discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

localization and diagonalization a review of functional integral techniques for low dimensional gauge theories and topological field theories localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low dimensional gauge theories are reviewed these are the functional integral counterparts of the mathai quillen formalism the duistermaat heckman theorem and the weyl integral formula respectively in each case the necessary mathematical background euler classes of vector bundles equivariant cohomology topology of lie groups is introduced and the finite dimensional integration formulae described then some applications to path integrals are discussed and an overview of the relevant literature is given the applications include supersymmetric quantum mechanics cohomological field theories phase space path integrals and two dimensional yang mills theory

approaches to t s fuzzy affine model based reliable output feedback control for nonlinear ito stochastic systems this paper deals with the problem of reliable and robust mathscr h infty static output feedback sof controller synthesis for continuous time nonlinear stochastic systems with actuator faults the nonlinear stochastic plant is expressed by an ito type takagi sugeno fuzzy affine model with parametric uncertainties and a markov process is employed to model the occurrence of actuator fault the purpose is to design an admissible piecewise sof controller such that the resulting closed loop system is stochastically stable with a prescribed disturbance attenuation level in an mathscr h infty sense specifically based on a markovian lyapunov function combined with ito differential formula s procedure and some matrix inequality convexification procedures two new approaches to the reliable sof controller analysis and synthesis are proposed for the underlying stochastic fuzzy affine systems it is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities finally simulation examples are presented to illustrate the effectiveness and advantages of the developed methods

a convex programming approach to h2 control of discrete time markovian jump linear systems in this paper we consider the h control problem for the class of discrete time 2 linear systems with parameters subject to markovian jumps using a convex programming approach we generalize the definition of the h norm from the deter2 ministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established the main contribution of the paper is to provide a convex programming formulation to the h control problem so that several 2 important cases to our knowledge not analysed in previous work can be addressed regarding the transition matrix p for the markov chain two ij situations are considered the case in which it is exactly known and the case in which it is not exactly known but belongs to an appropriated convex set regarding the state variable and the jump variable the cases in which t

the semiclassical limit of the two dimensional quantum yang mills model the semiclassical limit of the quantum yang mills partition function on a compact oriented surface is related to the symplectic volume of the moduli space of flat connections by using an explicit expression for the symplectic form this gives an independent proof of some recent results of witten and forman

some rigorous results for yang mills theories on a cylinder using an approach based on the canonical formalism the yang mills theories on a cylinder are rigorously analyzed in this way the moduli space a g can be explicitly described with a being the space of connections and g the group of gauge transformations in particular a g0 g0 being the group of the pointed gauge transformations is diffeomorphic to the structure group of the theory g whereas a g is g modulo the group of inner automorphisms it is also proven that a g is a principal fiber bundle with structure group g0

control design for fuzzy systems based on relaxed nonquadratic stability and h_ infty performance conditions in this paper new approaches to hinfin controller design for a class of discrete time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis dependent lyapunov functions are used first two relaxed conditions of nonquadratic stability with h infin norm bound are presented for this class of systems the two relaxed conditions are shown to be useful in designing fuzzy control systems by introducing some additional instrumental matrix variables the two relaxed conditions are used to develop hinfin controllers in the control design the first relaxed condition has fewer inequality constraints but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables finally two examples are given to demonstrate the applicability of the proposed approach

stability and stabilization of a class of fuzzy time delay descriptor systems this paper studies a class of fuzzy time delay descriptor systems in the extended takagi sugeno t s fuzzy model sufficient conditions are derived for the stability and stabilization in terms of linear matrix inequalities lmis illustrative examples are given to show the effectiveness and the advantages of the present results

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

mixed h 2 h control for discrete time systems via convex optimization abstract a mixed h 2 h control problem for discrete time systems is considered where an upper bound on the h 2 norm of a closed loop transfer matrix is minimized subject to an h constraint on another closed loop transfer matrix both state feedback and output feedback cases are considered it is shown that these problems are equivalent to finite dimensional convex programming problems in the state feedback case nearly optimal controllers can be chosen to be static gains in the output feedback case nearly optimal controllers can be chosen to have a structure similar to that of the central single objective h controller in particular the state dimension of nearly optimal output feedback controllers need not exceed the plant dimension

stabilization of discrete time markovian jump linear systems via time delayed controllers this paper is concerned with the stabilization problem for a class of discrete time markovian jump linear systems with time delays both in the system state and in the mode signal the delay in the system state may be time varying the delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system we first show that the resulting closed loop system is a time varying delayed markovian jump linear system with extended state space then a sufficient condition is proposed for the design of a controller such that the closed loop system is stochastically stable finally numerical simulation is used to illustrate the developed theory

robust jump linear quadratic control a mode stabilizing solution this correspondence is concerned with optimal feedback control of a class of linear stochastic systems for a quadratic performance index the solution to this problem is known but the resulting optimal regulator does not ensure stability in every mode of operation to improve robustness a new mode stabilizing solution is defined an example illustrates the advantages of the proposed controller

an asynchronous operation approach to event triggered control for fuzzy markovian jump systems with general switching policies this paper investigates the problem of event triggered control for a class of fuzzy markov jump systems with general switching policies a novel event triggered scheme is proposed to improve the transmission efficiency at each sampling instance each transition rate allows to be unknown known or only its uncertain domains value is known with the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller sufficient conditions for the resulting fuzzy markovian jump systems are established in terms of coupled linear matrix inequalities finally an example is given to illustrate the validity of the developed technique

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

yang mills measure and the master field on the sphere we study the yang mills measure on the sphere with unitary structure group in the limit where the structure group has high dimension we show that the traces of loop holonomies converge in probability to a deterministic limit which is known as the master field on the sphere the values of the master field on simple loops are expressed in terms of the solution of a variational problem we show that given its values on simple loops the master field is characterized on all loops of finite length by a system of differential equations known as the makeenko migdal equations we obtain a number of further properties of the master field on specializing to families of simple loops our results identify the high dimensional limit in non commutative distribution of the brownian bridge in the group of unitary matrices starting and ending at the identity

robust stabilization for uncertain markovian jump fuzzy systems based on free weighting matrix method this paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain markovian jump nonlinear systems the class of systems under consideration is represented by the t s fuzzy model with partly known transition probability matrix the free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain markovian jump fuzzy systems mjfss in terms of linear matrix inequalities lmis furthermore a sufficient condition for the mode dependent state feedback fuzzy controller is derived for the mjfss for all admissible parameter uncertainties finally a simulation example is provided to illustrate the effectiveness of the proposed methodology

optimal quadratic control of jump linear systems with separately controlled transition probabilities abstract the optimal control of discrete time jump systems that would be linear but for randomly jumping parameters are considered these parameter jumps which are indexed by a finite state form process can be used to model systems subject to component failures or structural changes the control of such systems when the jump probabilities can be controlled by choice of a finite valued input is considered this input form control can be thought of as corresponding to a maintenance or repair policy the optimal control problem with quadratic costs whose weighting matrices depend on the jumping parameters and form control is formulated for such systems the optimal solution for finite and infinite time horizon problems is developed in addition sufficient conditions for the existence of a steady state stabilizing solution to the infinite time problem are given in terms of appropriately defined controllability and observability properties

a quantum group version of quantum gauge theories in two dimensions for the special case of the quantum group slq 2 c q exp pi i r r or 3 the authors present an alternative approach to quantum gauge theories in two dimensions they exhibit the similarities to witten s combinatorial approach which is based on the ideas of migdal 1970 the main ingredient is the turaev viro combinatorial construction of topological invariants of closed compact 3 manifolds and its extension to arbitrary compact 3 manifolds as given by the authors in collaboration with w muller 1992

a convex approach to the mixed cal h _ 2 cal h _ infty control problem for discrete time uncertain systems this paper considers cal h 2 cal h infty control problems involving discrete time uncertain linear systems the uncertain domain is supposed to be convex bounded which naturally covers as a particular case the important class of interval matrices the cal h infty guaranteed cost control problem solved for this class of uncertain systems under no matching conditions can be stated as follows determine a state feedback gain if one exists such that the hi norm of a given transfer function remains bounded by a prespecified level for all possible models in the same context problems on the determination of the smallest cal h infty upper bound and the minimization of an cal h 2 cost upper bound subject to cal h infty constraints are also addressed the results follow from the fact that those problems are convex in the particular parametric space under consideration some examples illustrate the theory

robust observer design for ito stochastic time delay systems via sliding mode control this paper deals with the output feedback sliding mode control for ito stochastic time delay systems the system states are unmeasured and the uncertainties are unmatched a sliding mode control scheme is proposed based on the state estimates by utilizing a novel switching function the derivative of the switching function is ensured to be finite variation it is shown that the sliding mode in the estimation space can be attained in finite time the sufficient condition for the asymptotic stability in probability of the overall closed loop stochastic system is derived finally a simulation example is shown to illustrate the proposed method

functional integration on spaces of connections suppose thatgis a compact connected lie group andp mis a smooth principalg bundle we define a cylinder function on the space a of smooth connections onpto be a continuous complex function of the holonomies along finitely many piecewise smoothly immersed curves inm completing the algebra of cylinder functions in the sup norm we obtain a commutative c algebra fun a let a generalized measure on a be a bounded linear functional on fun a we construct a generalized measure 0on a that is invariant under all automorphisms of the bundlep not necessarily fixing the basem this result extends previous work which assumedmwas real analytic and used only piecewise analytic curves in the definition of cylinder functions as before any graph withnedges embedded inmdetermines a c subalgebra of fun a isomorphic toc gn and the generalized measure 0 fun a c restricts to the linear functional onc gn given by integration against normalized haar measure ongn our result implies that the group g of gauge transformations acts as unitary operators onl2 a the hilbert space completion of fun a in the norm f 2 0 f 2 1 2 using spin networks we construct explicit functions spanning the subspacel2 a g l2 a consisting of vectors invariant under the action of g

difference bodies in complex vector spaces abstract a complete classification is obtained of continuous translation invariant minkowski valuations on an m dimensional complex vector space which are covariant under the complex special linear group

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

state feedback control of continuous time t s fuzzy systems via switched fuzzy controllers this paper studies the problem of state feedback control of continuous time t s fuzzy systems switched fuzzy controllers are exploited in the control design which are switched based on the values of membership functions and the control scheme is an extension of the parallel distributed compensation pdc scheme sufficient conditions for designing switched state feedback controllers are obtained with meeting an h norm bound requirement and quadratic d stability constraints it is shown that the new control design method provides less conservative results than the corresponding ones via the parallel distributed compensation pdc scheme a numerical example is given to illustrate the effectiveness of the proposed method

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

path integrals supersymmetric quantum mechanics and the atiyah singer index theorem for twisted dirac feynman s time slicing construction approximates the path integral by a product determined by a partition of a finite time interval of approximate propagators this paper formulates general conditions to impose on a short time approximation to the propagator in a general class of imaginary time quantum mechanics on a riemannian manifold which ensure that these products converge the limit defines a path integral which agrees pointwise with the heat kernel for a generalized laplacian the result is a rigorous construction of the propagator for supersymmetric quantum mechanics with potential as a path integral further the class of laplacians includes the square of the twisted dirac operator which corresponds to an extension of n 1 2 supersymmetric quantum mechanics general results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the atiyah singer index theorem

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

technical communique metrics of performance for discrete time descriptor jump linear systems analytical tools to measure the performance of a control system described by a discrete time descriptor jump linear system are given specifically a closed form expression for the steady state output power as well as a bound for the performance index related to the h control problem are given the analysis is made by introducing new operators to handle the singularity of the system

filtering based robust fault detection of fuzzy jump systems this paper studies the robust fault detection filter rfdf design problems for uncertain nonlinear markov jump systems with state delays and parameter uncertainties by means of takagi sugeno fuzzy models the dynamics of filtering error generator and the fuzzy rfdf system are constructed with the aid of the selected weighting matrix function the design objective is to find an optimal rfdf which results in a minimal difference between the reference model ideal solution and the rfdf real solution to be designed a sufficient condition is firstly established on the stochastic stability by using stochastic lyapunov krasovskii functional approach then in terms of linear matrix inequalities techniques sufficient conditions on the existence of fuzzy rfdf are presented and proved finally the design problem is formulated as an optimization algorithm simulation results illustrate that the proposed rfdf can detect the faults shortly after the occurrences

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

improved fuzzy control design for nonlinear markovian jump systems with incomplete transition descriptions this paper addresses the state feedback control of nonlinear continuous time markovian jump systems the nonlinearity is represented by takagi sugeno fuzzy models and the transition probability matrix is assumed to be partly known some elements in the matrix are known some are unknown but with known lower and upper bounds and some are completely unknown by making full use of the continuous property of the transition probability matrix new sufficient conditions for the stochastic stability of the system are obtained in terms of linear matrix inequalities we show that the conditions given are less conservative than or at least the same as those for existing results moreover using the conditions obtained we establish a method for design of a h state feedback controller numerical examples illustrate the effectiveness of the proposed method

sewing yang mills measures and moduli spaces over compact surfaces consider a closed surface obtained by pasting two surfaces 1and 2along some of their boundary components a formula is derived expressing quantum yang mills functional integrals for in terms of the corresponding integrals for the surfaces i using this a formula is derived which expresses the symplectic volume measure on the moduli space of flatsu 2 connections over a closed riemann surface in terms of the corresponding volume measures for the surfaces 1and 2 when the latter have one boundary component each

a bounded real lemma for jump systems this note presents a bounded real lemma for discrete time markovian jump linear systems mjlss we show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems for the case of one plant mode this condition reduces to the standard necessary and sufficient condition for discrete time systems we envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for mjlss

a new look at the robust control of discrete time markov jump linear systems abstractin this paper we make a foray in the role played by a set of four operators on the study of robust h2 and mixed h2 h control problems for discrete time markov jump linear systems these operators appear in the study of mean square stability for this class of systems by means of new linear matrix inequality lmi characterisations of controllers which include slack variables that to some extent separate the robustness and performance objectives we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of h2 performance since each operator provides a different degree of conservatism the results are unified in the form of an iterative lmi technique for designing robust h2 controllers whose convergence is attained in a finite number of steps the method yields a new way of computing mixed h2 h controllers whose conservatism decreases with iteration two numerical examples illustrate the applicability

robust output feedback stabilization for uncertain discrete time fuzzy markovian jump systems with time varying delays this paper provides a delay dependent approach to the design of fuzzy dynamic output feedback controllers for uncertain discrete time fuzzy markovian jump systems with interval time varying delays first by a fuzzy basis dependent and mode dependent lyapunov functional a stochastic stability condition is derived by using the finsler s lemma second in terms of linear matrix inequalities lmis a delay dependent sufficient condition is presented under which there exists a fuzzy output feedback controller such that the resulting closed loop system is robustly stochastically stable a desired controller can be constructed when these lmis are feasible finally the effectiveness of the proposed design method is demonstrated by a simulation example

on the influence of noise on jump linear systems jump linear systems are considered in a random environment where they are subject to additive and multiplicative noises stochastic notions of stabilizability and detectability are introduced to characterize the asymptotic behavior of the optimal jump linear quadratic gaussian regulator and a dual kalman filter

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

quantum yang mills on a riemann surface we obtain the quantum expectations of gauge invariant functions of the connection on ag su n product bundle over a riemann surface of genusg we show that the spacea g m of connections modulo those gauge transformations which are the identity at one point is itself a principal bundle with affine linear fiber the base space path2gg consists of 2g tuples of paths ing subject to a relation on their endpoint values quantum expectations are iterated path integrals over first the fiber then over path2gg each with respect to the push forward toa g m of the measuree s a da here s a denotes the yang mills action ona we exhibit a global section ofa g m to define a choice of origin in each fiber relative to which the measure on the fiber is gaussian the induced measure on path2gg is the product of wiener measures on the component paths conditioned to preserve the endopoint relation conformal transformations of the metric onm act by reparametrizing these paths we explicitly compute the partition function in the general case and the expectations of functions of certain products of wilson loops in the caseg 1

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

quantum yang mills on the two sphere we obtain the quantum expectations of gauge invariant functions of the connection on a principalg su n bundle overs 2 we show that the spacea g m of connections modulo gauge transformations which are the identity at one point is itself a principal bundle over g based loops in the symmetry group the fiber ina g m is an affine linear space quantum expectations are iterated path integrals first over this fiber then over g each with respect to the push forward toa g m of the measure s s a da s a denotes the yang mills action ona there is a global section ofa g m on which the first integral is a gaussian the resulting measure on g is the conditional wiener measure we explicitly compute the expectations of a special class of wilson loops

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

energy in yang mills on a riemann surface sengupta s lower bound for the yang mills action on smooth connections on a bundle over a riemann surface generalizes to the space of connections whose action is finite in this larger space the inequality can always be saturated the yang mills critical sets correspond to critical sets of the energy action on a space of paths this may shed light on a conjecture of atiyah and bott concerning morse theory for a g

control synthesis of singularly perturbed fuzzy systems this paper considers the problem of designing stabilizing and hinfin controllers for nonlinear singularly perturbed systems described by takagi sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e for the synthesis problem of simultaneously designing the bound of e and stabilizing or hinfin controllers linear matrix inequalities lmi based methods are presented for evaluating the upper bound of e subject to stability or a prescribed hinfin performance bound constraint for the resulting closed loop system sufficient conditions are developed respectively for the stabilizing and hinfin control synthesis without the consideration of improving the bound of e new design methods are also given in terms of solutions to a set of lmis examples are given to illustrate the efficiency of the proposed methods

star valuations and dual mixed volumes since its creation by brunn and minkowski what has become known as the brunn minkowski theory has provided powerful machinery to solve a broad variety of inverse problems with stereological data the machinery of the brunn minkowski theory includes mixed volumes of minkowski symmetrization techniques such as those of steiner and blaschke isoperimetric inequalities such as the brunn minkowski minkowski and aleksandrov fenchel inequalities integral transforms such as the cosine transform and important auxiliary bodies associated with these transforms such as minkowski s projection bodies schneider s recent book 22 on the brunn minkowski theory is the best available introduction to the subject while the brunn minkowski theory has proven to be of enormous value in answering inverse questions regarding projections of convex bodies onto subspaces the theory has been of little value in answering inverse questions with data regarding intersections with subspaces however recent advancements have been made in the development of a dual brunn minkowski theory 3 4 5 6 8 9 11 13 16 23 26 27 28 29 which has been tailored specifically for dealing with such questions in contrast to the brunn minkowski theory in the dual theory convex bodies are replaced by star shaped sets and projections onto subspaces are replaced by intersections with subspaces the machinery of the dual theory includes dual mixed volumes introduced by lutwak 15 16 dual isoperimetric inequalities 16 and important auxiliary bodies known as intersection bodies first introduced by busemann for special centered convex bodies in 1 later defined for star shaped sets by lutwak 16 see also 9 a comprehensive introduction to geometric tomography including the dual brunn minkowski theory may be found in gardner s book 17 unfortunately there still remain fundamental and foundational problems with the dual brunn minkowski theory one of the most beautiful and article no 0048

robust fuzzy control for uncertain discrete time nonlinear markovian jump systems without mode observations this paper studies the robust fuzzy control problem of uncertain discrete time nonlinear markovian jump systems without mode observations the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with norm bounded parameter uncertainties and markovian jump parameters as a result an uncertain markovian jump fuzzy system mjfs is obtained a stochastic fuzzy lyapunov function flf is employed to analyze the robust stability of the uncertain mjfs which not only is dependent on the operation modes of the system but also directly includes the membership functions then based on this stochastic flf and a non parallel distributed compensation non pdc scheme a mode independent state feedback control design is developed to guarantee that the closed loop mjfs is stochastically stable for all admissible parameter uncertainties the proposed sufficient conditions for the robust stability and mode independent robust stabilization are formulated as a set of coupled linear matrix inequalities lmis which can be solved efficiently by using existing lmi optimization techniques finally it is also demonstrated via a simulation example that the proposed design method is effective

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

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

stabilization of uncertain fuzzy time delay systems via variable structure control approach in view of a recent new application of variable structure control vsc to the stabilization problem for takagi sugeno t s fuzzy models this paper aims to study the stabilization of uncertain fuzzy time delay systems in t s fuzzy model via vsc approach there are mainly two features in this paper one lies in the incorporation of time delays both smooth and nonsmooth delays in which case lyapunov functionals and razumikhin theorem are required to solve the stabilization problem the other feature is that not only matched uncertainties but also mismatched uncertainties in the state variables are considered as a sequence the contribution of this paper consists of various control schemes proposed for the vsc design and the present results are in terms of linear matrix inequalities lmis an illustrative example is given to show the effectiveness of our various results

worst case control of uncertain jumping systems with multi state and input delay information in this paper the problem of worst case also called h control for a class of uncertain systems with markovian jump parameters and multiple delays in the state and input is investigated the jumping parameters are modelled as a continuous time discrete state markov process and the parametric uncertainties are assumed to be real time varying and norm bounded that appear in the state input and delayed state matrices the time delay factors are unknowns and time varying with known bounds complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak delay dependent stochastic stability with a prescribed h performance the solutions are provided in terms of a finite set of coupled linear matrix inequalities lmis application of the developed theory to a typical example has been presented

stochastic stabilization of a class of nonhomogeneous markovian jump linear systems this paper deals with the problem of stochastic stability analysis and control synthesis of a class of markovian jump linear systems mjls with time varying transition probabilities tps in the discrete time domain the time varying character is considered to be in a polytopic sense the approach followed in this note is based on the use of a parameter dependent stochastic lyapunov function we give a stability condition in terms of a linear matrix inequality lmi feasibility problem the obtained results are illustrated in a numerical example

small volume limits of 2 d yang mills by examining the lattice gauge approximation we show that the small volume limit of the 2 dimensional yang mills functional integral is the natural symplectic measure on the moduli space of flat connections

robust h fuzzy control for uncertain nonlinear markovian jump systems with time varying delay this paper investigates the problem of robust h fuzzy control for a class of uncertain nonlinear markovian jump systems with time varying delay the class of systems under consideration is described by the takagi sugeno fuzzy model the goal of the paper is to design a mode dependent fuzzy state feedback controller such that the closed loop system is stochastically stable with a prescribed h performance of disturbance attenuation for all admissible parameter uncertainties in order to obtain a less conservative control design a new stochastic lyapunov krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals then by employing this functional a delay decomposition approach to the design of robust h fuzzy controllers is developed in terms of linear matrix inequalities finally two examples are given to illustrate the merit and usability of the proposed design method

even valuations on convex bodies the notion of eveil valuation is introduced as a natural generalization of volume on cornpact convex subsets of euclidean space a recent characterization theorem for volume leads in turn to a connection between even valuations on compact convex sets and continuous functions on grassmannians this connection can be described in part using generating distributions for symmetric compact convex sets we also explore some consequences of these characterization results in convex and integral geometry recent interest in volume as a valuation on compact conlvex sets stems from hilbert s third problem which is actually an ancient problem recast in modern terms hilbert asked if two polytopes p and q can be each cut into a finite number of pieces p pn and q qm with each pi congruent to qi by a rigid euclidean motion provided that p and q have the same volume 18 this question was answered in the negative by max dehn 2 4 29 who found a functionlal on polytopes that is invariant under dissections over rigid motions while varying in value among polytopes of equal volume in other words the dehn invariant is a simple rigid motion invariant valuation on polytopes that is not equal to volume under any normalization dehn s solution left open the question of exactly what conditions oil p and q imply equidissectability over the group of rigid motions although this problem was solved by hadwiger in the case where only translations and no rotations nor reflections are permitted see 2 16 17 26 29 in the course of studying this and related problems hadwiger discovered a characterization of euclidean volume as a continuous rigid motion invariant simple valuation on compact convex sets that is a continuous rigid motion invariant valuation that vanishes on convex sets of less than full dimension this result led in turn to a complete characterization of all continuous rigid motion inivariant valuations on compact convex sets in 1r as consisting of a real n 4 dimensional vector space spanned by the intrinsic volumes or quermassintegrals 16 also 20 21 31 since many standard functionals and integral operators can be interpreted as invariant valuations such as intrinsic volumes mean projections crofton and kinematic formulas what came to be known as hadwiger s chtracterization theorem proved to be a valuable tool for generating quick and effortless proofs of many formulas and equations in integral geometry unfortunately hadwiger s original proof was long and difficult 161 while seeking a shorter proof of hadwiger s volume characterization the author discovered received by the editors june 24 1996 and in revised form september 29 1997 1991 mathematics subject classification primary 52a22 52a38 52a39 52b45 research supported in part by nsf grants dms 9022140 to msri and dms 9626688 to the author 1999 american mathematical society 71 this content downloaded from 207 46 13 52 on mon 24 oct 2016 04 15 57 utc all use subject to http about jstor org terms

projection bodies in complex vector spaces the space of minkowski valuations on an m dimensional complex vector space which are continuous translation invariant and contravariant under the complex special linear group is explicitly described each valuation with these properties is shown to satisfy geometric inequalities of the brunn minkowski aleksandrov fenchel and minkowski type

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

robust finite time h control for uncertain discrete jump systems with time delay abstract this paper addresses the robust finite time h control problem for a family of uncertain discrete time markovian jump systems with time delay initially the concepts of stochastic finite time boundedness and stochastic h finite time stabilization are given then a stochastic finite time h controller is designed such that the underlying closed loop discrete jump time delay system is stochastic finite time boundedness and satisfies a prescribed h performance level in some given finite time interval based on lyapunov approach sufficient criteria on the stochastic h finite time stabilization are established for the solvability of the problem which can be handled by a feasibility problem in the form of linear matrix inequalities with a fixed parameter finally simulation examples are presented to demonstrate the validity of the developed techniques

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

optimal control of jump linear gaussian systems this paper investigates the problem of controlling a discrete time linear system with jump parameters a review of the literature is presented as well as a development of the application of dynamic programming to this class of control problems dynamic programming has been applied by many researchers and it was observed that no closed form analytical solution could be constructed because of the dual aspects of the controller the main contribution of the present work is an algorithm suitable for computer implementation for the optimal dual control the construction of the algorithm is based on transforming the dynamic programming relations into a space of sufficient statistics and using a finite dimensional optimization procedure to obtain the optimal control as a function of the statistics this is achieved by first developing a suitable recursive realization of a filter which generates the sufficient statistics for the problem and then embedding this filter into the dynamic programming equations

topological sectors and measures on moduli space in quantum yang mills on a riemann surface previous path integral treatments of yang mills on a riemann surface automatically sum over principal fiber bundles of all possible topological types in computing quantum expectations this paper extends the path integral formulation to treat separately each topological sector the formulation is sufficiently explicit to calculate wilson line expectations exactly further it suggests two new measures on the moduli space of flat connections one of which proves to agree with the small volume limit of the yang mills measure

finite time cluster synchronization of t s fuzzy complex networks with discontinuous subsystems and random coupling delays this paper is concerned with the cluster synchronization in finite time for a class of complex networks with nonlinear coupling strengths and probabilistic coupling delays the complex networks consist of several clusters of nonidentical discontinuous systems suffered from uncertain bounded external disturbance based on the takagi sugeno t s fuzzy interpolation approach we first obtain a set of t s fuzzy complex networks with constant coupling strengths by developing some novel lyapunov functionals and using the concept of filippov solution some new analytical techniques are established to derive sufficient conditions ensuring the cluster synchronization in a setting time in particular this paper extends the pinning control strategies for networks with continuous time dynamics to discontinuous networks numerical simulations demonstrate that the theoretical results are effective and the t s fuzzy approach is important for relaxed results

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

output feedback for a class of linear systems with stochastic jump parameters a class of linear systems subject to sudden jumps in parameter values is studied for a quadratic performance index the optimal controller has already been proposed it consists of a full state feedback that requires the synthesis of an observer for the plant state and mode to avoid this difficulty the present note develops new results that lead to the selection of the best feedback control law depending only on measurable outputs necessary optimality conditions are derived and two computationnal algorithms proposed an example is included

two dimensional quantum yang mills theory with corners the solution of quantum yang mills theory on arbitrary compact two manifolds is well known we bring this solution into a tqft like form and extend it to include corners our formulation is based on an axiomatic system that we hope is flexible enough to capture actual quantum field theories also in higher dimensions we motivate this axiomatic system from a formal schrodinger feynman quantization procedure we also discuss the physical meaning of unitarity the concept of vacuum partial wilson loops and non orientable surfaces

the leading term of the yang mills free energy abstract this article gives an explicit formula for the leading term of the free energy of three dimensional u n lattice gauge theory for any n as the lattice spacing tends to zero the proof is based on a novel technique that avoids phase cell renormalization the technique also yields a similar formula for the four dimensional theory but only in the weak coupling limit

discrete time coupled riccati equations for systems with markov switching parameters abstract this paper deals with a set of coupled riccati equations which arises in the study of filtering and quadratic optimal control of discrete time linear systems with markov switching parameters in this case the duality between the filtering and optimal control equations is not straightforward and a generalization of the concepts of detectability and stabilizability as well as a discussion of how the duality between these concepts should be understood is presented conditions for existence and uniqueness of a positive semi definite solution to a set of coupled riccati equations in a generic form are provided in terms of these concepts of detectability and stabilizability applications to the filtering and optimal control problems are presented giving a unified and rather complete picture of coupled riccati equations for discrete time markovian jump linear systems interpretations for the sub optimality of the filtering problem are also provided

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

on the solution of discrete time markovian jump linear quadratic control problems abstract a necessary and sufficient condition for the existence of a positive semidefinite solution of the coupled algebraic discrete time riccati like equation occurring in markovian jump control problems is derived by verifying a simple matrix inequality it is shown that such a solution exists and can be obtained as a limit of a monotonic sequence this leads to a straightforward numerical algorithm for the computation of the solution an example is given to illustrate the proposed method

full informationh control for discrete time infinite markov jump parameter systems abstract in this paper we consider the full information discrete timeh control problem for the class of linear systems with markovian jumping parameters the state space of the markov chain is assumed to take values in a countably infinite set full information here means that the controller has access to both the state variables and jump variables a necessary and sufficient condition for the existence of a feedback controller that makes the l 2 induced norm of the system less than a prespecified bound is obtained this condition is written in terms of a set of infinite coupled algebraic riccati equations

the yang mills measure for s2 abstract the yang mills measure for gauge fields over the two sphere is constructed using a conditioned white noise process stochastic differential equations are used to study parallel translation under this measure expectation values of a broad class of wilson loop configurations are computed explicitly and it is shown that these values are invariant under area preserving diffeomorphisms of the sphere