deformed preprojective algebras of generalized dynkin type we introduce the class of deformed preprojective algebras of generalized dynkin graphs an n 1 d n n 4 eg e 7 eg and l n n 1 and prove that it coincides with the class of all basic connected finite dimensional self injective algebras for which the inverse nakayama shift v 1 s of every non projective simple module s is isomorphic to its third syzygy 3 s

algebras of generalized quaternion type abstract we introduce and study the algebras of generalized quaternion type being natural generalizations of algebras which occurred in the study of blocks of group algebras with generalized quaternion defect groups we prove that all these algebras with 2 regular gabriel quivers are periodic algebras of period 4 and very specific deformations of the weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles the main result of the paper forms an important step towards the morita equivalence classification of all periodic symmetric tame algebras of non polynomial growth applying the main result we establish existence of wild periodic algebras of period 4 with arbitrary large number at least 4 of pairwise non isomorphic simple modules these wild periodic algebras arise as stable endomorphism rings of cluster tilting cohen macaulay modules over one dimensional hypersurface singularities

periodicity of self injective algebras of polynomial growth abstract let a be an indecomposable representation infinite tame finite dimensional algebra of polynomial growth over an algebraically closed field we prove that a is a periodic algebra with respect to action of the bimodule syzygy operator if and only if a is morita equivalent to a socle deformation of an orbit algebra b g where b is the repetitive category of a tubular algebra b and g is an admissible infinite cyclic automorphism group of b the main contribution in the paper is to prove the sufficiency part of this equivalence it is known that every orbit algebra b g of a tubular algebra b admits a presentation as an orbit algebra t b r h of an r fold trivial extension algebra t b r of b with respect to free action of a finite cyclic automorphism group h of t b r a significant part of the paper is devoted to explicit descriptions of the minimal projective bimodule resolutions of properly chosen ten exceptional self injective algebras of polynomial growth and showing that all of them are periodic algebras then we deduce the periodicity of all algebras socle equivalent to the orbit algebras b g t b r h of tubular algebras b from the periodicity of these ten exceptional algebras using invariance of periodicity for finite galois coverings and derived equivalences of algebras

an improved result on reachable set estimation and synthesis of time delay systems in this paper the problems of reachable set estimation and synthesis of time delay systems are investigated by introducing the non uniform delay partitioning method and the triple integral technique an improved reachable set estimation condition is proposed in terms of linear matrix inequality based on the criterion a sufficient condition for the existence of a state feedback controller is established to render the reachable set of the closed loop system be bounded by a given ellipsoid two numerical examples are given to demonstrate the effectiveness of the obtained results

primal dual approach to the single level capacitated lot sizing problem abstract the lagrangean relaxation of the single level capacitated dynamic lot sizing problem can be solved using the primal dual method the algorithm has monotone and finite convergence properties it works as a steepest ascent method a variant of this approach is also studied a heuristic routine used to obtain a feasible solution in each iteration is presented computational experiences show that this method usually yields better solutions than the subgradient method although it requires greater cpu times

anti disturbance control for nonlinear systems subject to input saturation via disturbance observer this paper is concerned with the problem of the disturbance observer based control for a class of continuous time uncertain systems subject to input saturation and nonlinearity the input of the system includes two parts the control input and the disturbance input the nonlinearity of the system which satisfies a global lipschitz condition is considered as two cases of known nonlinearity and unknown nonlinearity by virtue of the technique of the disturbance observer based controller the anti disturbance controllers are designed respectively with both the polytopic and dead zone representations of the saturation function which ensure that the resulting closed loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the lyapunov function further an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states an example of application design for a flight control system illustrates the effectiveness of the proposed results

resolutions of mesh algebras periodicity and calabi yau dimensions a triangulated category mathcal t sigma is said to be calabi yau of dimension d if d is a serre functor we determine which stable module categories of self injective algebras of finite type are calabi yau and compute their calabi yau dimensions correcting errors in previous work we first show that the calabi yau property of mod can be detected in the minimal projective resolution of the stable auslander algebra of over its enveloping algebra we then describe the beginning of such a minimal resolution for any mesh algebra of a stable translation quiver and apply covering theory to relate these minimal resolutions to those of the generalized preprojective algebras of dynkin graphs for representation finite self injective algebras of torsion order t 1 we obtain a complete description of their stable calabi yau properties but only partial results for those algebras of torsion order t 2 we also obtain some new information about the periods of the representation finite self injective algebras of torsion order t 1 finally we describe how these questions can also be approached by realizing the stable categories of representation finite self injective algebras as orbit categories of the bounded derived categories of hereditary algebras and illustrate this technique with several explicit computations that our previous methods left unsettled

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

lagrangean relaxation based heuristics for lot sizing with setup times we consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only the demand is dynamic over time and there is a single resource of limited capacity we show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case we examine the lagrangean relaxation lr of demand constraints in a strong reformulation of the problem we then design a primal heuristic to generate upper bounds and combine it with the lr problem within a subgradient optimization procedure we also develop a simple branch and bound heuristic to solve the problem computational results on test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature

dynamical feedback compensator for uncertain time delay systems containing saturating actuator abstract the problem of the stabilization of an uncertain time delay system with a saturating actuator is discussed these uncertainties may be linear non linear and or time varying but only the upper bounds are known a linear dynamical feedback compensator is used to stabilize this uncertain saturating and time delay system the concept of matrix measure and the comparison theory are employed to investigate the robust stability condition which assures asymptotic stability one example is given to illustrate the application of the proposed design method

new finite sum inequalities with applications to stability of discrete time delay systems this paper is concerned with the problem of stability analysis of discrete time delay systems new finite sum inequalities which encompass the ones based on abel lemma or wirtinger type inequality are first proposed the potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete time systems with delay the derived stability criteria are theoretically and numerically proved to be less conservative than existing results

exponential stabilization of switched time varying systems with delays and disturbances abstract this paper deals with exponential stabilization for a class of switched time varying systems by taking time varying delays and nonlinear disturbances into consideration time dependent switching signals have been characterized in terms of metzler matrices such that the resulting system is globally exponentially stable compared with preceding works we introduce a model transformation and an approach without involving the lyapunov krasovskii functional to derive new exponential stability criteria for switched time varying systems under the average dwell time switching numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results

a lagrangian based heuristic for the capacitated lot sizing problem in parallel machines this paper addresses the capacitated lot sizing problem involving the production of multiple items on unrelated parallel machines a production plan should be determined in order to meet the forecast demand for the items without exceeding the capacity of the machines and minimize the sum of production setup and inventory costs a heuristic based on the lagrangian relaxation of the capacity constraints and subgradient optimization is proposed initially the heuristic is tested on instances of the single machine problem and results are compared with heuristics from the literature for parallel machines and small problems the heuristic performance is tested against optimal solutions and for larger problems it is compared with the lower bound provided by the lagrangian relaxation

derived equivalence classification of algebras of dihedral semidihedral and quaternion type abstract algebras of dihedral semidihedral and quaternion type were introduced by k erdmann as a generalization of blocks of finite groups of tame representation type in a series of papers erdmann gave a description of the morita equivalence classes of these algebras the aim of the present article is to present a classification of algebras of dihedral semidihedral and quaternion type up to derived equivalence as an application we can show that all basic algebras in erdmann s list are actually of tame representation type

regulator problem for linear continuous time delay systems with nonsymmetrical constrained control the regulator problem is studied for linear continuous time delay systems with nonsymmetrical constrained control necessary and sufficient conditions allowing the autors to obtain the largest nonsymmetrical polyhedral positively invariant with respect to w r t the system in the closed loop are given the case of symmetrical constrained control is obtained as a particular case

an lmi condition for the robust stability of uncertain continuous time linear systems a new sufficient condition for the robust stability of continuous time uncertain linear systems with convex bounded uncertainties is proposed in this note the results are based on linear matrix inequalities lmis formulated at the vertices of the uncertainty polytope which provide a parameter dependent lyapunov function that assures the stability of any matrix inside the uncertainty domain with the aid of numerical procedures based on unidimensional search and the lmis feasibility tests a simple and constructive way to compute robust stability domains can be established

estimation and synthesis of reachable set for switched linear systems this paper focuses on the problems of reachable set estimation and state feedback controller design for discrete time switched linear systems under bounded peak disturbances for the reachable set estimation problem a lyapunov based inequality is developed based on the multiple lyapunov strategy by choosing appropriate lyapunov functions the ellipsoidal reachable set estimation conditions of discrete time switched linear systems are obtained in order to make the estimated ellipsoids as small as possible three optimization approaches are proposed specifically the genetic algorithm is used to search for the optimal parameters satisfying the obtained reachable set estimation conditions in addition the state feedback controller design problem for discrete time switched linear systems is considered the function of the controller is to manipulate the reachable set of the closed loop system to lie within a given ellipsoid or make the reachable set small finally the effectiveness of the obtained results is verified through some numerical examples

output reachable set estimation for switched linear systems and its application in safety verification this paper addresses the output reachable set estimation problem for continuous time switched linear systems consisting of hurwtiz stable subsystems based on a common lyapunov function approach the output reachable set is estimated by a union of bounding ellipsoids then multiple lyapunov functions with time scheduled structure are employed to estimate the output reachable set for switched systems under dwell time constraint furthermore the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation first a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed then the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters numerical examples are provided to illustrate our results

technical communique reachable set bounding for delayed systems with polytopic uncertainties the maximal lyapunov krasovskii functional approach this paper deals with the problem of reachable set estimation for time delay systems subject to both polytopic parameter uncertainties and bounded peak inputs the maximal lyapunov krasovskii functional is constructed as the pointwise maximum of a family of lyapunov krasovskii functionals each functional corresponds to a vertex of uncertain polytope some criteria bounding the reachable set are derived this approach shows great advantages over the traditional methods based on the common lyapunov functionals by introducing a modified integral inequality the limitation imposed on the derivative of time delay being less than one is relaxed furthermore the obtained results involve less computational burden when the number of vertices of the polytope is small two examples are given to illustrate the theoretical results

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

technical communique further result on reachable set bounding for linear uncertain polytopic systems with interval time varying delays the problem of reachable set estimation of linear uncertain polytopic time varying delay systems subject to bounded peak inputs is studied in this paper the delays considered in this paper are assumed to be non differentiable and vary within an interval where the lower and upper bounds are known based on the lyapunov krasovskii method and delay decomposition technique a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one dimensional search method and matlab s lmi toolbox and allow us to find the smallest radius a numerical example is given to illustrate the effectiveness of the proposed result

robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances this brief paper deals with the problem of robust exponential stabilization of a class of dynamic systems subject to time varying delays external disturbances and control saturation a linear memoryless state feedback controller is synthesized to guarantee that there is a domain of admissible initial conditions from which all solutions of the class of systems considered converge exponentially to a ball with a prespecified convergence rate the problem is formulated as a two step optimization problem with matrix inequality constraints to enlarge the size of the ball of admissible initial conditions

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

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

technical communique improved ellipsoidal bound of reachable sets for time delayed linear systems with disturbances we consider the problem of finding an ellipsoidal reachable set that bounds the states of time delayed linear systems with bounded peak disturbances the considered time delay is time varying but it has an upper bound in magnitude and rate based on the modified lyapunov krasovskii l k type functional we derive a delay dependent result expressed in the form of matrix inequalities containing only one non convex scalar the result is extended to uncertain time delayed linear systems finally we show the usefulness of our result by a comparative numerical example

technical communique on reachable sets for linear systems with delay and bounded peak inputs linear systems with constant coefficients and time varying delays are considered we address the problem of finding an ellipsoid that bounds the set of the states in the euclidean space that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar the system may encounter uncertainties in the matrices of its state space model and in the delay length the lyapunov razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper bound of the delay length

deformed preprojective algebras of generalized dynkin type ln classification and symmetricity abstract we give a complete classification of the isomorphism classes of the deformed preprojective algebras of generalized dynkin type l n and show that all these algebras are symmetric moreover we show that the deformed preprojective algebras of type l n are isomorphic to the stable auslander algebras of simple plane curve singularities of dynkin type a 2 n

periodicity of d cluster tilted algebras abstract it is well known that any maximal cohen macaulay module over a hypersurface has a periodic free resolution of period 2 auslander reiten 1996 4 and buchweitz 1998 8 have used this periodicity to explain the existence of periodic projective resolutions over certain finite dimensional algebras which arise as stable endomorphism rings of cohen macaulay modules these algebras are in fact periodic meaning that they have periodic projective resolutions as bimodules and thus periodic hochschild cohomology as well the goal of this article is to generalize this construction of periodic algebras to the context of iyama s higher ar theory let c be a maximal d 1 orthogonal subcategory of an exact frobenius category b and start by studying the projective resolutions of finitely presented functors on the stable category c over both c and c under the assumption that c is fixed by d we show that d induces the 2 d th syzygy on mod c if c has finite type i e if c add t for a d cluster tilting object t then we show that the stable endomorphism ring of t has a quasi periodic resolution over its enveloping algebra moreover this resolution will be periodic if some power of d is isomorphic to the identity on c it follows in particular that 2 c y tilted algebras arising as stable endomorphism rings of cohen macaulay modules over curve singularities as in the work of burban iyama keller and reiten 2008 9 have periodic bimodule resolutions of period 4

grasp heuristic with path relinking for the multi plant capacitated lot sizing problem this paper addresses the independent multi plant multi period and multi item capacitated lot sizing problem where transfers between the plants are allowed this is an np hard combinatorial optimization problem and few solution methods have been proposed to solve it we develop a grasp greedy randomized adaptive search procedure heuristic as well as a path relinking intensification procedure to find cost effective solutions for this problem in addition the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines the results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature the results are confirmed by statistical tests

componentwise ultimate bounds for positive discrete time delay systems perturbed by interval disturbances this paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time varying delays and bounded disturbances the disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero we first derive a sufficient condition for the existence of componentwise ultimate bounds this condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound then by using the comparison method we extend the obtained result to a class of nonlinear time delay systems which has linear positive bounds two numerical examples are given to illustrate the effectiveness of the obtained results

on reachable set estimation of singular systems in this paper the problem of reachable set estimation of singular systems is investigated based on the lyapunov method a sufficient condition is established in terms of a linear matrix inequality lmi to guarantee that the reachable set of singular system is bounded by the intersection of ellipsoids then the result is extended to the problem for singular systems with time varying delay by utilizing the reciprocally convex approach the effectiveness of the obtained results in this paper is illustrated by numerical examples

asymptotic behavior of switched delay systems with nonlinear disturbances the objective of this paper is to study the asymptotic behavior of switched delay systems with nonlinear disturbances by establishing a new delay gronwall bellman integral inequality and an elementary inequality we obtain some asymptotic results for the systems under arbitrary switching laws which extend some existing results in the literature to the more general nonlinear case finally two examples are provided to illustrate the effectiveness of our results

exponential estimates for retarded time delay systems an lmi approach exponential estimates and sufficient conditions for the exponential stability of linear time delay systems are given the proof make use of lyapunov krasovskii functionals and the conditions are expressed in terms of linear matrix inequalities

reachable set estimation of t s fuzzy systems with time varying delay in this paper the reachable set estimation problem is investigated for delayed discrete time takagi sugeno fuzzy systems with bounded input disturbances and nonzero initial conditions a reachable set estimation condition is derived by using the reciprocally convex combination approach to bound the forward difference of triple summable terms the derived condition guarantees that all the states of the system with the initial conditions from some domain are bounded in a compact set and all the states from other domain converge exponentially within another compact set moreover a less conservative stability condition is also obtained the effectiveness and the reduced conservatism of the proposed results are illustrated by numerical examples

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

on the reachable set bounding of uncertain dynamic systems with time varying delays and disturbances in this paper improved conditions are proposed for finding an ellipsoidal bound of reachable sets which bound the state trajectories of uncertain dynamic systems with time varying delays and bounded peak disturbances a more generalized time derivative condition is considered in comparison with previous work by the use of convex hull properties and application of the lyapunov method sufficient conditions for finding an ellipsoidal bound of reachable sets of the concerned systems are established in terms of linear matrix inequalities lmis two numerical examples are included to show the superiority and effectiveness of our results

an ultimate state bound for a class of linear systems with delay abstract a new method is given to estimate an ultimate state bound on a time varying linear system with delay and bounded disturbances by using some results on metzler matrices the effectiveness of the obtained results is illustrated by a numerical example

a tabu search heuristic for the capacitated lot sizing problem with set up carryover this paper presents a tabu search heuristic for the capacitated lot sizing problem clsp with set up carryover this production planning problems allows multiple items to be produced within a time period and setups for items to be carried over from one period to the next two interrelated decisions sequencing and lot sizing are present in this problem our tabu search heuristic consists of five basic move types three for the sequencing decisions and two for the lot sizing decisions we allow infeasible solutions to be generated at a penalty during the course of the search we use several search strategies such as dynamic tabu list adaptive memory and self adjusting penalties to strengthen our heuristic we also propose a lower bounding procedure to estimate the quality of our heuristic solution we have also modified our heuristic to produce good solutions for the clsp without set up carryover the computational study conducted on a set of 540 test problems indicates that on average our heuristic solutions are within 12 of a bound on optimality in addition for the set of test problems our results indicate an 8 reduction in total cost through set up carryover

linear functional state bounding for positive systems with disturbances varying within a bounded set in most of the existing works on state bounding for perturbed dynamical systems the disturbance vector is only considered under the assumption that its norms components are bounded by known constant bounds this paper considers a more general case where the disturbance vector is assumed to vary within a known bounded set furthermore instead of finding bounds of the full system state vector this paper focuses on finding the smallest componentwise bound of a given linear function of the system state vector a class of perturbed positive systems is considered and a new method for deriving the smallest bound is presented our presented method is also extended to positive systems with time delays and to nonlinear systems which are bounded by positive systems a numerical example is given to illustrate the effectiveness of the obtained results

a new approach to state bounding for linear time varying systems with delay and bounded disturbances abstract in this note the problem of state bounding for linear time varying systems with delay and bounded disturbances input is considered for the first time by using a novel approach which does not involve the lyapunov krasovskii functional method new explicit delay independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it a numerical example is given to illustrate the effectiveness of the obtained result

on uniform ultimate boundedness of linear systems with time varying delays and peak bounded disturbances abstract this paper is devoted to a problem of uniform ultimate boundedness uub for a class of linear systems with interval time varying delays and peak bounded disturbances by using the lyapunov krasovskii functional method a general uub condition and an estimation of the ultimate bound on system trajectories are developed on the basis of the above results linear matrix inequality lmi conditions on uub of the perturbed systems under consideration are derived by constructing an appropriate lyapunov krasovskii functional meanwhile the ultimate bound for a prescribed disturbance attenuation level is given in the form of an ellipsoidal surface the feasibility and effectiveness of the derived results are illustrated by two numerical examples

exponential stability of time delay systems via new weighted integral inequalities in this paper new weighted integral inequalities wiis are first derived based on jensen s integral inequalities in single and double forms it is theoretically shown that the newly derived inequalities in this paper encompass both the jensen inequality and its most recent improvement based on wirtinger s integral inequality the potential capability of wiis is demonstrated through applications to exponential stability analysis of some classes of time delay systems in the framework of linear matrix inequalities lmis the effectiveness and least conservativeness of the derived stability conditions using wiis are shown by various numerical examples

a new method of reachable set estimation for time delay systems with polytopic uncertainties we address the reachable set bounding problem of linear systems subject to both time varying delay and polytopic uncertainties a novel criterion is established to give a more accurate description of the set which bounds the states starting from the origin by inputs with peak values by combining the maximal lyapunov functional and the reciprocally convex approach we obtain a tighter reachable set estimation with lower computational complexity the corresponding reachable set condition for the common lyapunov functional can be obtained naturally as a special case of the above result finally two examples illustrate the advantages of our proposed method

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

exponential stability analysis for uncertain neural networks with interval time varying delays in this paper the problem of exponential stability analysis for neural networks is investigated it is assumed that the considered neural networks have norm bounded parametric uncertainties and interval time varying delays by constructing a new lyapunov functional new delay dependent exponential stability criteria with an exponential convergence rate are established in terms of lmis linear matrix inequalities which can be easily solved by various convex optimization algorithms two numerical examples are included to show the effectiveness of proposed criteria

derived equivalences for tame weakly symmetric algebras having only periodic modules abstract recently a classification up to morita equivalence of all weakly symmetric algebras which have tame representation type simply connected galois coverings and all of whose modules are periodic equivalently the stable auslander reiten quiver consist only of tubes has been completed in j bialkowski a skowronski on tame weakly symmetric algebras having only periodic modules arch math to appear we classify in this paper these algebras up to derived equivalence and give a set of representatives for the derived equivalence classes

almost sure estimation and synthesis of ultimate bounds for discrete time markov jump linear systems this paper is concerned with the problems of almost sure ultimate bound estimation and controller design for markov jump linear systems with bounded stochastic disturbances by utilising a lyapunov based scheme proposed in this paper an almost sure estimation of ellipsoidal ultimate bound eub of the system is obtained through tractable matrix inequalities on the basis of the estimation results the problem of designing mode dependent state feedback controllers that make the closed loop system admit a prescribed ellipsoid as an eub is considered the obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information finally a practical example in dc motor devices is presented to demonstrate the applicability of the obtained results

weighted surface algebras general version abstract we introduce the general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties in particular we prove that all these algebras except the singular disc triangle tetrahedral and spherical algebras are symmetric tame periodic algebras of period 4

robust controller design of uncertain discrete time delay systems with input saturation and disturbances this technical note deals with the problem of robust controller design of uncertain discrete time delay systems subject to control input saturation and bounded external disturbances a sufficient condition is obtained which guarantees the existence of state feedback controllers and an admissible initial condition domain such that the resulting closed loop system is uniformly exponentially convergent to a ball with certain exponential decay rate for every initial condition emanating from the admissible domain an iterative linear matrix inequality relaxation scheme can be used to construct desired state feedback controllers a simulation example is provided to demonstrate the effectiveness of the proposed method

synthesis of controllers for continuous time delay systems with saturating controls via lmis the stabilization of linear continuous time systems with time delay in the state and subject to saturating controls is addressed sufficient conditions obtained via a linear matrix inequality lmi formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements the method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed loop system is guaranteed when control saturations effectively occur

finite time stability of a class of non autonomous neural networks with heterogeneous proportional delays in this paper the problem of finite time stability analysis for a class of non autonomous neural networks with heterogeneous proportional delays is considered by introducing a novel constructive approach we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre specified finite time interval as a result we also obtain conditions for the power rate global stability of the system numerical examples are given to demonstrate the effectiveness and less restrictiveness of the results obtained in this paper

a lagrangean based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times in this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed with the help of lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single item lotsizing problems from the solutions of these single item problems lower bounds on the minimum objective function value are derived upper bounds are generated by means of a heuristic finite scheduling procedure the quality of the approach is tested with reference to various problem groups of differing sizes

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

robust stabilization for uncertain time delay systems containing saturating actuators a class of uncertain time delay systems containing a saturating actuator is considered these systems are characterized by delayed state equations including a saturating actuator with norm bounded parameter uncertainty possibly time varying in the state and input matrices the delay is assumed to be constant bounded but unknown using a razumikhin approach for the stability of functional differential equations upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable in the case of constrained input via memoryless state feedback control laws these bounds are given in terms of solutions of appropriate finite dimensional riccati equations

solving multi item capacitated lot sizing problems using variable redefinition mixed integer programming models are typically not used to solve realistic sized production scheduling problems because they require exorbitant solution times we impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy the linear programming relaxation of the new models is very effective in generating bounds we show that these bounds are equal to those that could be generated using lagrangian relaxation or column generation the linear programming bounds increase in effectiveness as the problems become larger perhaps of greatest significance is that practitioners can obtain our results using only standard off the shelf codes such as lindo or mpsx 370 we report computational experience in several computing environments hardware and software on problems with up to 200 products and 10 time periods 2000 0 1 variables