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

further results on exponential stability of neural networks with time varying delay this paper investigates the problem of the exponential stability for a class of neural networks with time varying delay a triple integral term and a term considering the delay information in a new way are introduced to the lyapunov krasovskii functional lkf the obtained criterion show advantages over the existing ones since not only a novel lkf is constructed but also several techniques such as wirtinger based inequality and convex combination technique are used to estimate the upper bound of the derivative of the lkf finally a numerical example is provided to verify the effectiveness and benefit of the proposed criterion

lmi approach to exponential stability of linear systems with interval time varying delays abstract this paper addresses exponential stability problem for a class of linear systems with time varying delay the time delay is assumed to be a continuous function belonging to a given interval but not necessary to be differentiable by constructing a set of augmented lyapunov krasovskii functional combined with the newton leibniz formula technique new delay dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities lmis an application to exponential stability of uncertain linear systems with interval time varying delay is given numerical examples are given to show the effectiveness of the obtained results

reducing conservatism of stability criteria for linear systems with time varying delay using an improved triple integral inequality abstract this paper focuses on stability analysis of linear systems with time varying delay where two cases of the time varying delay are discussed that is the time varying delay is either differentiable or just uniformly continuous first an improved triple integral inequality is proposed to estimate triple integrals tightly then by introducing two novel lyapunov krasovskii functionals catering for two cases of time varying delay two sufficient conditions on stability respectively for the system under two cases of time varying delay are derived using the improved triple integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently finally three numerical examples show that the obtained results outperform some existing ones

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

e bounded state estimation for time delay systems with bounded disturbances a new problem on e bounded functional state estimation for time delay systems with unknown bounded disturbances is studied in this paper in the presence of unknown bounded disturbances the common assumption regarding the observer s matching condition is no longer required in this regard instead of achieving asymptotic convergence for the observer error the error is now required to converge exponentially within a ball with a small radius e 0 this means that the estimate converges exponentially within an e bound of the true value a general observer that utilises multiple delayed output and input information is proposed sufficient conditions for the existence of the proposed observer are first given we then employ an extended lyapunov krasovskii functional which combines the delay decomposition technique with a triple integral term to study the e convergence problem of the observer error system moreover the obtained results are shown to be more effective than the existing results for the cases w

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

improved stability criteria for linear systems with interval time varying delays this paper suggests first order and second order generalized zero equalities and constructs a new flexible lyapunov krasovskii functional with more state terms also by applying various zero equalities improved stability criteria of linear systems with interval time varying delays are developed using wirtinger based integral inequality jensen inequality and a lower bound lemma the time derivative of the lyapunov krasovskii functional is bounded by the combinations of various state terms including not only integral terms but also their interval normalized versions which contributes to make the stability criteria less conservative numerical examples show the improved performance of the criteria in terms of maximum delay bounds

robust h_ infty control for t s fuzzy systems with state and input time varying delays via delay product type functional method this paper investigates the problem of robust h infty control for a class of nonlinear systems with state and input time varying delays the nonlinearity is presented by a continuous time takagi sugeno t s fuzzy model with parameter uncertainties a sufficient asymptotic stability condition is first proposed by constructing a delay product type augmented lyapunov krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a wirtinger based integral inequality then a state feedback controller is derived that guarantees the closed loop fuzzy system being asymptotically stable with an h infty performance index finally four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques

analysis on robust h performance and stability for linear systems with interval time varying state delays via some new augmented lyapunov krasovskii functional in this paper the problem of h performance and stability analysis for linear systems with interval time varying delays is considered first by constructing a newly augmented lyapunov krasovskii functional which has not been proposed yet an improved h performance criterion with the framework of linear matrix inequalities lmis is introduced next the result and method are extended to the problem of a delay dependent stability criterion finally numerical examples are given to show the superiority of proposed method

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

sampled data state estimation of markovian jump static neural networks with interval time varying delays abstract in this paper we consider the problem of sampled data state estimation of markovian jump delayed static neural networks by constructing a suitable lyapunov krasovskii functional with double and triple integral terms and using jensen inequality delay dependent criteria are presented so that the error system is asymptotically stable instead of the continuous measurement the sampled measurement is employed to estimate the neuron states it is further demonstrated that the configuration of the gain matrix of state estimator is changed to find a feasible solution of a linear matrix inequalities which is efficiently facilitated by available algorithms finally two numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

brief an efficient off line formulation of robust model predictive control using linear matrix inequalities the practicality of model predictive control mpc is partially limited by its ability to solve optimization problems in real time moreover on line computational demand for synthesizing a robust mpc algorithm will likely grow significantly with the problem size in this paper we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained mpc algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off line one within another in state space this off line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed loop system and substantial reduction of the on line mpc computation the controller design is illustrated with two examples

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

robust model predictive control for discrete time takagi sugeno fuzzy systems with structured uncertainties and persistent disturbances in this paper robust model predictive control for uncertain discrete time takagi sugeno t s fuzzy systems with input constraints and persistent disturbances is considered the robust positively invariant set for t s fuzzy systems is investigated based on this result computation of the terminal constraint set is proposed which is of crucial importance in the robust predictive controller design a zero step predictive controller is discussed first which has a time varying terminal constraint set the recursive feasibility and input to state stability can be ensured then a novel controller with n step prediction is further proposed which can be used to deal with the case of fixed terminal constraint set the implementation of the n step controller involves both online and offline computations it is shown that a sequence of approximating robust one step sets can be computed offline then bisection searches are carried out online as well as a constrained convex optimization problem the n step controller guarantees that the system state can be steered to the terminal constraint set in less than n steps if the initial state lies in a specific region simulation results are finally presented to show the effectiveness of the proposed controllers

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

an improved delay dependent stability criterion for linear uncertain systems with multiple time varying delays in this paper the problem of delay dependent robust stability for a class of linear uncertain systems with multiple time varying delays is investigated a new multiple time varying delays criterion for improving the delay dependent robust stability in the form linear matrix inequalities is proposed using the augmented lyapunov krasovskii functional and jensen s inequality the result enlarges the existing maximum allowable bound of the time delay furthermore we theoretically consider the relationship of the maximum allowable delay bound of each time varying delay to reduce the conservatism an illustrative example is given to show the efficacy of the obtained result

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

combined convex technique on delay dependent stability for delayed neural networks in this brief by employing an improved lyapunov krasovskii functional lkf and combining the reciprocal convex technique with the convex one a new sufficient condition is derived to guarantee a class of delayed neural networks dnns to be globally asymptotically stable since some previously ignored terms can be considered during the estimation of the derivative of lkf a less conservative stability criterion is derived in the forms of linear matrix inequalities whose solvability heavily depends on the information of addressed dnns finally we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods

improved delay dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components abstract this paper focuses on the problem of delay dependent state feedback control for a class of networked control systems ncss with nonlinear perturbations and two delay components based on the dynamic delay interval ddi method and the wirtinger integral inequality some improved delay dependent stability analysis are obtained furthermore the results are extended to the conditions of ncss with one time delay and the corresponding stability analysis results and state feedback controller are obtained finally some numerical examples and simulations are given to show the effectiveness of the proposed methods

modeling multistage cutting stock problems abstract in multistage cutting stock problems csp the cutting process is distributed over several successive stages every stage except the last one produces intermediate products the list of intermediate products may be given or arbitrary the goal is to minimize the total amount of material taken out of stock to cut finished products sufficient to meet customer demands if the intermediate sizes are given the column generation technique can be applied to multistage cutting problems if the intermediate sizes are not given then another dimension is added to the problem complexity we propose a special procedure for this case that dynamically generates both rows intermediate sizes and columns patterns we refer to this method as row and column generation the method uses an auxiliary problem embedded into the frame of the revised simplex algorithm it is a non linear knapsack problem that can be solved efficiently in contrast to the column generation method the developed technique cannot guarantee the optimal solution however the results of computational experiments are very promising and prove that the method is a valuable addition to the set of tools for modeling and solving multistage csps

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

a generalization of column generation to accelerate convergence this paper proposes a generalization of column generation reformulating the master problem with fewer variables at the expense of adding more constraints the sub problem structure does not change it shows both analytically and computationally that the reformulation promotes faster convergence to an optimal solution in application to a linear program and to the relaxation of an integer program at each node in the branch and bound tree further it shows that this reformulation subsumes and generalizes prior approaches that have been shown to improve the rate of convergence in special cases

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

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

on delay dependent stability under model transformations of some neutral linear systems this paper focuses on the stability analysis of a class of neutral linear systems some sufficient delay dependent stability conditions are derived in terms of an appropriate model transformation of the original system transformation similar to the one used in the retarded case the analysis makes use of an appropriate construction of a degenerate lyapunov krasovskii functional several computational schemes and frequency domain interpretations as well as an example are also presented

dynamic output feedback guaranteed cost control for linear systems with interval time varying delays in states and outputs abstract this paper addresses the dynamic output feedback guaranteed cost control problem of a class of time delay systems where the state and output contain interval non differentiable time varying delays the proposed controller uses only the delayed output measurement to stabilize the closed loop system and guarantee an adequate level of system performance by constructing a set of multiple lyapunov krasovskii functionals which include triple integral terms a new criterion for the existence of dynamic output feedback guaranteed cost controllers is established and expressed in terms of linear matrix inequality lmi a numerical example is given to illustrate the obtained results

stability analysis of linear systems with two delays of overlapping ranges in this paper a delay dependent stability criterion is derived for linear time delay systems with two constant delays having overlapping ranges this overlapping feature of the delays is exploited in delay dependent analysis of the system using lyapunov krasovskii approach the developed treatment of the delays reduces conservatism in analysis compared to the approaches treating the delays individually numerical examples are used to demonstrate the less conservativeness of the derived criterion

robust h state feedback control for linear systems this paper investigates the problem of robust h control for linear systems first the state feedback closed loop control algorithm is designed second by employing the geometric progression theory a modified augmented lyapunov krasovskii functional lkf with the geometric integral interval is established then parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill this technique can eliminate the unnecessary enlargement of the lkf derivative estimation which gives less conservatism in addition the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed h performance in the presence of a disturbance input and parameter uncertainties a liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example it shows that this proposed state feedback control approach achieves the expected results for linear systems in the sense of the prescribed h performance

a generalized free matrix based integral inequality for stability analysis of time varying delay systems abstract this paper focuses on the delay dependent stability problem of time varying delay systems a generalized free matrix based integral inequality gfmbii is presented this inequality is able to deal with time varying delay systems without using the reciprocal convexity lemma it overcomes the drawback that the bessel legendre inequality is inconvenient to cope with a time varying delay system as the resultant bound contains a reciprocal convexity through the use of the derived inequality and by constructing a suitable lyapunov krasovskii function lkf improved stability criteria are presented in the form of linear matrix inequalities lmis two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature

delays dependent region partitioning approach for stability criterion of linear systems with multiple time varying delays abstract this paper considers a delay dependent stability criterion for linear systems with multiple time varying delays to exploit all possible information for the relationships among the marginally delayed states x t i m x t i 1 m the exactly delayed states x t i t x t i 1 t and the current state x t for each pair i i 1 of time varying delays a delays dependent region partitioning approach in double integral terms is proposed by applying the wirtinger based integral inequality and the reciprocally convex approach to terms resulted from the region partitioning a stability criterion is derived in terms of linear matrix inequalities numerical examples show that the resulting criterion outperforms the existing one in literature

a fast ellipsoidal mpc scheme for discrete time polytopic linear parameter varying systems this paper proposes a fast ellipsoidal model predictive control mpc strategy to address feedback regulation problems for constrained polytopic linear parameter varying lpv systems subject to bounded disturbances in order to deal with the specific non convex structure of the state prediction tubes arising in lpv contexts a new convexification procedure is proposed and based on the off line computation of a sequence of inner ellipsoidal approximations of exact one step controllable sets a computationally low demanding mpc algorithm is presented comparisons with state of the art mpc control algorithms for lpv systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction control performance numerical burdens and memory requirements

analytical expression of explicit mpc solution via lattice piecewise affine function an analytical expression of the explicit solution to linear model predictive control mpc is proposed by the introduction of a lattice piecewise affine pwa function a systematic procedure is developed for building a lattice pwa representation from a continuous explicit mpc solution obtained by a multi parametric program a simple method is presented to remove the redundant parameters in the lattice expression of mpc control laws the effectiveness of this approach is supported by the study of three benchmark mpc problems the proposed analytical expression provides a very efficient and practically viable method for implementing the explicit mpc solutions regarding its online calculation and memory space requirements

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

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 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

delay partitioning approach for systems with interval time varying delay and nonlinear perturbations this paper considers the problem of robust stability for a class of linear systems with interval time varying delay and nonlinear perturbations less conservative stability criteria was put forward by using delay partitioning approach by decomposing the delay interval into multiple equidistant subintervals new lyapunov krasovskii l k functional contains some triple integral terms and augment terms which are introduced on these intervals thus resulting in being much less conservative than most existing results in the literature in addition in deriving the stability conditions in linear matrix inequality lmi framework neither model transformations nor superfluous free weighting matrix are employed for dealing the cross terms that emerge from the time derivative of the l k functional instead they are dealt using tighter integral inequalities which only contain a minimal number of slack matrix variables numerical examples are given to demonstrate the effectiveness of the proposed approach

a stabilized structured dantzig wolfe decomposition method we discuss an algorithmic scheme which we call the stabilized structured dantzig wolfe decomposition method for solving large scale structured linear programs it can be applied when the subproblem of the standard dantzig wolfe approach admits an alternative master model amenable to column generation other than the standard one in which there is a variable for each of the extreme points and extreme rays of the corresponding polyhedron stabilization is achieved by the same techniques developed for the standard dantzig wolfe approach and it is equally useful to improve the performance as shown by computational results obtained on an application to the multicommodity capacitated network design problem

a lp based heuristic for a time constrained routing problem abstract in this paper we present a lp based heuristic for the solution of a time constrained routing problem arising from innovative services accessible via world wide web the problem consists of scheduling the visit of a tourist to a given geographical area in order to maximize his satisfaction degree whilst respecting time windows restrictions we refer to this problem as the intelligent tourist problem itp itp is formulated as a set packing problem with side constraints due to the huge number of variables in the formulation the lp relaxation is solved by a column and row generation approach then we run a mip solver over the active columns to get a feasible solution computational experience on real world instances is reported showing the effectiveness of the proposed approach

an ellipsoidal off line mpc scheme for uncertain polytopic discrete time systems an off line model predictive control mpc method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances in order to reduce the computational burdens and conservativeness of traditional polytopic mpc schemes the present approach carries out off line most of the computations and it makes use of closed loop predictions to improve the control performance this is done by recursively pre computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on line a simple and numerically low demanding optimization problem subject to a set membership constraint comparisons with three other recent off line mpc approaches are also provided in the final example

stability analysis for linear delayed systems via an optimally dividing delay interval approach this paper addresses the problem of stability for linear systems with time varying delay a novel augmented lyapunov krasovskii functional is constructed by using the idea of optimally dividing the delay interval 0 t into some variable sub intervals and line integral technology using the novel augmented functional the new delay dependent stability criteria are proposed for linear systems with time varying delay the gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay two numerical examples are provided to verify the effectiveness of the proposed criteria

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

robust control of constrained linear systems with bounded disturbances this technical note develops a novel robust control algorithm for linear systems subject to additive and bounded disturbances the approach is based on the constraint tightening method while this problem can be tackled using existing robust model predictive control techniques the proposed method has an advantage in that it is computationally efficient and avoids the need to solve repeatedly an online optimization problem while the optimization problem solved at initialization is a simple linear programming problem the algorithm elaborated in this technical note guarantees convergence to a minimal disturbance invariant set and the terminal predicted state constraint set is allowed to be larger than the minimal disturbance invariant set as an illustration the developed algorithm is applied to constrained roll control of a ship operating in a wave field simulation results show that the proposed approach reduces the ship roll motion while the input and dynamic stall constraints are satisfied

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

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method

simultaneous column and row generation for large scale linear programs with column dependent rows in this paper we develop a simultaneous column and row generation algorithm that could be applied to a general class of large scale linear programming problems these problems typically arise in the context of linear programming formulations with exponentially many variables the defining property for these formulations is a set of linking constraints which are either too many to be included in the formulation directly or the full set of linking constraints can only be identified if all variables are generated explicitly due to this dependence between columns and rows we refer to this class of linear programs as problems with column dependent rows to solve these problems we need to be able to generate both columns and rows on the fly within an efficient solution approach we emphasize that the generated rows are structural constraints and distinguish our work from the branch and cut and price framework we first characterize the underlying assumptions for the proposed column and row generation algorithm these assumptions are general enough and cover all problems with column dependent rows studied in the literature up until now to the best of our knowledge we then introduce in detail a set of pricing subproblems which are used within the proposed column and row generation algorithm this is followed by a formal discussion on the optimality of the algorithm to illustrate our approach the paper is concluded by applying the proposed framework to the multi stage cutting stock and the quadratic set covering problems

novel summation inequalities and their applications to stability analysis for systems with time varying delay the inequality technique plays an important role in stability analysis for time delay systems this technical note presents a new sequence of novel summation inequalities by introducing some free matrices which includes the newly developed wirtinger based and free matrix based summation inequalities as special cases moreover the idea can be easily extended to the multiple summation inequality case based on the proposed inequalities relaxed stability conditions are obtained for systems with time varying delay numerical examples are given to demonstrate the effectiveness of the proposed approach

improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

improved approach to robust stability and h performance analysis for systems with an interval time varying delay abstract an improved delay and range dependent robust stability and h performance analysis criterion for systems with an interval time varying delay is investigated a novel lyapunov krasovskii functional containing triple integral terms is established and an extended free weighting matrix method double integral inequality method is subsequently proposed numerical examples validate the effectiveness of the proposed double integral inequality method and show that our approach is less conservative than existing methods

new insights on stability of sampled data systems with time delay abstract this paper analyses the stability of sampled data systems with time delay by employing a two sided looped functional approach some improved conditions are derived to guarantee the stability of the system under consideration then based the conditions some intrinsic relationships between sampled data period and time delay are obtained from the illustrative example being solved by the proposed approach it is observed that the results obtained are significantly better than those obtained by existing methods more importantly from the simulation being carried out it is discovered that contrary to the findings in previous studies time delays in a system may enlarge the interval of sampled data periods and accelerate the rate of convergence of the system states rather than deteriorate the system performance

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

efficient robust constrained model predictive control with a time varying terminal constraint set abstract an efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints the approach is novel in that it off line constructs a continuum of terminal constraint sets and on line achieves robust stability by using a relatively short control horizon even n 0 with a time varying terminal constraint set this algorithm not only dramatically reduces the on line computation but also significantly enlarges the size of the allowable set of initial conditions moreover this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium the controller design is illustrated through a benchmark problem

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

novel delay dependent stability criterion for time varying delay systems with parameter uncertainties and nonlinear perturbations this study proposes a novel approach to obtain less conservative conditions for the robust stability analysis for time varying delay systems with parameter uncertainties and nonlinear perturbations specifically first we divide the time varying delay into non uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms more exactly second novel delay derivation dependent stability criteria are derived by introducing a parameter c in the lyapunov krasovskii functional third we define some new variables to deal with uncertain parameters finally two numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results

some novel approaches on state estimation of delayed neural networks this paper studies the issue of state estimation for a class of neural networks nns with time varying delay a novel lyapunov krasovskii functional lkf is constructed where triple integral terms are used and a secondary delay partition approach sdpa is employed compared with the existing delay partition approaches the proposed approach can exploit more information on the time delay intervals by taking full advantage of a modified wirtinger s integral inequality mwii improved delay dependent stability criteria are derived which guarantee the existence of desired state estimator for delayed neural networks dnns a better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities lmis in addition a new activation function dividing method is developed by bringing in some adjustable parameters three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods

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

finite time h fuzzy control of nonlinear markovian jump delayed systems with partly uncertain transition descriptions abstract this paper addresses a finite time h fuzzy control problem for a class of nonlinear markovian jump delayed systems with partly uncertain transition descriptions which is represented as a takagi sugeno t s fuzzy model a new homogeneous polynomial of partly uncertain transition rates is chosen free matrix based and double integral forms of the wirtinger based integral inequalities are employed to make the proposed approach less conservative then sufficient conditions are derived such that the fuzzy nonlinear makovian jump delayed system exhibits stochastic finite time boundedness finally two numerical examples are given to illustrate the effectiveness of the proposed design methodology

improved delay dependent stability criteria for linear systems with multiple time varying delays this paper concentrates on the stability analysis of continuous time linear systems with multiple time varying delays the time delays are assumed to be bounded and have or not lower and upper boun

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

passivity criteria for continuous time neural networks with mixed time varying delays abstract this paper is concerned with the problem of passivity analysis for uncertain continuous time neural networks with mixed time varying delays the mixed time varying delays consist of both discrete and distributed delays in which the discrete delays are assumed to be varying within a given interval in addition the uncertainties are assumed to be norm bounded by employing a novel lyapunov krasovskii functional new passivity delay interval dependent criteria are established to guarantee the passivity performance when estimating an upper bound of the derivative of the lyapunov krasovskii functional we handle the terms related to the discrete and distributed delays appropriately so as to develop less conservative results these passivity conditions are presented in terms of linear matrix inequalities which can be easily solved via standard numerical software some numerical examples are given to illustrate the effectiveness of the proposed method

stability of discrete time systems with time varying delays via a novel summation inequality this technical note is concerned with the stability analysis of discrete linear systems with time varying delays the novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated jensen inequality employed in the context of discrete time delay systems this inequality is a discrete time counterpart of the wirtinger based integral inequality that was recently employed for the improved analysis of continuous tine systems with delays however differently from the continuous time case the proof of the new inequality is not based on the wirtinger inequality the method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the lmis optimization setup the effectiveness of the proposed result is illustrated by some classical examples from the literature

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

stability of linear systems with time varying delays using bessel legendre inequalities this paper addresses the stability problem of linear systems with a time varying delay hierarchical stability conditions based on linear matrix inequalities are obtained from an extensive use of the bessel inequality applied to legendre polynomials of arbitrary orders while this inequality has been only used for constant discrete and distributed delays this paper generalizes the same methodology to time varying delays we take advantages of the dependence of the stability criteria on both the delay and its derivative to propose a new definition of allowable delay sets a light and smart modification in their definition leads to relevant conclusions on the numerical results

single multiple integral inequalities with applications to stability analysis of time delay systems this technical note is concerned with the problem of stability analysis for time delay systems a new series of integral inequalities to bound a single integral term is presented by introducing some free matrices which produces tighter bounds than some existing ones similarly based on orthogonal polynomials defined in integral inner spaces new series of multiple integral inequalities are presented as well which include the existing double ones to show the effectiveness of the proposed inequalities their applications to stability analysis of systems with discrete and distributed delays are provided with numerical examples

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

a note on a lp based heuristic for a time constrained routing problem in their paper avella et al 2006 investigate a time constrained routing problem the core of the proposed solution approach is a large scale linear program that grows both row and column wise when new variables are introduced thus a column and row generation algorithm is proposed to solve this linear program optimally and an optimality condition is presented to terminate the column and row generation algorithm we demonstrate by using lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two 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

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

improved criteria on robust stability and h performance for linear systems with interval time varying delays via new triple integral functionals this paper analyzes delay dependent robust stability and h performance of linear systems with an interval time varying delay based on a new lyapunov krasovskii functional containing new triple integral terms the time derivative of the lyapunov krasovskii functional produces not only the strictly proper rational functions but also the non strictly proper rational functions of the time varying delays with first order denominators the combinations of the rational functions are directly handled via the jensen inequality lemma and the lower bound lemma for reciprocal convexity whereas such combinations were approximated in the literature the proposed criteria become less conservative with the significantly smaller number of decision variables than the existing criteria which will be demonstrated by some numerical examples

benders decomposition and column and row generation for solving large scale linear programs with column dependent rows in a recent work muter birbil and bulbul 2013a identified and characterized a general class of linear programming lp problems known as problems with column dependent rows cdr problems these lps feature two sets of constraints with mutually exclusive groups of variables in addition to a set of structural linking constraints in which variables from both groups appear together in a typical cdr problem the number of linking constraints grows very quickly with the number of variables which motivates generating both columns and their associated linking constraints simultaneously on the fly in this paper we expose the decomposable structure of cdr problems via benders decomposition however this approach brings on its own theoretical challenges one group of variables is generated in the benders master problem while the generation of the linking constraints is relegated to the benders subproblem along with the second group of variables a fallout of this separation is that only a partial description of the dual of the benders subproblem is available over the course of the algorithm we demonstrate how the pricing subproblem for the column generation applied to the benders master problem does also update the dual polyhedron and the existing benders cuts in the master problem to ensure convergence ultimately a novel integration of benders cut generation and the simultaneous generation of columns and constraints yields a brand new algorithm for solving large scale cdr problems we illustrate the application of the proposed method on a time constrained routing problem our numerical experiments confirm the outstanding performance of the new decomposition method

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

technical communique improving off line approach to robust mpc based on nominal performance cost this paper gives two alternative off line synthesis approaches to robust model predictive control rmpc for systems with polytopic description in each approach a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off line in order to accommodate a wider class of systems nominal performance cost is chosen to substitute the worst case one in an existing technique in the design of control law for a larger ellipsoid the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids so as to further improve feasibility and optimality the effectiveness of the alternative approaches is illustrated by a simulation example

finite time synchronization of sampled data t s fuzzy complex dynamical networks subject to average dwell time approach abstract the problem of finite time synchronization for takagi sugeno t s fuzzy complex dynamical networks with coupling delays via sampled data control is presented in this paper to change the sampled data control system into a continuous time delayed system an input delay approach is applied based on the lyapunov stability theory a suitable lyapunov krasovskii functional lkf is constructed with the kronecker products furthermore by applying the average dwell time approach a novel sufficient condition is established to ascertain the finite time stabilization of fuzzy complex dynamical networks cdns with switching signals the proposed method is less conservative than conventional approaches since the newly developed time dependent fuzzy lkf is used the proposed sufficient condition can be represented in the form of linear matrix inequalities lmis finally the effectiveness and superiority of the proposed approach is validated through both numerical and practical examples

stability analysis of static recurrent neural networks with interval time varying delay the problem of stability analysis of static recurrent neural networks with interval time varying delay is investigated in this paper a new lyapunov functional which contains some new double integral and triple integral terms are introduced information about the lower bound of the delay is fully used in the lyapunov functional integral and double integral terms in the derivative of the lyapunov functional are divided into some parts to get less conservative results some sufficient stability conditions are obtained in terms of linear matrix inequality lmi numerical examples are given to illustrate the effectiveness of the proposed method

state estimation for delayed genetic regulatory networks with reaction diffusion terms this paper addresses the problem of state estimation for delayed genetic regulatory networks dgrns with reaction diffusion terms using dirichlet boundary conditions the nonlinear regulation function of dgrns is assumed to exhibit the hill form the aim of this paper is to design a state observer to estimate the concentrations of mrnas and proteins via available measurement techniques by introducing novel integral terms into the lyapunov krasovskii functional and by employing the wirtinger type integral inequality the convex approach green s identity the reciprocally convex approach and wirtinger s inequality an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities lmis the stability criterion depends upon the bounds of delays and their derivatives it should be noted that if the set of lmis is feasible then the desired observation of dgrns is possible and the state estimation can be determined finally two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design

an ellipsoidal off line model predictive control strategy for linear parameter varying systems with applications in chemical processes abstract in this paper a novel off line model predictive control strategy for linear parameter varying systems is presented the on line computational burdens are reduced by pre computing off line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids the number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope at each sampling instant the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured the real time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains an overall algorithm is proved to guarantee robust stability the controller design is illustrated with two examples of continuous stirred tank reactors