symbolic model checking for real time systems abstract we describe finite state programs over real numbered time in a guarded command language with real valued clocks or equivalently as finite automata with real valued clocks model checking answers the question which states of a real time program satisfy a branching time specification given in an extension of ctl with clock variables we develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates without constructing the state space for this purpose we introduce a calculus on computation trees over real numbered time unfortunately many standard program properties such as response for all nonzeno execution sequences during which time diverges cannot be characterized by fixpoints we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed ctl fortunately this result does not impair the symbolic verification of implementable real time programs those whose safety constraints are machine closed with respect to diverging time and whose fairness constraints are restricted to finite upper bounds on clock values all timed ctl properties of such programs are shown to be computable as finitely approximable fixpoints in a simple decidable theory

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

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

new results on stability analysis for systems with discrete distributed delay the integral inequality technique is widely used to derive delay dependent conditions and various integral inequalities have been developed to reduce the conservatism of the conditions derived in this study a new integral inequality was devised that is tighter than existing ones it was used to investigate the stability of linear systems with a discrete distributed delay and a new stability condition was established the results can be applied to systems with a delay belonging to an interval which may be unstable when the delay is small or nonexistent three numerical examples demonstrate the effectiveness and the smaller conservatism of the method

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

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

dissipativity analysis for neural networks with two delay components using an extended reciprocally convex matrix inequality abstract this paper focuses on the problem of strictly q s r dissipativity analysis for neural networks with two delay components based on the dynamic delay interval method a lyapunov krasovskii functional is constructed by solving its self positive definite and derivative negative definite conditions via an extended reciprocally convex matrix inequality several new sufficient conditions that guarantee the neural networks strictly q s r dissipative are derived furthermore the dissipativity analysis of neural networks with two delay components is extended to the stability analysis finally two numerical examples are employed to illustrate the advantages of the proposed 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

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

stochastic finite time h state estimation for discrete time semi markovian jump neural networks with time varying delays in this article the finite time h infty state estimation problem is addressed for a class of discrete time neural networks with semi markovian jump parameters and time varying delays the focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite time bounded with a prescribed h infty performance level via finite time lyapunov stability theory by constructing a delay product type lyapunov functional in which the information of time varying delays and characteristics of activation functions are fully taken into account and using the jensen summation inequality the free weighting matrix approach and the extended reciprocally convex matrix inequality some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator finally numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results

generalized discrete timed automata decidable approximations for safety verification we consider generalized discrete timed automata with general linear relations over clocks and parameterized constants as clock constraints and with parameterized durations we look at three approximation techniques i e the r reset bounded approximation the b bounded approximation and the b r crossing bounded approximation and derive automata theoretic characterizations of the binary reachability under these approximations the characterizations allow us to show that the safety analysis problem is decidable for generalized discrete timed automata with unit durations and for deterministic generalized discrete timed automata with parameterized durations an example specification written in astral is used to run a number of experiments using one of the approximation techniques

lyapunov conditions for finite time stability of time varying time delay systems in this paper we develop the lyapunov razumikhin method to finite time stability fts and finite time contractive stability ftcs of time delay systems several lyapunov based sufficient conditions for establishing these fts properties are obtained then the theoretical results are applied to fts and ftcs for a class of linear time varying ltv time delay system the efficiency of the proposed criteria is illustrated by three numerical examples where a stabilizing memoryless controller for ftcs of a second order ltv system with time delay is proposed

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

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

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

extended dissipativity analysis for markovian jump neural networks with time varying delay via delay product type functionals this paper investigates the problem of extended dissipativity for markovian jump neural networks mjnns with a time varying delay the objective is to derive less conservative extended dissipativity criteria for delayed mjnns toward this aim an appropriate lyapunov krasovskii functional lkf with some improved delay product type terms is first constructed then by employing the extended reciprocally convex matrix inequality ercmi and the wirtinger based integral inequality to estimate the derivative of the constructed lkf a delay dependent extended dissipativity condition is derived for the delayed mjnns an improved extended dissipativity criterion is also given via the allowable delay sets method based on the above mentioned results the extended dissipativity condition of delayed nns without markovian jump parameters is directly derived finally three numerical examples are employed to illustrate the advantages of the proposed method

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

an improved summation inequality to discrete time systems with time varying delay the summation inequality plays an important role in developing delay dependent criteria for discrete time systems with time varying delay this note proposes an improved summation inequality to estimate the summation terms appearing in the forward difference of lyapunov krasovskii functional compared with the inequality recently developed by the wirtinger based summation inequality and the reciprocally convex lemma the proposed one reduces the estimation gap while requires the same number of decision variables a relaxed stability criterion of a linear discrete time system with a time varying delay is established by using such novel inequality two numerical examples are given to demonstrate the advantages of the proposed method

stability analysis and control design of singular markovian jump systems via a parameter dependent reciprocally convex matrix inequality abstract this paper is concerned with the problems of stochastic stability and control design for singular markovian jump systems smjss with time varying delay the derivative coefficient is considered to be mode dependent a parameter dependent reciprocally convex matrix inequality pdrcmi is constructed which covers some existing ones as its special cases different from some existing ones the introduced parameters are completely known which can be optimized by an iteration algorithm to decrease the redundant decision variables a mild assumption is given for the case of mode dependent coefficient such that the considered system is decomposed into differential equations and algebraic ones in this case the components of state vectors of the subsystem are applied to construct a new augmented lyapunov krasovkii functional lkf based on the pdrci and the new augmented lkf a novel stochastic stability condition with both less computational demands and less conservativeness is derived based on the decomposed subsystems and the stability condition a set of state feedback controller is designed in terms of linear matrix inequalities lmis some numerical examples are introduced to illustrate the effectiveness of the proposed results

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

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

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

new results on dissipativity analysis of singular systems with time varying delay abstract this paper focuses on the dissipativity analysis of singular systems with time varying delay the objective is to obtain a less conservative criterion with less computational demand based on the state decomposition method singular systems are rewritten as differential subsystems and algebraic ones first of all the components of state vectors are applied to design a novel lyapunov krasovskii functional lkf for the differential subsystems then in the derivative of the lkf the algebraic ones are introduced and the wirtinger based integral inequality together with the extended reciprocally convex matrix inequality is adopted to estimate the single integral term therefore a new dissipativity criterion is obtained which realizes both less conservativeness and less computational demand finally two numerical examples are given to verify the superiority of the proposed method

reachable set estimation for markov jump lpv systems with time delays abstract this paper investigates the reachable set estimation problem for discrete time markov jump lpv systems with time varying delays and bounded disturbance the main consideration is that under zero initial conditions how to obtain a bound set as small as possible that includes system states based on this by applying a novel summation inequality integrated with the reciprocally convex approach under the framework of the lyapunov functional method the delay dependent conditions are provided to guarantee the presence of an ellipsoid that bounds the system state in the existence of bounded disturbances some derived conditions expressed by linear matrix inequalities can be solved via utilizing different computational tools and the minimum possible ellipsoidal bound can also be determined additionally the obtained results are extensively used in the case with partially known transition probability and some conditions with more universality are derived finally a numerical example is given to illustrate the effectiveness of the results

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

correlation functions of the nonstationary quantum singular oscillator the exact density matrix elements and the correlation functions of the one dimensional non stationary singular oscillator the potential u x t omega 2 t x2 2 g x2 excited from the thermodynamic equilibrium states are obtained generating functions for rho nm and also for transition probabilities are constructed

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

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

integrability of difference calogero moser systems a general class of n particle difference calogero moser systems with elliptic potentials is introduced besides the step size and two periods the hamiltonian depends on nine coupling constants we prove the quantum integrability of the model for n 2 and present partial results for n 3 in degenerate cases rational hyperbolic or trigonometric limit the integrability follows for arbitrary particle number from previous work connected with the multivariable q polynomials of koornwinder and macdonald liouville integrability of the corresponding classical systems follows as a corollary limit transitions lead to various well known models such as the nonrelativistic calogero moser systems associated with classical root systems and the relativistic calogero moser system

the relativistic linear singular oscillator exactly solvable model of the linear singular oscillator in the relativistic configurational space is considered we have found wavefunctions and energy spectrum for the model under study it is shown that they have the correct non relativistic limits

stabilization of t s fuzzy system with time delay under sampled data control using a new looped functional this paper investigates the sampled data stabilization problem for a takagi sugeno t s fuzzy system with time delay by taking the information of states within the intervals from t k to t and t to t k 1 into account a new two side delay dependent looped functional is introduced which can not only relax the monotonic constraint of lyapunov krasovskii functional lkf but also make better use of the actual sampling pattern furthermore the sampled data fuzzy controller is designed to contain both the present and delayed state information thereby enhancing the control performance and design flexibility based on the novel augmented lkf and improved bounding technique less conservative stability criteria are derived in the form of linear matrix inequalities the superiority of proposed results is shown by two simulation 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

stability analysis of systems with uncertain time varying delays stability of systems in the presence of bounded uncertain time varying delays in the feedback loop is studied the delay parameter is assumed to be an unknown time varying function for which the upper bounds on the magnitude and the variation are given the stability problem is treated in the integral quadratic constraint iqc framework criteria for verifying robust stability are formulated as feasibility problems over a set of frequency dependent linear matrix inequalities the criteria can be equivalently formulated as semi definite programs sdp using kalman yakubovich popov lemma as such checking robust stability can be performed in a computationally efficient fashion

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

stability analysis of sampled data systems via free matrix based time dependent discontinuous lyapunov approach in this paper a new time dependent discontinuous lyapunov functional namely free matrix based time dependent discontinuous fmbtdd lyapunov functional is introduced for stability analysis of sampled data systems first a modified free matrix based integral inequality mfmbii is derived based on the existing free matrix based integral inequality 1 and it is applied to develop a stability criterion for sampled data systems and then inspired by mfmbii fmbtdd term is established that leads to efficient stability conditions four numerical examples are given to demonstrate the effectiveness of the proposed methods

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

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

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

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

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

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

a relativistic model of the n dimensional singular oscillator an exactly solvable n dimensional model of the quantum isotropic singular oscillator in the relativistic configurational space is proposed it is shown that through the simple substitutions the finite difference equation for the n dimensional singular oscillator can be reduced to the similar finite difference equation for the relativistic isotropic three dimensional singular oscillator we have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra

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

stability analysis of lur e systems with additive delay components via a relaxed matrix inequality abstract this paper is concerned with the stability analysis of lur e systems with sector bounded nonlinearity and two additive time varying delay components in order to accurately understand the effect of time delays on the system stability the extended matrix inequality for estimating the derivative of the lyapunov krasovskii functionals lkfs is employed to achieve the conservatism reduction of stability criteria it reduces estimation gap of the popular reciprocally convex combination lemma rccl combining the extended matrix inequality and two types of lkfs lead to several stability criteria which are less conservative than the rccl based criteria under the same lkfs finally the advantages of the proposed criteria are demonstrated through two examples

new decidability results concerning two way counter machines the authors study some decision questions concerning two way counter machines and obtain the strongest decidable results to date concerning these machines in particular it is shown that the emptiness containment and equivalence ece for short problems are decidable for two way counter machines whose counter is reversal bounded i e the counter alternates between increasing and decreasing modes at most a fixed number of times this result is used to give a simpler proof of a recent result in which the ece problems for two way reversal bounded pushdown automata accepting bounded languages i e subsets of w 1 ldots w k for some nonnull words w 1 ldots w k are decidable other applications concern decision questions about simple programs finally it is shown that nondeterministic two way reversal bounded multicounter machines are effectively equivalent to finite automata on unary languages and hence their ece problems are decidable also

recurrence relations for radial wavefunctions for the nth dimensional oscillators and hydrogenlike atoms we present a general procedure for finding recurrence relations of the radial wavefunctions for nth dimensional isotropic harmonic oscillators and hydrogenlike atoms