abel lemma based finite sum inequality and its application to stability analysis for linear discrete time delay systems this paper is concerned with stability of linear discrete time delay systems note that a tighter estimation on a finite sum term appearing in the forward difference of some lyapunov functional leads to a less conservative delay dependent stability criterion by using abel lemma a novel finite sum inequality is established which can provide a tighter estimation than the ones in the literature for the finite sum term applying this abel lemma based finite sum inequality a stability criterion for linear discrete time delay systems is derived it is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a jensen type inequality approach and a free weighting matrix approach

h filtering for nonlinear networked systems with randomly occurring distributed delays missing measurements and sensor saturation this paper is concerned with the h filtering problem for a class of networked systems subject to randomly occurring distributed state delays nonlinearities sensor saturation as well as missing measurements via unreliable communication channels the output measurements are affected by sensor saturation which is described by sector nonlinearities the missing measurement is modeled as a linear random variable satisfying the bernoulli distribution and the nonlinearities with the form of global lipschitz cover the well known nonlinear functions the purpose of the addressed problem is to design a full order filter such that in the simultaneous presence of distributed delays randomly occurring nonlinearities sensor saturation and missing measurements the filtering dynamic system is guaranteed to be exponentially mean square stable and the h filtering performance index is achieved a sufficient condition for the solution of the addressed problem is derived and the explicit expression of the desired filter gains is described in terms of the solution to linear matrix inequality lmi finally a numerical example is provided to show the effectiveness of the designed method

auxiliary function based summation inequalities and their applications to discrete time systems auxiliary function based summation inequalities are addressed in this technical note by constructing appropriate auxiliary functions several new summation inequalities are obtained a novel sufficient criterion for asymptotic stability of discrete time systems with time varying delay is obtained in terms of linear matrix inequalities the advantage of the proposed method is demonstrated by two classical examples from the literature

filtering on sampled data systems with parametric uncertainty the paper is concerned with the problem of robust h sub spl infin filtering for a class of systems with parametric uncertainties and unknown time delays under sampled measurements the parameter uncertainties considered are real time varying and norm bounded appearing in the state equation an approach has been proposed for the designing of h sub spl infin filters using sampled measurements which would guarantee a prescribed h sub spl infin performance in the continuous time context irrespective of the parameter uncertainties and unknown time delays both cases of finite and infinite horizon filtering are studied it has been shown that the above robust h sub spl infin filtering problem can be solved in terms of differential riccati inequalities with finite discrete jumps

a novel event triggered transmission scheme and cal l _ 2 control co design for sampled data control systems this note is concerned with the event triggered l2 control for a sampled data control system a novel event triggered transmission scheme is first proposed to determine whether or not the sampled data should be transmitted under this scheme the sampled data transmission should be executed only when a threshold is violated which means that less sampled data is transmitted this scheme does not require any special hardware for continuous measurement then the sampled data control system is modeled as a sampled data error dependent system a stability criterion is derived by constructing a novel lyapunov krasovskii functional which fully utilizes the sawtooth structure characteristic of an artificial delay based on this stability criterion a sufficient condition on the existence of a state feedback controller is given a co design algorithm is provided to obtain the parameters of the event triggered transmission scheme and the controller gain simultaneously finally an inverted pendulum example is given to show the effectiveness of the event triggered transmission scheme and the co design algorithm

event based robust h filtering for affine fuzzy systems abstract this paper investigates the event based robust h filter design problem for a class of nonlinear systems described by affine fuzzy models different from the existing results an event triggered scheme is introduced to reduce the burden of the communication by judging whether the data transmitted condition is satisfied or not under this scheme the premise variables of fuzzy model and filter to be designed are unsynchronized which will lead to the plant and the filter cannot always evolve in the same region at the same time to solve this problem a novel fuzzy basis dependent nonsynchronized h filter is proposed by using the piecewise quadratic lyapunov functions and the s procedure technique finally a numerical example illustrates the effectiveness of the proposed method

event based state estimation of linear dynamic systems with unknown exogenous inputs in this work an event based optimal state estimation problem for linear time varying systems with unknown inputs is investigated by treating the unknown input as a process with a non informative prior the event based minimum mean square error mmse estimator is obtained in a recursive form it is shown that for the general time varying case the closed loop matrix of the optimal event based estimator is exponentially stable and the estimation error covariance matrix is asymptotically bounded for each sample path of the event triggering process the results are also extended to the multiple sensor scenario where each sensor is allowed to have its own event triggering condition the efficiency of the proposed results is illustrated by a numerical example and comparative simulation with the mmse estimators obtained based on time triggered measurements the results are potentially applicable to event based secure state estimation of cyber physical systems

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

wirtinger based multiple integral inequality for stability of time delay systems abstractnote that the conservatism of the delay dependent stability criteria can be reduced by increasing the integral terms in lyapunov krasovskii functional lkf this brief revisits the stability problem for a class of linear time delay systems via multiple integral approach the novelty of this brief lies in that a wirtinger based multiple integral inequality is employed to estimate the derivative of a class of lkf with multiple integral terms based on these innovations a new delay dependent stability criterion is derived in terms of linear matrix inequalities two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method

a state dependent sampling for linear state feedback in this work a new state dependent sampling control enlarges the sampling intervals of state feedback control we consider the case of linear time invariant systems and guarantee the exponential stability of the system origin for a chosen decay rate the approach is based on lmis obtained thanks to sufficient lyapunov razumikhin stability conditions and follows two steps in the first step we compute a lyapunov razumikhin function that guarantees exponential stability for all time varying sampling intervals up to some given bound this value can be used as a lower bound of the state dependent sampling function in a second step an off line computation provides a mapping from the state space into the set of sampling intervals the state is divided into a finite number of regions and to each of these regions is associated an allowable upper bound of the sampling intervals that will guarantee the global exponential or asymptotic stability of the system the results are based on sufficient conditions obtained using convex polytopes therefore they involve some conservatism with respect to necessary and sufficient conditions however at each of the two steps an optimization on the sampling upper bounds is proposed the approach is illustrated with numerical examples from the literature for which the number of actuations is shown to be reduced with respect to the periodic sampling case

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical results

h 2 and h_ infty robust filtering for discrete time linear systems this paper investigates robust filtering design problems in h2 and h infty spaces for discrete time systems subjected to parameter uncertainty which is assumed to belong to a convex bounded polyhedral domain it is shown that by a suitable change of variables both design problems can be converted into convex programming problems written in terms of linear matrix inequalities lmi the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h2 and h infty filters are proven to be of the same order as the order of the system comparisons with robust filters for systems subjected to norm bounded uncertainty are provided in both theoretical and practical settings in particular it is shown that under the same assumptions the results here are generally better as far as the minimization of a guaranteed cost expressed in terms of h2 or h infty norms is considered some numerical examples illustrate the theoretical results

investigation on the existence of solutions for some nonlinear functional integral equations abstract we prove an existence theorem for a nonlinear integral equation which is a volterra counterpart of an integral equation arising in traffic theory using the technique of the measure of noncompactness in banach algebra we prove an existence theorem for a nonlinear functional integral equation basic fixed point theorems such as darbo s theorem are employed to obtain the aforementioned aims in banach algebra

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

network based h control for singular systems with event triggered sampling scheme in this paper the problem of event triggered h control is investigated for networked singular systems to make full use of the characteristics of networked control system a discrete event triggered communication scheme which only needs to supervise the system state in discrete instants is proposed the sampling interval is employed to unify the networked singular system and the event triggered condition into a new time delay system based on this model sufficient criteria are derived to guarantee the networked singular system regular impulse free and stable with an h norm bound the corresponding state feedback controller is designed a practical example is given to show that the proposed event triggered scheme is more effective and useful than some existing works

global asymptotic stability for delayed neural networks using an integral inequality based on nonorthogonal polynomials this brief is concerned with global asymptotic stability of a neural network with a time varying delay first by introducing an auxiliary vector with some nonorthogonal polynomials a slack matrix based integral inequality is established which includes some existing one as its special case second a novel lyapunov krasovskii functional is constructed to suit for the use of the obtained integral inequality as a result a less conservative stability criterion is derived whose effectiveness is finally demonstrated through two well used numerical examples

robust h_ infty filtering for switched stochastic system with missing measurements this paper considers the design of robust h infin filtering problem for switched stochastic discrete time delay system with missing measurements via switched lyapunov function approach attention is focused on the design of an exponentially stable filter guaranteeing a prescribed noise attenuation level in the h infin sense and missing measurements probability by using switched lyapunov functionals some sufficient conditions in terms of linear matrix inequalities lmis are obtained finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

event triggered generalized dissipativity filtering for neural networks with time varying delays this paper is concerned with event triggered generalized dissipativity filtering for a neural network nn with a time varying delay the signal transmission from the nn to its filter is completed through a communication channel it is assumed that the network measurement of the nn is sampled periodically an event triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured on the one hand the event triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted which directly leads to saving of precious communication resources on the other hand the filtering error system is modeled as a time delay system closely dependent on the parameters of the event triggered scheme based on this model a suitable filter is designed such that certain filtering performance can be ensured provided that a set of linear matrix inequalities are satisfied furthermore since a generalized dissipativity performance index is introduced several kinds of event triggered filtering issues such as h infty filtering passive filtering mixed h infty and passive filtering q s r dissipative filtering and mathcal l 2 mathcal l infty filtering are solved in a unified framework finally two examples are given to illustrate the effectiveness of the proposed method

the validity of the test of individual equivalence ratios summary we evaluate the validity of the test of individual equivalence ratios tier a term coined by anderson hauck 1990 the test was also proposed in wellek 1989 it is proved to be a valid test under a class of unimodal symmetric distributions this includes normal distributions since most bioequivalence studies involve data which are normal or at least unimodal and symmetric the test is typically valid it is however not always valid as shown by counter examples

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

brief on the sampled data h filtering problem in this paper the h filtering problem of a continuous time process is considered under the assumption that the measurement is sampled by a generalized sampling device both cases of known and unknown initial conditions are considered the problem is treated via the lifting transformation which converts the problem to a pure discrete time setting it is shown that if a suboptimal filter exists it can always be presented in the form of a finite dimensional discrete time possibly time varying filter followed by a stationary generalized hold function this extends previous results in the literature where a suboptimal filter of this structure with an lti discrete time part of the filter was obtained for the case of known initial conditions only also the existence conditions of a suboptimal filter derived in this paper are simpler than those known in the literature

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

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

distributed event triggered cooperative attitude control of multiple groups of rigid bodies on manifold so 3 in this note the distributed event triggered cooperative attitude control of multiple groups of rigid bodies evolved on nonlinear manifold so 3 is investigated the distributed event triggered mechanism is introduced into the controller design to reduce the communication pressure it is verified that the orientations of rigid bodies in each group converge to a common value with zero angular velocities and these common values in all groups achieve an anti consensus configuration under the proposed intra and inter group cooperative control law simulation results show the effectiveness of the proposed method

output feedback stabilization of networked control systems with a logic zero order hold this paper is concerned with output feedback stabilization of a networked control system in the discrete time domain first a logical zero order hold is introduced to select the newest data packets to drive the plant with which network induced delays and data packet dropouts can be expressed explicitly second an auxiliary vector valued function is introduced to establish a novel finite sum inequality which can provide a tighter bound than some existing ones for some finite sum term third this finite sum inequality is employed to formulate a stability criterion for the closed loop system under consideration it is proven that the stability criterion is of less conservatism than some existing ones reported in the literature fourth a cone complementary linearization based algorithm is presented to design suitable output feedback controllers finally three examples are given to show the effectiveness of the proposed method

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

robust cal h _ infty filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation the finite horizon case this paper addresses the robust h filtering problem for a class of discrete time varying markovian jump systems with randomly occurring nonlinearities and sensor saturation two kinds of transition probability matrices for the markovian process are considered namely the one with polytopic uncertainties and the one with partially unknown entries the nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the bernoulli distributions the main purpose of this paper is to design a robust filter over a given finite horizon such that the h disturbance attenuation level is guaranteed for the time varying markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation sufficient conditions are established for the existence of the desired filter satisfying the h performance constraint in terms of a set of recursive linear matrix inequalities simulation results demonstrate the effectiveness of the developed filter design scheme

cal h _ infty filter for bilinear systems using lpv approach the aim of this technical note is to present a linear paramater varying lpv approach for the design of a functional filter for bilinear systems with a disturbance attenuation specification the unbiasedness requirement on the observation error is guaranteed by the solution of sylvester equations obtained by parametrizing the filter gain matrix this parametrization leads to a non convex optimization problem which is overcome by introducing a constraint on the gain matrix to take into account the whole set of the inputs in the filter design an lpv approach is used to obtain the gain matrix guaranteeing the quadratic stability of the observation error and a given level of disturbance attenuation this approach is then applied to the high gain observer design in order to consider the level of disturbance attenuation

event based h filtering for sampled data systems this paper is concerned with event based h filtering for sampled data systems first an event based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated as a result communication resources can be saved significantly while preserving the desired h performance second the resulting filtering error system is modeled as a system with an interval time varying delay by employing the lyapunov krasovskii functional approach a new bounded real lemma brl is established such that the filtering error system is asymptotically stable with the prescribed h performance third by performing an invertible linear transformation on the filtering error system a linear matrix inequality lmi based sufficient condition which is equivalent to the condition in the brl is obtained on the feasibility of the event based h filtering problem consequently suitable h filters and the event parameters in the event condition can be co designed provided that a set of lmis are satisfied finally a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method

an improved result on exponential stabilization of sampled data fuzzy systems this brief paper studies the exponential stabilization problem for the takagi sugeno fuzzy systems with a variable sampling different from previous results the gains of fuzzy state feedback controller adopted in this paper are time varying during two consecutive sampling instants which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter to reduce the design conservativeness a novel fuzzy time dependent lyapunov functional ftdlf is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions moreover a more relaxed constraint condition is presented to ensure the positive definiteness of the ftdlf on sampling intervals by resorting to the novel ftdlf and the relaxed constraint condition new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established by which a larger sampling interval can be achieved one example is offered to demonstrate the validity and superiorities of the obtained new results

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

technical communique new stability criteria for linear systems with interval time varying delay this paper investigates robust stability of uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and is a fast time varying function the uncertainty under consideration includes polytopic type uncertainty and linear fractional norm bounded uncertainty a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the interval time varying delay is proposed to drive some new delay dependent stability criteria in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no redundant matrix variable is introduced finally three numerical examples are given to show the effectiveness of the proposed stability criteria

an h_ i h_ infty optimization approach to event triggered fault detection for linear discrete time systems in this article a new event triggered h i h infty optimization fault detection fd scheme is proposed for linear discrete time systems a linear discrete time system with varying sampling periods is first presented to describe the dynamics of an event triggered system based on this an observer based fault detection filter fdf is constructed as an event triggered residual generator so that the generated residual signal is completely decoupled from the event triggered transmission error the design of event triggered fdf is formulated as a multiobjective optimization problem denoted by h i h infty and an optimal solution can be obtained by recursive calculation of riccati equations in addition an event triggered residual evaluation strategy is also presented comparing with the existing event triggered fd schemes the major contribution of this article is to decouple the residual signals from the event triggered transmission errors completely and consequently the fd performance can be improved significantly moreover an optimal tradeoff between the robustness of residual to unknown input and the sensitivity of residual to fault is achieved in the sense of h i h infty optimization while the design of fdf and event generator can be carried out independently to demonstrate the effectiveness of the proposed method a vehicle lateral dynamic system is used as a simulation example

self triggering under state independent disturbances this note extends the prior work in l2 stability of self triggered feedback systems where the next task release time and finishing time are predicted based on the sampled states a self triggering scheme is proposed which relaxes the assumption in the prior work that the magnitude of the process noise is bounded by a linear function of the norm of the system state we show that the sample periods generated by this scheme are always greater than a positive constant we also provide state based deadlines for delays and propose a way that may enlarge those deadlines without breaking l2 stability

sampled data control for a class of linear time varying systems this paper is concerned with the sampled data control for a class of linear time varying system a classic halanay inequality is first extended to the time varying sampled data system then based on the comparison principle and the extended halanay inequality new criteria for globally uniformly exponential stability and globally uniformly asymptotic stability of the corresponding closed loop system are derived furthermore an algorithm is presented to solve the gain synthesis problem finally one example is given to show the effectiveness of the obtained results

an improved reciprocally convex inequality and an augmented lyapunov krasovskii functional for stability of linear systems with time varying delay this paper is concerned with stability of a linear system with a time varying delay first an optimal reciprocally convex inequality is proposed compared with the extended reciprocally convex inequality recently reported the optimal reciprocally convex inequality not only provides an optimal bound for the reciprocally convex combination but also introduces less slack matrix variables second a new lyapunov krasovskii functional is tailored for the use of auxiliary function based integral inequality third based on the optimal reciprocally convex inequality and the new lyapunov krasovskii functional a stability criterion is derived for the system under study finally two well studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time varying delay than some existing methods

robust event triggered state estimation a risk sensitive approach in this work we investigate a robust event triggered remote state estimation problem for linear gaussian systems with a stochastic event triggering condition the reference measure approach is used to obtain a robust event triggered estimate that minimizes the so called risk sensitive criterion which refers to the expectation of the exponential of the sum of the squared estimation error we introduce the reference measure under which the measurements are identically independently distributed i i d and independent of the states and propose a map to link the real world measure to the reference measure so that the recursions of the information states under the reference measure can be obtained based on these results the risk sensitive criteria are reformulated under the reference measure and closed form expressions of the risk sensitive event triggered posterior and prior estimates are presented which are shown to evolve in simple recursive kalman like structures moreover two sufficient stability conditions for the proposed estimators are given where the first requires the solution of a time varying riccati equation to be positive definite and satisfy a specific inequality which can be further extended to the scenario when the weighting matrix in the risk sensitive criterion is time variant the second gives the range of values of the risk sensitive parameter and covariance of the initial state for which the proposed estimators are stable comparative simulation results demonstrate that the proposed risk sensitive event triggered estimator is more robust to model uncertainties compared with a typical minimum mean squared error mmse estimator with stochastic event triggered sensor scheduling

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

robust and reduced order filtering new lmi based characterizations and methods this paper addresses several challenging problems of robust filtering we derive new linear matrix inequality lmi characterizations of minimum variance or h sub 2 performance and demonstrate that they allow the use of parameter dependent lyapunov functions while preserving tractability of the problem the resulting conditions are less conservative than earlier techniques which are restricted to fixed not parameter dependent lyapunov functions the remainder of the paper discusses reduced order filter problems new lmi based nonconvex optimization formulations are introduced for the existence of reduced order filters and several efficient optimization algorithms of local and global optimization are proposed nontrivial and less conservative relaxation techniques are presented as well the viability and efficiency of the proposed approaches are then illustrated through computational experiments and comparisons with existing methods