stabilization of neural network based control systems via event triggered control with nonperiodic sampled data this paper focuses on a problem of event triggered stabilization for a class of nonuniformly sampled neural network based control systems nnbcss first a new event triggered data transmission mechanism is designed based on the nonperiodic sampled data different from the previous works the proposed triggering scheme enables the nnbcss design to enjoy the advantages of both nonuniform and event triggered sampling schemes second under the nonperiodic event triggered data transmission scheme the nonperiodic sampled data three layer fully connected feedforward neural network tlfcffnn based event triggered controller is constructed and the resulting closed loop tlfcffnn based event triggered control system is modeled as a state delay system based on time delay system modeling approach then the stability criteria for the closed loop system is formulated using lyapunov krasovskii functional approach third the sufficient conditions for the codesign of the tlfcffnn based controller and triggering parameters are given in terms of solvability of matrix inequalities to guarantee the asymptotical stability of the closed loop system and an upper bound on the given cost function while reducing the updates of the controller finally three numerical examples are provided to illustrate the effectiveness and benefits of the proposed results

an obstruction based approach to the kochen specker theorem in isham and butterfield 1998 int j theor phys 37 2669 733 it was shown that the kochen specker theorem can be written in terms of the non existence of global elements of a certain varying set over the category of boolean subalgebras of projection operators on some hilbert space in this paper we show how obstructions to the construction of such global elements arise and how this provides a new way of looking at proofs of the theorem

the discrete time h control problem with measurement feedback this paper is concerned with the discrete time h infty control problem with measurement feedback it follows that as in the continuous time case the existence of an internally stabilizing controller that makes the h infty norm strictly less than 1 is related to the existence of stabilizing solutions to two algebraic riccati equations however in the discrete time case the solutions of these algebraic riccati equations must satisfy extra conditions

event driven observer based output feedback control for linear systems this paper concerns the problem of event driven observer based output feedback control of linear systems contrary to normal sampled data control systems where the controller is updated periodically in event driven systems it is updated only when an event happens and a typical event is defined as some error signals exceeding a given threshold both continuous and discrete time event detector cases are considered it is shown that even with the significantly reduced sampling frequency the global uniform ultimate boundedness of the event driven closed loop systems can also be guaranteed a numerical example is finally used to illustrate the effectiveness and advantages of the proposed approaches

the robust h sub 2 control problem a worst case design the worst case effect of a disturbance system on the h sub 2 norm of the system is analyzed an explicit expression is given for the worst case h sub 2 norm when the disturbance system is allowed to vary over all nonlinear time varying and possibly noncausal systems with bounded l sub 2 induced operator norm an upper bound for this measure which is equal to the worst case h sub 2 norm if the exogeneous input is scalar is defined some further analysis of this upper bound is done and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given the latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature

filtering on sampled data systems with parametric uncertainty the paper is concerned with the problem of robust h sub spl infin filtering for a class of systems with parametric uncertainties and unknown time delays under sampled measurements the parameter uncertainties considered are real time varying and norm bounded appearing in the state equation an approach has been proposed for the designing of h sub spl infin filters using sampled measurements which would guarantee a prescribed h sub spl infin performance in the continuous time context irrespective of the parameter uncertainties and unknown time delays both cases of finite and infinite horizon filtering are studied it has been shown that the above robust h sub spl infin filtering problem can be solved in terms of differential riccati inequalities with finite discrete jumps

sampled data output feedback control based on a new event triggered control scheme abstract in this paper a new event triggered control etc scheme is proposed to investigate the observer based output feedback control problems to reduce the usage of communication resources the control input is designed as a specific time varying signal between two consecutive event triggering instants which is different from the general etc methods for the continuous time event detection case it is shown that the obtained lower bound of the minimum inter event interval is not smaller than the one using the existing method in addition a novel discrete time event detection scheme and the corresponding etc policy based on the sampling output is proposed employing the stability analysis method for the time delay system a sufficient condition on the existence of an observer based controller is presented finally the simulation results are given to show that the proposed etc scheme is beneficial to further reduce the frequency of the communication between sensors and the control unit

a solvability condition of an extended control problem using riccati inequalities in this paper we consider an h infinity problem using unstable weighting functions such weights are used to achieve asymptoticaly disturbance at enuation and or asymptotically reference tracking and they cannot be handled by the standard h infinity control theory for this problem we present a necessary and sufficient condition to exist a solution using riccati inequalities this condition is derived under no unnecessary assumption to enlarge the applicability to various control problems moreover introducing the assumption that the image of the zero vectors of g12 and g21 are unique we obtain a lmi condition in order to check the solvability numerically a numerical example is presented to demonstrate how to calculate a controller

proposed experimental tests of the bell kochen specker theorem for a two particle two state system sets of compatible propositions exist for which quantum mechanics and noncontextual hidden variable theories make conflicting predictions for every individual system whatever its quantum state this permits a simple all or nothing state independent experimental verification of the bell kochen specker theorem

event triggered h stabilization for networked stochastic systems with multiplicative noise and network induced delays this paper is concerned with event triggered h stabilization in the mean square sense for networked stochastic system with multiplicative noise and network induced delays firstly a new discrete event triggered transmission protocol dettp is proposed to reduce the utilization rate of communication bandwidth the main features of the proposed protocol involve three aspects 1 it allows the presence of external disturbances and multiplicative noise 2 it is more general than some existing event triggered transmission schemes in the deterministic setting and 3 the minimum inter event time is implicity defined and is naturally given by the sampling period chosen for the plant secondly under the dettp a new closed loop stochastic networked control system model is established remarkably to facilitate theoretical analysis the resultant event based stochastic networked control system is further transformed into a system with two successive delay components in the state considering the effects of network induced delays multiplicative noise and dettp in a unified framework by using stochastic system theory sufficient conditions on the existence of the desired event based h state feedback controller are derived such that the resultant event based stochastic networked control system is exponentially stable in the mean square sense with a prescribed h performance while reducing the number of sampled state transmission along the feedback link as much as possible thirdly a co design algorithm for determining the parameters of the dettp and the state feedback controller gain matrix are also proposed finally two practical examples are given to illustrate the effectiveness and advantage of the proposed method over some existing results in the literature

exact computation of the infimum in h sub infinity optimization via output feedback the authors present a simple and noniterative procedure for the computation of the exact value of the infimum in the standard h sub infinity optimal control with output feedback the problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables the method is applicable to systems that satisfy the following conditions 1 the transfer function from the control input to the controlled output is right invertible and has no invariant zeros on the j omega axis and 2 the transfer function from the disturbance to the measurement output is left invertible and has no invariant zeros on the j omega axis

stronger two observer all versus nothing violation of local realism we introduce a two observer all versus nothing proof of bell s theorem which reduces the number of required quantum predictions from 9 a cabello phys rev lett 87 010403 2001 z b chen et al phys rev lett 90 160408 2003 to 4 provides a greater amount of evidence against local realism reduces the detection efficiency requirements for a conclusive experimental test of bell s theorem and leads to a bell inequality which resembles mermin s inequality for three observers n d mermin phys rev lett 65 1838 1990 but requires only two observers

event triggered non fragile control for linear systems with actuator saturation and disturbances abstract this paper investigates the problem of event triggered non fragile dynamic output feedback controller design for linear systems with actuator saturation and disturbances the controller to be designed is supposed to include additive gain variations by using lyapunov stability theory and adding slack matrix variables new sufficient conditions are derived to design the event triggered parameters and the controller gains compared with the existing non fragile dynamic output feedback controller design methods the structural restriction on the lyapunov matrix is relaxed the effectiveness of the proposed method is demonstrated by two examples

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

two simple proofs of the kochen specker theorem a new proof of the kochen specker theorem uses 33 rays instead of 117 in the original proof if the number of dimensions is increased from 3 to 4 only 24 rays are needed

the singular h 2 control problem in this paper we discuss the standard h2 control problem for linear finite dimensional time invariant systems without any assumptions on the system parameters we give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained

the finite horizon singular h control problem with dynamic measurement feedback this paper is concerned with the finite horizon version of the h problem with measurement feedback given a finite dimensional linear time varying system together with a positive real number we obtain necessary and sufficient conditions for the existence of a possibly time varying dynamic compensator such that the l2 0 t1 induced norm of the closed loop operator is smaller than these conditions are expressed in terms of a pair of quadratic differential inequalities generalizing the well known riccati differential equations introduced recently in the context of finite horizon h control

entropic tests of multipartite nonlocality and state independent contextuality we introduce a multipartite extension of an information theoretic distance introduced by zurek nature london 341 119 1989 we use it to develop a new tool for studying quantum correlations from an information theoretic perspective in particular we derive entropic tests of multipartite nonlocality for three qubits and for an arbitrary even number of qubits as well as a test of state independent contextuality in addition we rederive the tripartite mermin inequality and a state independent noncontextuality inequality by cabello phys rev lett 101 210401 2008 this suggests that the information theoretic distance approach to multipartite nonlocality and state independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions

perfect commuting operator strategies for linear system games linear system games are a generalization of mermin s magic square game introduced by cleve and mittal they show that perfect strategies for linear system games in the tensor product model of entanglement correspond to finite dimensional operator solutions of a certain set of non commutative equations we investigate linear system games in the commuting operator model of entanglement where alice and bob s measurement operators act on a joint hilbert space and alice s operators must commute with bob s operators we show that perfect strategies in this model correspond to possibly infinite dimensional operator solutions of the non commutative equations the proof is based around a finitely presented group associated with the linear system which arises from the non commutative equations

connes embedding problem and tsirelson s problem we show that tsirelson s problem concerning the set of quantum correlations and connes embedding problem on finite approximations in von neumann algebras known to be equivalent to kirchberg s qwep conjecture are essentially equivalent specifically tsirelson s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting c algebras connes embedding problem asks whether any separable ii1 factor is a subfactor of the ultrapower of the hyperfinite ii1 factor we show that an affirmative answer to connes question implies a positive answer to tsirelson s conversely a positive answer to a matrix valued version of tsirelson s problem implies a positive one to connes problem

j j lossless factorization for descriptor systems abstract the j j lossless factorization for descriptor systems based on the theory of conjugation is studied the result on j j lossless factorization for proper functions are extended to descriptor systems and those on j lossless factorization for square matrices are extended to nonsquare cases since j j lossless factorization contains both the inner outer factorization and the wiener hopf spectral factorization as special cases and the descriptor system contains the state space system asa special case the results obtained here unify the previous results on factorization problems also j j lossless factorization can be used to solve 4 block h control problems with j axis zeros

brief paper robust sampled data h control with stochastic sampling in this paper the problem of robust h control is investigated for sampled data systems with probabilistic sampling the parameter uncertainties are time varying norm bounded and appear in both the state and input matrices for the simplicity of technical development only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy bernoulli distribution which can be further extended to the case with multiple stochastic sampling periods by applying an input delay approach the probabilistic sampling system is transformed into a continuous time delay system with stochastic parameters in the system matrices by linear matrix inequality lmi approach sufficient conditions are obtained which guarantee the robust mean square exponential stability of the system with an h performance moreover an h controller design procedure is then proposed an illustrative example is included to demonstrate the effectiveness of the proposed techniques

nonlinear h almost disturbance decoupling the l2 gain almost disturbance decoupling problem for siso nonlinear systems is formulated sufficient conditions are identified for the existence of a parametrized state feedback controller such that the l2 gain from disturbances to output can be made arbitrarily small by increasing its gain the controller is explicity constructed using a lyapunov based recursive scheme sufficient conditions for the solvability of the h almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems

the strict dissipativity synthesis problem and the rank of the coupling qdf the problem of existence of a controlled behavior that is strictly dissipative with respect to a quadratic supply rate is studied the relation between strictness and the rank of a suitable coupling condition that combines the dissipativity properties of the hidden behavior and the orthogonal complement of the plant behavior is analyzed

hedging bets with correlated quantum strategies this paper studies the potential advantages of correlated answers in hypothetical tests of a simple interactive type in these tests an individual is presented with a question to which he or she must respond with an answer leading to an outcome of pass or fail in quantum information theoretic variants of these tests we show it is possible for an individual to correlate their answers across multiple tests in a way that produces a striking non classical behaviour specifically there exist tests for which no strategy can lead to the outcome pass with certainty but where answers to multiple independently administered tests can be correlated so that at least one test is passed with certainty this phenomenon which gives rise to a perfect form of hedging when considered in a game theoretic setting is quantum in nature it is not possible in classical variants of the tests we consider

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

j factorizations of a general discrete time system abstract the problems of extending the j lossless conjugation the j j spectral factorization and the j j lossless factorization to a completely general discrete time system are considered existence conditions together with a numerically sound prototype algorithm for computing the factors are provided for a system having any type of singularity including arbitrary normal rank poles and zeros at infinity at zero or on the unit circle

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

bell kochen specker theorem for any finite dimension the bell kochen specker theorem against non contextual hidden variables can be proved by constructing a finite set of totally non colourable directions as kochen and specker did in a hilbert space of dimension n 3 we generalize kochen and specker s set to hilbert spaces of any finite dimension in a three step process that shows the relationship between different kinds of proofs continuum probabilistic state specific and state independent of the bell kochen specker theorem at the same time this construction of a totally non colourable set of directions in any dimension explicitly solves the question raised by zimba and penrose about the existence of such a set for n 5

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

quadratic controllability strong controllability and a related output feedback property quadratic controllability and strong controllability are the two system properties to be discussed for a special class of norm bounded uncertain linear systems the main contribution of this paper is twofold first we show that it is possible to reduce the problem of checking quadratic controllability or strong controllability of a given uncertain system to the same problem for a reduced order subsystem which we call the essential subsystem then we use this result to examine a related output feedback property specifically for a given uncertain system we will answer the following question what condition is necessary and sufficient for the existence of a dynamic output feedback controller such that the states of the closed loop system converge to the origin with an arbitrarily fast rate our aim is to provide an insight and better understanding of uncertain systems through these results

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

estimating quantum chromatic numbers abstract we develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors we prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an sdp algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it we introduce the tracial rank of a graph a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank and prove that it is multiplicative we describe the tracial rank the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number the quantum chromatic number and the classical chromatic number respectively finally we present a new sdp algorithm that yields a parameter larger than the lovasz number and is yet a lower bound for the tracial rank of the graph we determine the precise value of the tracial rank of an odd cycle

h_ infty observer design for fuzzy system with immeasurable state variables via a new lyapunov function this paper is concerned with the design of h infty observers for fuzzy system with immeasurable state variables via a new lyapunov function by decomposing the space of premise variables into crisp regions and fuzzy regions piecewise fuzzy h infty observers are established at different instants to cope with the challenges caused by the mismatch of the premise variables and exogenous disturbances based on the proposed new lyapunov functions that depend on the different regions where the premise variables are located sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the stability and desired performance of the error systems finally a simulation example is provided to show that the new design technology proposed in this paper achieves better h infty performance than the existing design methods

the singular control problem with dynamic measurement feedback this paper is concerned with the h infty problem with measurement feedback the problem is to find a dynamic feedback from the measured output to the control input such that the closed loop system has an h infty norm strictly less than some a priori given bound gamma and such that the closed loop system is internally stable necessary and sufficient conditions are given under which such a feedback exists the only assumption that must be made is that there are no invariant zeros on the imaginary axis for two subsystems contrary to recent publications no assumptions are made on the direct feedthrough matrices of the plant it turns out that this problem can be reduced to an almost disturbance decoupling problem with measurement feedback and internal stability i e the problem in which we can make the h infty norm arbitrarily small

necessary conditions for extended noncontextuality in general sets of random variables in this paper we explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by kujala et al phys rev lett 115 150401 2015 using graph theoretical terms this extended definition avoids the assumption of the pre sheaf or non disturbance condition which states that if two contexts overlap then the marginal distribution obtained for the intersection must be the same a restriction that will never be perfectly satisfied in real experiments with this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non disturbance condition is satisfied

geometry of uncertainty relations for linear combinations of position and momentum for a quantum particle with a single degree of freedom we derive preparational sum and product uncertainty relations satisfied by n linear combinations of position and momentum observables the state independent bounds depend on their degree of incompatibility defined by the area of a parallelogram in an n dimensional coefficient space maximal incompatibility occurs if the observables give rise to regular polygons in phase space we also conjecture a hirschman type uncertainty relation for n observables linear in position and momentum generalizing the original relation which lower bounds the sum of the position and momentum shannon entropies of the particle

constraints on quantum hidden variables and the bohm theory the no hidden variables arguments of mermin and peres 1990 are assessed in the light of the bohm formulation of quantum theory

state independent proof of kochen specker theorem with 13 rays quantum contextuality as proved by kochen and specker and also by bell should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified however for the simplest system capable of exhibiting contextuality a qutrit the quantum contextuality is verified only state dependently in experiment because too many at least 31 observables are involved in all the known state independent tests here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states thus our inequality facilitates a state independent test of the quantum contextuality for an indivisible quantum system we also provide a record breaking state independent proof of the kochen specker theorem with 13 directions determined by 26 points on the surface of a magic cube

riccati equation approach to maximizing the complex stability radius by state feedback in this paper we study the problem of maximizing the complex stability radius of a linear time invariant state space system by linear state feedback we show that the supreme achievable stability radius can be characterized via parametrized riccati equations the dependency on the parameters is examined and the limiting behaviour described finally the relationship between the supremum of the achievable stability radii and the distance of a system from non stabilizabilky is investigated

h control problem with jω axis zeros abstract in this paper we discuss the so called one block h control problem in the case where the plant has j axis including infinity poles and zeros first we derive a necessary and sufficient condition for the h model matching problem to have a solution in the transfer function setting second we give a solvability condition which enables us to check the solvability by i examining matrix norm conditions related to j axis zeros and ii solving two generalized riccati equations finally we extend our result to the standard h problem

the veldkamp space of multiple qubits we introduce a point line incidence geometry in which the commutation relations of the real pauli group of multiple qubits are fully encoded its points are pairs of pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two up to sign we study the properties of its veldkamp space enabling us to identify subsets of operators which are distinguished from the geometric point of view these are geometric hyperplanes and pairwise intersections among the geometric hyperplanes one can find the set of self dual operators with respect to the wootters spin flip operation well known from studies concerning multiqubit entanglement measures in the two and three qubit cases a class of hyperplanes gives rise to mermin squares and other generalized quadrangles in the three qubit case the hyperplane with points corresponding to the 27 wootters self dual operators is just the underlying geometry of the e6 6 symmetric entropy formula describing black holes and strings in five dimensions

a complete and simple parametrization of controllers for a nonstandard h control problem abstract a complete and simple parametrization of all h controllers is derived for a class of nonstandard h control problems with d 12 and d 21 being of full row and column ranks respectively by making use of the youla parametrization and standard h control theory

self triggering under state independent disturbances this note extends the prior work in l2 stability of self triggered feedback systems where the next task release time and finishing time are predicted based on the sampled states a self triggering scheme is proposed which relaxes the assumption in the prior work that the magnitude of the process noise is bounded by a linear function of the norm of the system state we show that the sample periods generated by this scheme are always greater than a positive constant we also provide state based deadlines for delays and propose a way that may enlarge those deadlines without breaking l2 stability

reduced order controllers for continuous and discrete time singular h control problems based on lmi this paper describes a method for constructing a petri net controller for a discrete event system modeled by a petri net the controller consists only of places and arcs and is computed based on the concept of petri net place invariants the size of the controller is proportional to the number of constraints that must be satisfied this method is computationally efficient and can accommodate constraints written as boolean logic formulas in the conjunctive normal form or algebraic inequalities that contain elements of the marking and or the firing vectors

the singular minimum entropy h control problem abstract in this paper we search for controllers which minimize an entropy function of the closed loop transfer matrix under the constraint of internal stability and under the constraint that the closed loop transfer matrix has h norm less than some a priori given bound we find an explicit expression for the infimum moreover we give a characterization when the infimum is attained contrary to the regular case for the singular minimum entropy h control problem the infimum is not always attained

a polynomial solution to the scalar 4 block h general distance problem the h mixed sensitivity with measurement noise problem is considered for the scalar case using a polynomial description the problem results in a 4 block general distance scalar problem which is solved in a general way by using a polynomial equation approach as an example the solution is then applied to the mixed sensitivity with measurement noise problem where all relevant simplifications are carried out the solution requires solving two spectral factorization problems and one linear polynomial equation further new insight into the connections with the nehari problem is provided

event triggered integral sliding mode control for uncertain fuzzy systems abstract an event triggered integral sliding mode controller design problem for uncertain t s fuzzy systems is investigated in this paper a novel triggering condition with the time varying threshold is proposed in which the system state error and the sliding variable error are considered simultaneously the system state error with the time varying threshold is included in the triggering condition thus the system trajectory is guaranteed to converge to a bounded region the sliding variable error is added in the triggering condition to remove the assumption that the inter execution time has a uniform upper bound then a sufficient condition of the ultimate boundedness for sliding motion is established and the controller gain can be obtained via solving the linear matrix inequality moreover the zeno phenomenon can be avoided by the proposed triggering condition and sliding mode controller finally the effectiveness of obtained theoretical results is illustrated by two numerical examples

nonlocal games and quantum permutation groups we present a strong connection between quantum information and quantum permutation groups specifically we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups and then show that this is equivalent to the previously defined notion of quantum isomorphism corresponding to perfect quantum strategies to the isomorphism game moreover we show that two connected graphs x and y are quantum isomorphic if and only if there exists x v x and y v y that are in the same orbit of the quantum automorphism group of the disjoint union of x and y this connection links quantum groups to the more concrete notion of nonlocal games and physically observable quantum behaviours we exploit this link by using ideas and results from quantum information in order to prove new results about quantum automorphism groups and about quantum permutation groups more generally in particular we show that asymptotically almost surely all graphs have trivial quantum automorphism group furthermore we use examples of quantum isomorphic graphs from previous work to construct an infinite family of graphs which are quantum vertex transitive but fail to be vertex transitive answering a question from the quantum group literature our main tool for proving these results is the introduction of orbits and orbitals orbits on ordered pairs of quantum permutation groups we show that the orbitals of a quantum permutation group form a coherent configuration algebra a notion from the field of algebraic graph theory we then prove that the elements of this quantum orbital algebra are exactly the matrices that commute with the magic unitary defining the quantum group we furthermore show that quantum isomorphic graphs admit an isomorphism of their quantum orbital algebras which maps the adjacency matrix of one graph to that of the other

the discrete time h sub spl infin control problem with strictly proper measurement feedback this paper is concerned with the discrete time h sub spl infin control problem with strictly proper measurement feedback we derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given h sub spl infin norm bound note that contrary to the continuous time in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator finally we give an explicit formula for one controller which achieves this bound

application of facial reduction to h state feedback control problem one often encounters numerical difficulties in solving linear matrix inequality lmi problems obtained from h control problems for semidefinite programming sdp relaxations for combinatorial p

synthesis of dissipative systems using quadratic differential forms part ii the problem discussed is that of designing a controller for a linear system that renders a quadratic functional nonnegative our formulation and solution of this problem is completely representation free the system dynamics are specified by a differential behavior and the performance is specified through a quadratic differential form we view control as interconnection a controller constrains a distinguished set of system variables the control variables the resulting behavior of the to be controlled variables is called the controlled behavior the constraint that the controller acts through the control variables only can be succinctly expressed by requiring that the controlled behavior should be wedged in between the hidden behavior obtained by setting the control variables equal to zero and the plant behavior obtained by leaving the control variables unconstrained the main result is a set of necessary and sufficient conditions for the existence of a controlled behavior that meets the performance specifications the essential requirement is a coupling condition an inequality that combines the storage functions of the hidden behavior and the orthogonal complement of the plant behavior

luenberger observer based h sub spl infin compensator design for nonstandard problems this paper presents luenberger observer based h sub spl infin compensator design methods for different nonstandard cases these design methods are developed based on the bounded real lemma and the resultant design algorithms are two riccati inequalities which are not mutually coupled

the morita theory of quantum graph isomorphisms we classify instances of quantum pseudo telepathy in the graph isomorphism game exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups specifically we show that graphs quantum isomorphic to a given graph are in bijective correspondence with morita equivalence classes of certain frobenius algebras in the category of finite dimensional representations of the quantum automorphism algebra of that graph we show that such a frobenius algebra may be constructed from a central type subgroup of the classical automorphism group whose action on the graph has coisotropic vertex stabilisers in particular if the original graph has no quantum symmetries quantum isomorphic graphs are classified by such subgroups we show that all quantum isomorphic graph pairs corresponding to a well known family of binary constraint systems arise from this group theoretical construction we use our classification to show that of the small order vertex transitive graphs with no quantum symmetry none is quantum isomorphic to a non isomorphic graph we show that this is in fact asymptotically almost surely true of all graphs

optimal classical simulation of state independent quantum contextuality simulating quantum contextuality with classical systems requires memory a fundamental yet open question is what is the minimum memory needed and therefore the precise sense in which quantum systems outperform classical ones here we make rigorous the notion of classically simulating quantum state independent contextuality qsic in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite qsic set we obtain the minimum memory needed to simulate arbitrary qsic sets via classical systems under the assumption that the simulation should not contain any oracular information in particular we show that while classically simulating two qubits tested with the peres mermin set requires log 2 24 4 585 bits simulating a single qutrit tested with the yu oh set requires at least 5 740 bits

non standard h control problem a generalized chain scattering representation approach the non standard h x control problem is the case where the direct feedthroughs from the input to the error and from the exogenous signal to the output are not necessarily of full rank in this paper this problem is reformulated based on the generalized chain scattering representation gcsr the gcsr approach leads naturally to a generalization of the homographic transformation the state space realization for this generalized homographic transformation and a number of fundamental cascade structures of the h x control systems are further studied in a unified framework of gcsr certain sufficient conditions for the solvability of the non standard h x control problem are therefore established via a j j lossless factorization of gcsr these results present extensions to kimura s results on the chain scattering representation csr approach to the h x control in the standard case