stability of asynchronous systems with poisson transitions we consider the stability of an asynchronous system modeled as a collection of coupled processes with independent poisson state transitions using lyapunov functions sufficient conditions for both mean square and almost sure convergence independent of state transition rates are developed for the linear case and weaker transition rate dependent conditions are derived for the linear and nonlinear case an illustrative example is discussed and simulated

a relaxed quadratic function negative determination lemma and its application to time delay systems abstract the quadratic function with respect to the time varying delay has often been introduced for the analysis of systems with time varying delays to determine the negative definiteness of such function this paper develops a parameter adjustable based lemma which contains the lemma popularly used in literature as a special case and has potential to reduce the conservatism without requiring extra decision variables a stability criterion for a linear time delay system is established by using the proposed lemma whose advantage is demonstrated via a numerical example and the criterion is finally applied to analyze the stability of load frequency control scheme for a single area power system

decentralized finite time h filtering for interconnected markovian jump system with interval mode dependent delays this paper concerns with the problem of finite time h filtering for a class of interconnected markovian jump system with mode dependent delays in the interconnection sufficient conditions guaranteeing the interconnected markovian jump systems to be finite time bounded are established by constructing an augmented lyapunov krasovskii functional the obtained conditions are delay range dependent and mode dependent based on the results the decentralized filter is proposed to guarantee the finite time bounded and h performance of the resulting augmented system for admissible disturbances the desired filter parameters can be obtained via solving a group of linear matrix inequalities lmis finally a numerical example is employed to illustrate the effectiveness of the proposed methods

delay dependent decentralized h_ infty filtering for discrete time nonlinear interconnected systems with time varying delay based on the t s fuzzy model this paper is concerned with the problem of delay dependent h filter design for a class of discrete time nonlinear interconnected system with time varying delays via the takagi sugeno t s fuzzy model the t s fuzzy model consists of n time delay t s fuzzy subsystems and a decentralized h filter is designed for each subsystem based on the delay dependent piecewise lyapunov krasovskii functional ddplkf and with an improved free weighting matrix technique the delay dependent stability and a prescribed h performance index are guaranteed for the overall filtering error system a sufficient condition for the existence of such a filter is established by using linear matrix inequalities lmis that are numerically feasible two numerical examples are given to demonstrate the effectiveness and advantage of the proposed approach

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

delay dependent synchronization of t s fuzzy markovian jump complex dynamical networks abstract in this paper a delay dependent synchronization criteria for markovian jump complex dynamical networks subject to time varying coupling delays and external disturbances are proposed via takagi sugeno t s fuzzy approach the class of markovian jump complex dynamical networks is described by a fuzzy model composed of two levels such as a crisp level which represents the jumps and a fuzzy level which describes the system nonlinearities an asymptotic synchronization criterion is obtained by employing fuzzy controller with the mixed h and passivity performance index 0 further by constructing a novel lyapunov krasovskii functional along with the extended integral inequality and using the properties of kronecker product and convex combination approach a set of sufficient constraints is derived in the form of linear matrix inequalities and checked for its feasibility using matlab software at last numerical simulations including the lorentz system are given to demonstrate the applicability and effectiveness of the developed results

robust stability conditions for large scale interconnected systems with structured and unstructured uncertainties the paper is mainly concerned with the problem of decentralized robust stability of large scale interconnected systems with structured and unstructured uncertainties a simple method is presented whereby some sufficient conditions are derived so that asymptotic stability of large scale interconnected systems can be guaranteed in the presence of uncertain perturbations the method is also extended to large scale discrete time systems and the corresponding robust stability conditions are established for uncertain large scale discrete time systems finally two numerical examples are given to demonstrate that our robust stability conditions are less conservative than those reported in the control literature

robust non fragile control for uncertain discrete delay large scale systems with a class of controller gain variations this paper considers the problems of robust non fragile control for uncertain discrete delay large scale systems under state feedback gain variations two classes of controller gain variations are considered based on the lyapunov method the state feedback control design for robust stability is given in terms of solutions to a linear matrix inequality lmi the solutions of the lmi can be easily obtained using efficient convex optimization techniques a numerical example is included to illustrate the design procedures

on the convergence of parallel asynchronous block iterative computations abstract this paper considers the convergence problem of parallel asynchronous block iterative computation schemes a new mathematical state space model for a class of nonlinear time varying parallel iterative schemes is proposed using this model which generalizes several models of the chazan miranker type together with large scale systems and liapunov techniques it is shown that the well known quasidominance condition on a certain aggregated matrix guarantees exponential convergence of this class of methods

decentralized stabilization of large scale systems with multiple delays in the interconnections in this paper the problem of robust stabilization of a class of time varying large scale systems subject to external disturbances uncertain parameters and multiple time varying delays in the interconnections and non linear inputs is considered linear memory less controllers are developed to guarantee that all solutions of the class of systems considered are uniformly ultimately bounded also non linear memoryless controllers are synthesized to guarantee that the solutions are uniformly ultimately bounded with respect to a bound with any prespecified convergence rate towards it finally an example is included to illustrate the results developed in this paper

uniform approximation to fractional derivatives of functions of algebraic singularity fractional derivative d qf x 0 1 with g x being a well behaved function we propose a quadrature method for uniformly approximating d q x ag x the present method consists of interpolating g x at abscissae in 0 1 by a finite sum of chebyshev polynomials it is shown that the use of the lower endpoint x 0 as an abscissa is essential for the uniform approximation namely to bound the approximation errors independently of x 0 1 numerical examples demonstrate the performance of the present method

an approximation method for high order fractional derivatives of algebraically singular functions the fractional derivative d qf s email protected email protected 1 of a given function f s with a positive non integer q is defined in terms of an indefinite integral we propose a uniform approximation scheme to d qf s for algebraically singular functions f s s ag s a 1 with smooth functions g s the present method consists of interpolating g s at sample points t j in 0 1 by a finite sum of the chebyshev polynomials we demonstrate that for the non negative integer m such that m q m 1 some numerical examples in the simplest case 1

an algorithm based on the fft for a generalized chebyshev interpolation an algorithm for a generalized chebyshev interpolation procedure increasing the number of sample points more moderately than doubling is pre sented the fft for a real sequence is incorporated into the algorithm to enhance its efficiency numerical comparison with other existing algorithms is given

decentralized stabilization of interconnected systems with time varying delays this technical note establishes decentralized delay dependent stability and stabilization methods for two classes of interconnected continuous time systems the two classes cover the linear case and the lipschitz type nonlinear case in both cases the subsystems are subjected to convex bounded parametric uncertainties and time varying delays within the local subsystems and across the interconnections an appropriate lyapunov functional is constructed to exhibit the delay dependent dynamics at the subsystem level in both cases decentralized delay dependent stability analysis is performed to characterize linear matrix inequalities lmis based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an gamma level l 2 gain then we design a decentralized state feedback stabilization scheme such that the family of closed loop feedback subsystems enjoys the delay dependent asymptotic stability with a prescribed gamma level l 2 gain for each subsystem the decentralized feedback gains are determined by convex optimization over lmis all the developed results are tested on a representative example

decentralized stabilization of large scale interconnected systems with delays in this note we study the decentralized stabilization problem of linear time invariant large scale interconnected systems with delays without any assumption of system structure our main result here is the sufficient condition for the decentralized stabilization one application of the procedures to the decentralized observers is also presented

general decentralized stabilization of large scale linear continuous and discrete time delay systems we consider the general stabilization problem of linear time invariant large scale multivariable decentralized systems with delays we have established sufficient stabilization conditions for a general class of decentralized systems namely in the continuous case the requirement is that the matrix measure of the closed loop subsystem matrices can be made sufficiently negative by appropriate local feedback control whereas in the discrete case the requirement is that the norm of the closed loop subsystem matrices can be made arbitrarily small by feedback control

delay independent stability criteria for discrete delay systems several sufficient conditions for stability of linear discrete delay systems are derived since these conditions are independent of the delay and possess simple forms they will provide useful tools to check stability of the systems at the first stage

an extended reciprocally convex matrix inequality for stability analysis of systems with time varying delay abstract the reciprocally convex combination lemma rccl is an important technique to develop stability criteria for the systems with a time varying delay this note develops an extended reciprocally convex matrix inequality which reduces the estimation gap of the rccl based matrix inequality and reduces the number of decision variables of the recently proposed delay dependent rccl a stability criterion of a linear time delay system is established through the proposed matrix inequality finally a numerical example is given to demonstrate the advantage of the proposed method

distributed control design for systems interconnected over an arbitrary graph we consider the problem of synthesizing a distributed dynamic output feedback controller achieving h sub spl infin performance for a system composed of different interconnected sub units when the topology of the underlying graph is arbitrary first using tools inspired by dissipativity theory we derive sufficient conditions in the form of finite dimensional linear matrix inequalities when the interconnections are assumed to be ideal these inequalities are coupled in a way that reflects the spatial structure of the problem and can be exploited to design distributed synthesis algorithms we then investigate the case of lossy interconnection links and derive similar results for systems whose interconnection relations can be captured by a class of integral quadratic constraints that includes constant delays

technical communique stabilization of a class of uncertain large scale stochastic systems with time delays this paper focuses on a class of large scale interconnected bilinear stochastic systems with time delays and time varying parameter uncertainties the problem we address is to design a robust decentralized controller such that the closed loop interconnected stochastic system is globally asymptotically stable in probability for all admissible uncertainties and time delays first robust stability analysis is given in terms of a set of linear matrix inequalities lmis then it is shown that the robust decentralized stabilization can be solved by an lmi based design method

distributed asynchronous computation of fixed points we present an algorithmic model for distributed computation of fixed points whereby several processors participate simultaneously in the calculations while exchanging information via communication links we place essentially no assumptions on the ordering of computation and communication between processors thereby allowing for completely uncoordinated execution we provide a general convergence theorem for algorithms of this type and demonstrate its applicability to several classes of problems including the calculation of fixed points of contraction and monotone mappings arising in linear and nonlinear systems of equations optimization problems shortest path problems and dynamic programming

decentralized adaptive output feedback control for a class of nonlinear large scale systems with unknown time varying delayed interactions in this paper the authors investigate a decentralized adaptive output feedback controller design for large scale nonlinear systems with input saturations and time delayed interconnections unmatched in control inputs the interaction terms with unknown time varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems this point is a main contribution of this paper compared with previous output feedback control approaches which assume that the time delayed bounding functions only depend on measurable output variables the bounding functions are compensated by using appropriate lyapunov krasovskii functionals and the function approximation technique based on neural networks the observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem in addition we prove that all signals in the closed loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin finally an example is provided to illustrate the effectiveness of the proposed control system

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

decentralized adaptive robust control for a class of large scale systems including delayed state perturbations in the interconnections the problem of decentralized stabilization is considered for a class of large scale time varying systems with delayed state perturbations in the interconnections in this note the upper bounds of the uncertainties in the interconnections are assumed to be unknown the adaptation laws are proposed to estimate such unknown bounds and by making use of their updated values a class of decentralized memoryless state feedback controllers is constructed based on lyapunov stability theory and lyapunov krasovskii functional it is shown that the solutions to the resulting adaptive closed loop large scale time delay system can be guaranteed to be uniformly ultimately bounded finally a numerical example is given to demonstrate the validity of the results

delay dependent robust and reliable h fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems this paper develops the delay dependent robust and reliable h fuzzy hyperbolic control for nonlinear large scale interconnected systems with parameter uncertainties firstly the modeling method of fuzzy hyperbolic model fhm is given for the general large scale interconnected systems the main advantages of using fhm over t s fuzzy model are that neither premise structure identification nor completeness design of premise variables space is needed therefore the required computational effort is less than that of using t s fuzzy model especially when a lot of fuzzy rules are needed to model complex nonlinear systems then according to the lyapunov direct method and the decentralized control theory of large scale interconnected systems linear matrix inequality lmi based conditions with some free weighting matrices are derived which guarantee the closed loop interconnected systems to be robustly stable with the h performance even in the presence of some possible actuator failures moreover precise failure parameters of actuators are not required and the only requirements are the lower and upper bounds of failure parameters the restriction that the derivative of the time varying delay is smaller than one is removed therefore the results obtained are less conservative three simulation examples are provided to show the effectiveness of the proposed approach

brief paper robust finite word length controller design a novel finite word length fwl controller design is proposed in the framework of a mixed m theory a robust fwl controller performance measure is first developed which takes into account the standard robust control requirements as well as the fwl implementation considerations and the corresponding controller design problem is naturally reformulated as a mixed m problem which can be treated effectively with the results of the mixed m theory

robust non fragile lq controllers the static state feedback case this paper describes the synthesis of non fragile or resilient regulators for linear systems a general framework for fragility is described using state space methodologies and the lq h2 static state feedback problem is examined in detail we discuss the multiplicative structured uncertainties case and propose remedies of the fragility problem using an optimization programming framework via matrix inequalities a special case that leads to a convex optimization framework via linear matrix inequalities lmis will be considered the benchmark problem is taken as an example to show how special controller gain variations can affect the performance of the closed loop system

some recent advances in theory and simulation of fractional diffusion processes to offer an insight into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of current interest i the well scaled passage to the limit from continuous time random walk under power law assumptions to space time fractional diffusion ii the asymptotic universality of the mittag leffler waiting time law in time fractional processes iii our method of parametric subordination for generating particle trajectories

stability analysis of systems with time varying delay via novel augmented lyapunov krasovskii functionals and an improved integral inequality abstract delay dependent stability analysis of linear systems with a time varying delay is investigated in this paper firstly instead of developing a lyapunov krasovskii functional lkf including augmented non integral quadratic terms as usual this paper proposes two augmented integral function based lkfs which can reflect closer relationships among system states secondly to bound the derivative of lkf more accurately a new integral inequality with several free matrices is developed compared with the free matrix based integral inequality this inequality can provide additional freedom due to the free matrices introduced then by employing those lkfs and the improved integral inequality several delay dependent stability criteria are established for two types of delays finally two numerical examples are given to demonstrate the superiority of the proposed method

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

on the riemann liouville fractional calculus g jacobi functions and f gauss functions this paper refers to a fractional extension of the classical jacobi polynomials a fractional order rodrigues type representation formula is considered by means of the riemann liouville operator of fractional calculus new g jacobi functions are defined some of their properties are given and compared with the corresponding properties of the classical jacobi polynomials furthermore the hypergeometric equation of gauss is extended to a fractional order a new f gauss hypergeometric function is defined as a solution to the extended fractional differential equation and considered as a candidate for a fractional hypergeometric function of gauss 2007 elsevier inc all rights reserved

stabilization of continuous and discrete linear systems subjected to control structure constraints in this paper we present a simple procedure for obtaining stabilization of a class of continuous and discrete linear systems subjected to control structure constraints giving more attention to the so called decentralized control contrary to the continuous case where much work has been done the solution presented here for the discrete case is one of the first to be presented some examples are treated and for the continuous case some comparisons are made with other methods found in the literature

stability analysis of systems with time varying delays via the second order bessel legendre inequality this paper is concerned with the delay dependent stability of systems with time varying delays the novelty relies on the use of the second order bessel legendre integral inequality which is less conservative than the jensen and wirtinger based inequalities unlike similar contributions the features of this inequality are fully integrated into the construction of augmented lyapunov krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities the stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method

generalized reciprocally convex combination lemmas and its application to time delay systems various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with time varying delays this paper provides more insights on the relationship between some of them we present an equivalent formulation of moon et al s inequality allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in 14 or free matrix based inequality more especially it is proved that these existing inequalities can be captured as particular cases of moon et al s inequality examples show the best tradeoff between the reduction of conservatism and the numerical complexity

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

stabilization and estimation for perturbed discrete time delay large scale systems based on a derived algebraic inequality a criterion to guarantee the robust stabilization and the state estimation for perturbed discrete time delay large scale systems is proposed this criterion is independent of time delay and does not need the solution of a lyapunov equation or riccati equation furthermore the same problem for the continuous time systems is also solved by a much simpler derivation

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

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

an inclusion principle for hereditary systems abstract given two hereditary dynamic systems having different dimensions the conditions are provided under which a part of the motion of the larger system is reproduced by the smaller system that is the larger system includes the smaller one the conditions for inclusion are useful in applying the concept of vector liapunov functions to stability analysis of systems composed of overlapping subsystems by expanding the systems into a larger space the overlapping subsystems appear as disjoint and standard methods can be used to conclude stability of the expanded system under the inclusion conditions stability of the expansion implies stability of the original system an example is provided to show stability where the standard disjoint decompositions fail

stabilization analysis for discrete time systems with time delay the stabilization problem for a class of discrete time systems with time varying delay is investigated by constructing an augmented lyapunov function some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality lmi technique when norm bounded parameter uncertainties appear in the delayed discrete time system a delay dependent robust exponential stabilization criterion is also presented all of the criteria obtained in this paper are strict linear matrix inequality conditions which make the controller gain matrix can be solved directly three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results

existence and stability of a unique equilibrium in continuous valued discrete time asynchronous hopfield neural networks it is shown that the assumption of d stability of the interconnection matrix together with the standard assumptions on the activation functions guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes for the synchronous mode these assumptions are also shown to imply local asymptotic stability of the equilibrium for the asynchronous mode of operation two results are derived first it is shown that symmetry and stability of the interconnection matrix guarantee local asymptotic stability of the equilibrium under a class of asynchronous modes this is referred to as local absolute asymptotic stability second it is shown that under the standard assumptions if the nonnegative matrix whose elements are the absolute values of the corresponding elements of the interconnection matrix is stable then the equilibrium is globally absolutely asymptotically stable under a class of asynchronous modes the results obtained are discussed from the points of view of their applications robustness and their relationship to earlier results

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

decentralized h_ infty filter design for discrete time interconnected fuzzy systems this paper describes a decentralized h infin filter design for discrete time interconnected fuzzy systems based on piecewise quadratic lyapunov functions the systems consist of j discrete time interconnected takagi sugeno t s fuzzy subsystems and a decentralized h infin filter is designed for each subsystem it is shown that the stability of the overall filtering error system with h infin performance can be established if a piecewise quadratic lyapunov function can be constructed moreover the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible two simulation examples are given to show the effectiveness of the proposed approach

numerical integration of functions with poles near the interval of integration abstract an automatic quadrature scheme is presented for approximating integrals of functions that are analytic in the interval of integration but contain pole or poles of order 2 i e a double pole on the real axis or a complex conjugate pair of double poles near the interval of integration the present scheme is based on product integration rules of interpolatory type using function values of the abscissae only in the interval of integration the integral is approximated and evaluated by using recurrence relations and some extrapolation method after the smooth part of the integrand is expanded in terms of the chebyshev polynomials the fast fourier transform fft technique is used to generate efficiently the sequence of the finite chebyshev series expansions until an approximation of the integral satisfying the required tolerance is obtained with an adequate estimate of the error numerical examples are included to illustrate the performance of the method