stability and stabilization of t s fuzzy systems with time varying delays via augmented lyapunov krasovskii functionals this paper is concerned with the problem of stability and stabilization for takagi sugeno t s fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional sufficient conditions for ensuring the asymptotic stability and stabilization of the concerned fuzzy systems have been derived within the framework of linear matrix inequalities lmis the advantage and effectiveness of the proposed criteria will be shown through the comparison of maximum delay bounds with some results obtained by recently published papers via four numerical examples

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

state estimation for static neural networks with time varying delays based on an improved reciprocally convex inequality this brief is concerned with the problem of neural state estimation for static neural networks with time varying delays notice that a luenberger estimator can produce an estimation error irrespective of the neuron state trajectory this brief provides a method for designing such an estimator for static neural networks with time varying delays first in depth analysis on a well used reciprocally convex approach is made leading to an improved reciprocally convex inequality second the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time derivative of some lyapunov krasovskii functional as a result a novel bounded real lemma brl for the resultant error system is derived third the brl is applied to present a method for designing suitable luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters finally it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones

network based h filtering using a logic jumping like trigger this paper is concerned with the network based h filtering for a stochastic system where data transmission from the stochastic system to a filter is completed via a communication network network induced delays packet dropouts and packet disorders are unavoidable due to the use of the network first a logic zero order hold zoh is designed to discard the disordered packets actively the network induced delays and packet dropouts are modeled as an interval time varying delay by decomposing the delay interval into n subintervals uniformly the filter to be designed is modeled as a markov jumping filter with n modes governed by a markov chain in order to work out the transition rate from one mode to another a logic jumping like trigger is embedded into the logic zoh to simulate the switching of the markov process second based on the markov jumping filter model together with a new integral inequality in the stochastic setting a novel bounded real lemma is presented to ensure that the resultant filtering error system is mean exponentially stable with a prescribed h performance then a sufficient condition on the existence of desired markov jumping filters is provided in terms of a set of linear matrix inequalities finally an air vehicle system is employed to show effectiveness of the proposed design method

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

reliable mixed h passive control for t s fuzzy delayed systems based on a semi markov jump model approach abstract this paper investigates the problem of the reliable mixed h passive control for takagi sugeno t s fuzzy delayed systems based on a semi markov jump model smjm approach the focus is to design a fuzzy fault tolerant controller such that the resulting closed loop system is stochastically stable with a prescribed mixed h passive performance level even if the actuator failures appear a semi markov process is employed to describe the encountered failures of the actuator by applying the lyapunov krasovskii method in combination with some novel inequalities some conditions on the performance analysis are established where some negative quadratic terms are fully considered to reduce the conservatism based on the conditions an explicit expression for the desired controller is given three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

new results on h filtering for fuzzy systems with interval time varying delays this paper investigates the problem of h filtering for continuous takagi sugeno t s fuzzy systems with an interval time varying delay in the state based on the delay partitioning idea a new approach is proposed for solving this problem which can achieve much less conservative feasibility conditions the attention is focused on the design of an h filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the h attenuation level from disturbance to estimation error is below a prescribed scalar the constructed lyapunov krasovskii functional by applying the delay partitioning method can potentially guarantee the obtained delay dependent conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software finally an example is illustrated to show the reduction in conservatism of the proposed filter design method

delay range dependent robust stabilization for uncertain t s fuzzy control systems with interval time varying delays this paper is concerned with robust stabilization for a class of t s fuzzy control systems with interval time varying delays an approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities the main points of the approach are i two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria ii an appropriate lyapunov krasovskii functional is constructed by including both the lower and upper bounds of the interval time varying delays and iii neither model transformation nor free weighting matrices are employed in the theoretical result derivation as a result some improved sufficient stability criteria are derived and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem numerical examples are given to demonstrate the effectiveness of the proposed approach

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

transfer functions of regular linear systems part i characterizations of regularity we recall the main facts about the representation of regular linear systems essentially that they can be described by equations of the form x t ax t bu t y t cx t du t like finite dimensional systems but now a b and c are in general unbounded operators regular linear systems are a subclass of abstract linear systems we define transfer functions of abstract linear systems via a generalization of a theorem of foures and segal we prove a formula for the transfer function of a regular linear system which is similar to the formula in finite dimensions the main result is a simple to state but hard to prove necessary and sufficient condition for an abstract linear system to be regular in terms of its transfer function other conditions equivalent to regularity are also obtained the main result is a consequence of a new tauberian theorem which is of independent interest

stability analysis and design of takagi sugeno fuzzy systems this work presents stable composite control criteria for multivariable takagi sugeno t s fuzzy systems on the basis of the linear matrix inequality lmi control strategy and parametric optimization the composite fuzzy control algorithms are derived unlike earlier studies of fuzzy control systems on an lmi framework this investigation develops a supervisory control approach such that a fuzzy controller can be synthesized more efficiently moreover a robust control scheme is applied to the t s fuzzy model with parametric uncertainties the sufficient conditions are deduced in the form of reduced lmis and adaptive tuning rules finally numeric simulations are given to validate the proposed approach

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

stability analysis and controller synthesis for discrete time delayed fuzzy systems via small gain theorem this paper investigates the problems of stability analysis and controller synthesis of discrete time takagi sugeno t s fuzzy systems with time varying delay via an input output approach the original system is reformulated as a feedback subsystem and a forward subsystem with two constant time delays and a delay uncertainty satisfying the scaled small gain theorem the lifting method is employed to convert the forward subsystem to a delay free system where the main result concerning the stability analysis of the system is obtained based on the scaled small gain theorem the merit of the new stability condition lies in its reduced conservatism which is made possible by a more precise estimation of the time varying delay additionally a state feedback controller is designed through the lyapunov krasovskii functional approach combined with the utilization of the scaled small gain theorem two illustrative examples are given to demonstrate the less conservatism of the stability condition and the effectiveness of the controller design method

further robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delay via relaxed integral inequality abstract this paper focuses on robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delays two delay product type terms are introduced for constructing a new lyapunov krasovskii functional which contains more information of time varying delay and a novel relaxed integral inequality is applied to estimate the derivative of lkf for achieving reduction of estimation gap as a result several further robust stability criteria with less conservativeness are proposed finally three numerical examples and an application to control of a truck trailer are provided to show the effectiveness and advantages of the presented methods

delay variation dependent stability of delayed discrete time systems this note is concerned with the stability analysis of linear discrete time system with a time varying delay a generalized free weighting matrix gfwm approach is proposed to estimate summation terms in the forward difference of lyapunov functional and theoretical study shows that the gfwm approach encompasses several frequently used estimation approaches as special cases moreover an augmented lyapunov functional with a delay product type term is constructed to take into account delay changing information as a result the proposed gfwm approach together with the augmented lyapunov functional leads to a less conservative delay variation dependent stability criterion finally numerical examples are given to illustrate the advantages of the proposed criterion

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

new delay dependent stability criteria for t s fuzzy systems with time varying delay this paper is concerned with the stability problem of uncertain t s fuzzy systems with time varying delay by employing a further improved free weighting matrix approach by taking the relationship among the time varying delay its upper bound and their difference into account some less conservative lmi based delay dependent stability criteria are obtained without ignoring any useful terms in the derivative of lyapunov krasovskii functional finally two numerical examples are given to demonstrate the effectiveness and the merits of the proposed methods

improved stability criteria for time varying delayed t s fuzzy systems via delay partitioning approach this paper focuses on the stability analysis for uncertain takagi sugeno t s fuzzy systems with interval time varying delay the uncertainties of system parameter matrices are assumed to be time varying and norm bounded some new lyapunov krasovskii functionals lkfs are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different lyapunov functionals to different segments in the lkfs by employing these lkfs some new delay derivative dependent stability criteria are established for the nominal and uncertain t s fuzzy systems in a convex way these stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay by employing the new delay partitioning approach the obtained stability criteria are stated in terms of linear matrix inequality lmi they are equivalent or less conservative while involving less decision variables than the existing results finally numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results

bifurcation analysis of a predator prey system with nonmonotonic functional response we consider a predator prey system with nonmonotonic functional response p x frac mx ax 2 bx 1 by allowing b to be negative b 2 sqrt a p x is concave up for small values of x 0 a

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

augmented lyapunov krasovskii functional approaches to robust stability criteria for uncertain takagi sugeno fuzzy systems with time varying delays this paper considers the problem of robust stability analysis for uncertain takagi sugeno t s fuzzy systems with time varying delays by constructing an augmented lyapunov krasovskii functional and utilizing finsler s lemma a novel criterion for delay dependent robust stability of t s fuzzy model with time varying delay is derived in terms of linear matrix inequalities lmis also a further improved stability criterion is proposed by utilizing free weighting techniques finally three numerical examples are included to show the superiority of the proposed criteria

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