general form are also considered using a linear matrix inequality lmi approach two examples are given to illustrate the effectiveness and potential of the proposed design techniques

collective synchronization in the presence of reactive coupling and shear diversity we analyze the synchronization dynamics of a model obtained from the phase reduction of the mean field complex ginzburg landau equation with heterogeneity we present exact results that uncover the role of dissipative and reactive couplings on the synchronization transition when shears and natural frequencies are independently distributed as it occurs in the purely dissipative case an excess of shear diversity prevents the onset of synchronization but this does not hold true if coupling is purely reactive in this case the synchronization threshold turns out to depend on the mean of the shear distribution but not on all the other distribution s moments

delay dependent exponential stability of stochastic systems with time varying delay nonlinearity and markovian switching the problem of delay dependent stability in the mean square sense for stochastic systems with time varying delays markovian switching and nonlinearities is investigated both the slowly time varying delays and fast time varying delays are considered based on a linear matrix inequality approach delay dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

observer design of discrete time t s fuzzy systems via multi instant homogenous matrix polynomials this paper is concerned with the design of observer for discrete time nonlinear systems in the takagi sugeno t s fuzzy form under the framework of multi instant homogenous matrix polynomials a novel fuzzy observer and a new lyapunov function which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the m steps past time normalized fuzzy weighting functions are proposed for conceiving less conservative observer design conditions since the algebraic properties of both the current time normalized fuzzy weighting functions and the m steps past time normal ized fuzzy weighting functions are fully considered the relaxation quality of the fuzzy observer design of discrete time t s fuzzy systems is significantly improved in particular some existing fuzzy lyapunov functions and fuzzy observers are special cases of the lyapunov function and the fuzzy observer given in this paper respectively finally a numerical example is provided to illustrate the effectiveness of the proposed approach index terms discrete time system homogenous matrix polynomials multi instant observer design takagi sugeno t s fuzzy model

scaling behaviour at the onset of mutual entrainment in a population of interacting oscillators scaling behaviour of an order parameter and its fluctuations is numerically investigated at the onset of macroscopic mutual entrainment in a population of interacting self oscillators in particular evidence is presented for the power law divergence of the fluctuations with exponents near 1 8 finite size scaling forms are also proposed and verified

travelling waves in chains of pulse coupled integrate and fire oscillators with distributed delays abstract we analyse travelling waves in a chain of pulse coupled integrate and fire oscillators with nearest neighbour coupling and delayed interactions this is achieved by approximating the equations for phase locking in terms of a singularly perturbed two point continuum boundary value problem the latter has a solution provided that a self consistent value for the collective frequency of oscillations can be found we investigate how the qualitative behaviour of travelling waves depends on the distribution of natural frequencies across the chain and the form of delayed interactions a linear stability analysis of phase locked solutions is carried out in terms of perturbations of the firing times of the oscillators it is shown how travelling waves destabilize when the detuning between oscillators or the strength of the coupling becomes too large

an efficient approach for reducing the conservatism of lmi based stability conditions for continuous time t s fuzzy systems this paper deals with reducing the conservatism of stability conditions for continuous time t s fuzzy systems previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions some redundant terms are removed from the problem formulation furthermore more slack matrix variables are introduced to enlarge the design space consequently less conservative stability conditions are obtained finally a well known numerical example is provided to illustrate the effectiveness of the proposed result

stability and stabilization of t s fuzzy systems with two additive time varying delays abstract in this paper new stability and stabilization conditions are proposed for a novel t s fuzzy system the novel t s fuzzy model considered contains two additive time varying delays and has strong application background in networked control systems in contrast to earlier models new lyapunov krasovskii functionals and integral inequalities are used to investigate these criteria as a result new stability and stabilization conditions involving two delay components are established in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the criteria

control synthesis of discrete time t s fuzzy systems based on a novel non pdc control scheme this paper proposes relaxed stabilization conditions of discrete time nonlinear systems in the takagi sugeno t s fuzzy form by using the algebraic property of fuzzy membership functions a novel nonparallel distributed compensation non pdc control scheme is proposed based on a new class of fuzzy lyapunov functions thus relaxed stabilization conditions for the underlying closed loop fuzzy system are developed by applying a new slack variable technique in particular some existing fuzzy lyapunov functions and non pdc control schemes are special cases of the new lyapunov function and fuzzy control scheme respectively finally two numerical examples are provided to illustrate the effectiveness of the proposed method

simulating memory effects with discrete dynamical systems abstract we propose using discrete dynamical systems to model non markovian processes this implies a whole hierarchy of dynamical systems with dimensionality increasing proportional to the memory specific long range memory effects are investigated for a quadratic a cubic and a quartic map markovian processes transform the quadratic map into a normal form of the logistic equation the henon map corresponds to non markovian first generation memory effects higher memories imply new high dimensional systems non markovian processes imply new memory routes to chaos for the three polynomial maps discussed here it is possible to define critical memory lengths above which the systems essentially lose memory

event based reliable dissipative filtering for t s fuzzy systems with asynchronous constraints in this paper event triggered reliable dissipative filtering is investigated for a class of takagi sugeno t s fuzzy systems first a reliable event triggered communication scheme is introduced to release sampled measurement outputs only if the variation of the sampled vector exceeds a prescribed threshold condition second an asynchronous premise reconstruct method for t s fuzzy systems is presented which relaxes the assumption of the prior work that the premises of the plant and the filter are synchronous third the resulting filtering error system is modeled under consideration of event triggered communication sensor failure and asynchronous premise in a unified framework by adopting the lyapunov functional method and integral inequality approach a delay dependent criterion is developed to guarantee asymptotic stability for the filtering error systems and achieve strict q s r alpha dissipativity consequently suitable filters and the event parameters can be derived by solving a set of linear matrix inequalities finally an example is given to show the effectiveness of the proposed method

razumikhin method and exponential stability of hybrid stochastic delay interval systems this paper deals with the exponential stability of hybrid stochastic delay interval systems also known as stochastic delay interval systems with markovian switching the known results in this area see e g x mao exponential stability of stochastic delay interval systems with markovian switching ieee trans automat control 47 10 2002 1604 1612 require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics the main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only the razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay

reliable state feedback control of t s fuzzy systems with sensor faults this paper is concerned with reliable state feedback control synthesis for takagi and sugeno t s fuzzy systems with sensor multiplicative faults by considering the influence of sensor faults on both the system states and premise variables of fuzzy controllers a class of new convex reliable stabilization conditions are proposed for t s fuzzy systems using the properties of fuzzy product inference engines furthermore the obtained result is extended to the h infty reliable control case the resulting controllers are reliable in that they provide guaranteed asymptotic stability and h infty performance when all sensors are operational as well as when some sensor experiences failures different from the proposed approach the influence of sensor faults on premise variables is not considered in the existing results then it might not guarantee the stability and control performance for t s fuzzy systems with premise variables dependent on the system states a numerical example is given to illustrate the effectiveness of the proposed method

the mathematics of asymptotic stability in the kuramoto model now a standard in nonlinear sciences the kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators while its basic phenomenology has been sketched in early works the corresponding rigorous validation has long remained problematic and was achieved only recently this paper reviews the mathematical results on asymptotic stability of stationary solutions in the continuum limit of the kuramoto model and provides insights into the principal arguments of proofs this review is complemented with additional original results various examples and possible extensions to some variations of the model in the literature

further improvement of periodic control approach for relaxed stabilization condition of discrete time takagi sugeno fuzzy systems in this paper we present a new stabilization condition for discrete time takagi sugeno t s fuzzy systems to this end the previously developed periodic nonparallel distributed compensation non pdc control law is extended to the more general one whose gain matrix has a block lower triangular matrix form a distinguished feature of the proposed control law is that it uses a discrete time feedback loop incorporating information from the previous states of the system the resultant stabilization condition is represented in the form of linear matrix inequalities lmis in addition we show that the proposed condition includes the existing one based on the periodic control approach as a particular case finally examples are given to show that the proposed condition provides less conservative results than those of the existing ones published in the literature

further studies on control synthesis of discrete time t s fuzzy systems via useful matrix equalities this paper is concerned with further studies on the control synthesis of discrete time nonlinear systems in the takagi sugeno t s fuzzy form to do this a novel slack variable technique is presented by developing some useful matrix equalities which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions under the framework of homogenous matrix polynomials the algebraic properties of both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices consequently the relaxation quality of control synthesis of discrete time t s fuzzy systems is improved i e the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up finally a numerical example is provided to illustrate the effectiveness of the proposed result

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

dynamics of a large system of coupled nonlinear oscillators abstract we consider the interaction of a large number of limit cycle oscillators with linear all to all coupling and a distribution of natural frequencies the system exhibits extremely rich dynamics as the coupling strength and the width of the frequency distribution are varied we find a variety of steady behaviors that can be described by a stationary distribution in phase space frequency locking amplitude death incoherence and partial locking an unexpected result is that the system can also exhibit unsteady behavior in which the phase space distribution evolves periodically quasiperiodically or even chaotically the simple form of the model allows us to derive several analytical results the stability boundaries of amplitude death and incoherence are found explicitly rigorous results on the existence and stability of frequency locking are also obtained

nonfragile distributed filtering for t s fuzzy systems in sensor networks this paper is concerned with the nonfragile distributed h infty filtering problem for a class of discrete time takagi sugeno t s systems in sensor networks additive filter gain uncertainties that reflect imprecision in filter implementation are considered based on the robust control approach sufficient conditions are obtained to ensure that the filtering error system is asymptotically stable with a prescribed h infty performance level and the eigenvalues of the filtering error system in a given circular region the filter parameters are determined by solving a set of linear matrix inequalities a simulation study on the nonlinear tunnel diode circuit system is presented to show the effectiveness of the proposed design method

comparison theorem of one dimensional stochastic hybrid delay systems the comparison theorem of stochastic differential equations has been investigated by many authors however little research is available on the comparison theorem of stochastic hybrid systems which is the topic of this paper the systems discussed is stochastic delay differential equations with markovian switching it is an important class of hybrid systems

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

brief paper approaches to extended non quadratic stability and stabilization conditions for discrete time takagi sugeno fuzzy systems this paper provides simple and effective linear matrix inequality lmi characterizations for the stability and stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this more general classes of non parallel distributed compensation non pdc control laws and non quadratic lyapunov functions are presented unlike the conventional non quadratic approaches using only current time normalized fuzzy weighting functions we consider not only the current time fuzzy weighting functions but also the l step past l 0 and one step ahead ones when constructing the control laws and lyapunov functions consequently by introducing additional decision variables it can be shown that the proposed conditions include the existing ones found in the literature as particular cases examples are given to demonstrate the effectiveness of the approaches

solution sets of finite fuzzy relation equations with sup inf composition over bounded brouwerian lattices this paper considers the resolution of finite fuzzy relation equations with sup inf composition over a bounded brouwerian lattice the solution sets of finite fuzzy relation equations on a bounded brouwerian lattice are described in a similar way as those of linear spaces of n dimensional vectors in linear algebra

phase diagram for the kuramoto model with van hemmen interactions we consider a kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van hemmen in his model of spin glasses the phase diagram is obtained analytically for the case of zero noise and a lorentzian distribution of the oscillators natural frequencies depending on the size of the attractive and random coupling terms the system displays four states complete incoherence partial synchronization partial antiphase synchronization and a mix of antiphase and ordinary synchronization

improvement on nonquadratic stabilization of discrete time takagi sugeno fuzzy systems multiple parameterization approach this paper presents the relaxed nonquadratic stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this we propose a new fuzzy controller and lyapunov function by generalizing the nonparallel distributed compensation non pdc control law and nonquadratic lyapunov function respectively by exploiting po lya s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions an infinite family of sufficient conditions for the asymptotic stabilizability is derived these conditions are formulated in the format of linear matrix inequalities lmis and hence are numerically tractable via convex programming techniques finally an example is given to illustrate advantages of the proposed method

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

stability of incoherence in a population of coupled oscillators we analyze a mean field model of coupled oscillators with randomly distributed frequencies this system is known to exhibit a transition to collective oscillations for small coupling the system is incoherent with all the oscillators running at their natural frequencies but when the coupling exceeds a certain threshold the system spontaneously synchronizes we obtain the first rigorous stability results for this model by linearizing the fokker planck equation about the incoherent state an unexpected result is that the system has pathological stability properties the incoherent state is unstable above threshold butneutrally stable below threshold we also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise

noise controlled oscillations and their bifurcations in coupled phase oscillators we derive in gaussian approximation dynamical equations for the first two cumulants of the mean field fluctuations in a system of globally coupled stochastic phase oscillators in these equations the intensity of noise serves as an explicit control parameter its variation generates transitions between three dynamical regimes i stationary ii rotatory and iii locally oscillatory breathing the latter regime has previously not been reported in studies of globally coupled noisy phase oscillators our detailed bifurcation analysis is supported by numerical simulations of an ensemble of coupled stochastic phase oscillators similar regimes are also found in simulations of globally coupled stochastic fitzhugh nagumo elements

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

a note on almost sure asymptotic stability of neutral stochastic delay differential equations with markovian switching in this paper we consider neutral stochastic delay differential equations with markovian switching our key aim is to establish lasalle type stability theorems for the underlying equations the key techniques used in this paper are the method of lyapunov functions and the convergence theorem of nonnegative semi martingales the key advantage of our new results lies in the fact that our results can be applied to more general non autonomous equations

multi instant observer design of discrete time fuzzy systems a ranking based switching approach this paper generalizes recent results on multi instant observer design for discrete time takagi sugeno fuzzy systems through a valid ranking based switching approach the approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking based switching mechanism by taking advantage of this ranking based switching mechanism a class of new fuzzy multi instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system two illustrative examples are provided to validate the effectiveness of the result given in this study

an efficient lyapunov function for discrete t s models observer design this paper deals with the design of a new observer synthesis for discrete takagi sugeno t s fuzzy models it is well established that quadratic synthesis for discrete t s models and or linear parameter varying systems can be outperformed easily via nonquadratic syntheses several lyapunov functions can be used nevertheless this paper shows that with a small change in the initial lyapunov function a better in the sense of solutions to the linear matrix inequality constraints problem lyapunov function can be reached this one can introduce very important improvements

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

on the generalized local stability and local stabilization conditions for discrete time takagi sugeno fuzzy systems in this paper local stability and local stabilization problems are considered for discrete time nonlinear systems represented by takagi sugeno t s fuzzy systems improved methods to assess the local stability design locally stabilizing control laws and estimate the domain of attraction are developed in terms of single parameter minimization problems subject to linear matrix inequality lmi constraints the improvement is achieved by applying a convergent lmi relaxation technique to prove positivity of homogeneous polynomial parameter dependent matrices of arbitrary degree with variables in the simplex we also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the t s fuzzy systems is bounded and less than one finally several illustrative examples demonstrate the validity and efficiency of the proposed method

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

conformists and contrarians in a kuramoto model with identical natural frequencies we consider a variant of the kuramoto model in which all the oscillators are now assumed to have the same natural frequency but some of them are negatively coupled to the mean field these contrarian oscillators tend to align in antiphase with the mean field whereas the positively coupled conformist oscillators favor an in phase relationship the interplay between these effects can lead to rich dynamics in addition to a splitting of the population into two diametrically opposed factions the system can also display traveling waves complete incoherence and a blurred version of the two faction state exact solutions for these states and their bifurcations are obtained by means of the watanabe strogatz transformation and the ott antonsen ansatz curiously this system of oscillators with identical frequencies turns out to exhibit more complicated dynamics than its counterpart with heterogeneous natural frequencies

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

partial synchronization in populations of pulse coupled oscillators i study the long term behavior of populations of nonlinear oscillators with all to all noninstantaneous pulse coupling with fast enough excitatory coupling both the fully synchronized and the asynchronous state are unstable in this case individual units fire quasiperiodically even though the network as a whole shows a periodic firing pattern the behavior of networks with three or more units is different in this regard from that of two unit networks with inhibitory coupling the network can break up into a variable number of fully synchronized clusters for fast inhibition the number of clusters tends to be large while the number of clusters is smaller for slow inhibition textcopyright 1996 the american physical society

reliable state estimation of switched neutral system with nonlinear actuator faults via sampled data control this paper aims to solve the reliable state estimation problem of an uncertain switched neutral system subject to nonlinear actuator faults and time varying delay by using sampled data approach to be precise the well known luenberger estimator is constructed to determine the immeasurable states of the addressed system and a general actuator fault model is employed to describe the nonlinearities encountering in the control design after that by defining an error variable the corresponding estimation error system is formulated by the virtue of lyapunov krasovskii stability theory and average dwell time method a new delay dependent sufficient criterion is established to guarantee the existence of the desired estimator and sampled data gains and subsequently the explicit expression of those gains is presented by means of the solution to a set of linear matrix inequalities moreover two numerical examples are given to show the efficiency of the proposed estimator design schemes where it is shown that the estimator gains can ensure the exponential stability of the considered switched neutral systems

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

on almost sure stability of hybrid stochastic systems with mode dependent interval delays this note develops a criterion for almost sure stability of hybrid stochastic systems with mode dependent interval time delays which improves an existing result by exploiting the relation between the bounds of the time delays and the generator of the continuous time markov chain the improved result shows that the presence of markovian switching is quite involved in the stability analysis of delay systems numerical examples are given to verify the effectiveness

amplitude death in an array of limit cycle oscillators we analyze a large system of limit cycle oscillators with mean field coupling and randomly distributed natural frequencies we prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance the system undergoes amplitude death the oscillators pull each other off their limit cycles and into the origin which in this case is astable equilibrium point for the coupled system we determine the region in couplingvariance space for which amplitude death is stable and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

delay range dependent robust h filtering for uncertain stochastic systems with mode dependent time delays and markovian jump parameters abstract this paper investigates the problem of robust h filtering for uncertain stochastic time delay systems with markovian jump parameters both the state dynamics and measurement of the system are corrupted by wiener processes the time delay varies in an interval and depends on the mode of operation a markovian jump linear filter is designed to guarantee robust exponential mean square stability and a prescribed disturbance attenuation level of the resulting filter error system a novel approach is employed in showing the robust exponential mean square stability the exponential decay rate can be directly estimated using matrices of the lyapunov krasovskii functional and its derivative a delay range dependent condition in the form of lmis is derived for the solvability of this h filtering problem and the desired filter can be constructed with solutions of the lmis an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

uncertainty in phase frequency synchronization of large populations of globally coupled nonlinear oscillators abstract numerical evidence as well as an analytical description is given for the existence of a kind of uncertainty principle in the mean field model of the kuramoto type of large populations of nonlinearly coupled oscillators here the noise plays the role of the planck constant this means that there is a limit to the possibility of synchronizing both phases and frequencies the collective phase synchronization competes in fact within such a model with the frequency synchronization the explanation rests on the effect of the noise which is responsible for loss of accuracy comparison is made with a more sophisticated model where such uncertainty is absent when the coupling parameter is sufficiently large

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

stochastic population dynamics under regime switching ii this is a continuation of our paper q luo x mao stochastic population dynamics under regime switching j math anal appl 334 2007 69 84 on stochastic population dynamics under regime switching in this paper we still take both white and color environmental noise into account we show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population in some special but important situations we precisely describe the limit of the average in time of the population

asymptotic description of transients and synchronized states of globally coupled oscillators abstract a two timescale asymptotic method has been introduced to analyze the multimodal mean field kuramoto model of oscillator synchronization in the high frequency limit the method allows to uncouple the probability density in different components corresponding to the different peaks of the oscillator frequency distribution each component evolves towards a stationary state in a comoving frame and the overall order parameter can be reconstructed by combining them synchronized phases are a combination of traveling waves and incoherent solutions depending on parameter values our results agree very well with direct numerical simulations of the nonlinear fokker planck equation for the probability density numerical results have been obtained by finite differences and a spectral method in the particular case of bimodal symmetric and asymmetric frequency distribution with or without external field we also recover in a very easy and intuitive way the only other known analytical results those corresponding to reflection symmetric bimodal frequency distributions near bifurcation points

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

stability and stabilization of nonlinear switched systems under average dwell time in this paper the problems of stability and stabilization of nonlinear discrete time switched systems is investigated firstly in order to implement the lower bound of minimum average dwell time adt of discrete time switched nonlinear systems the open chain and quasi cyclic switching signals are introduced secondly the problem of these underlying nonlinear discrete time switched systems are solved by using the interval type 2 it2 fuzzy modeling approach thirdly a novel delayed it2 fuzzy controller is devised to guarantee the asymptotically stable of the resulting systems finally a numerical simulation example is given to show the merit and effectiveness of the proposed approach

stability analysis of systems with stochastically varying delays abstract a stability analysis of linear systems with stochastically varying delay is performed it is assumed that the delay function has the form of a sawtooth with switches occurring at the arrival times of a homogeneous poisson process several notions of stochastic stability are considered and corresponding stability criteria are derived for two examples the different criteria are compared and the effect on stability of various deterministic approximations is examined

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

an approach to observer design of continuous time takagi sugeno fuzzy model with bounded disturbances this paper addresses the problem of designing the observer for a class of nonlinear systems by using the t s takagi sugeno fuzzy model first two lemmas are obtained to demonstrate how to design the observer then based on the non quadratic lyapunov function a new method is proposed to locally stabilize the t s fuzzy system the new method can be applied to any t s models no matter whether the rules are even or odd naturally the new method is extended to get some lmis linear matrix inequalities to design the observer for practical reason the disturbances considered in this paper are bounded by magnitude and energy finally three examples are given to illustrate the effectiveness of the new approach

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

fault detection filtering for nonlinear switched stochastic systems in this note the fault detection filtering problem is solved for nonlinear switched stochastic system in the t s fuzzy framework our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with brownian motion based on observer based fault detection fuzzy filter as a residual generator the proposed fault detection is formulated as a fuzzy filtering problem by the utilization of the average dwell time technique and the piecewise lyapunov function technique the fuzzy parameter dependent fault detection filters are designed that guarantee the resulted error system to be mean square exponential stable with a weighted mathcal h infty error performance then the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique finally simulation has been presented to show the effectiveness of the proposed fault detection technique

population dynamics of spiking neurons fast transients asynchronous states and locking an integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate and fire type is discussed it is analytically shown that transients from a state of incoherent firing can be immediate the stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived the response of a population of noisy integrate and fire neurons to an input current of small amplitude is calculated and characterized by a linear filter l the stability of perfectly synchronized locked solutions is analyzed