finiteness of teichmuller curves in non arithmetic rank 1 orbit closures we show that in any non arithmetic rank 1 orbit closure of translation surfaces there are only finitely many teichm uller curves we also show that in any non arithmetic rank 1 orbit closure any completely parabolic surface is veech

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

the motion of a vortex on a closed surface of constant negative curvature the purpose of this work is to present an algorithm to determine the motion of a single hydrodynamic vortex on a closed surface of constant curvature and of genus greater than one the algorithm is based on a relation between the laplace beltrami green function and the heat kernel the algorithm is used to compute the motion of a vortex on the bolza surface this is the first determination of the orbits of a vortex on a closed surface of genus greater than one the numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the bolza surface some of these equilibria allow for the construction of the first two examples of infinite vortex crystals on the hyperbolic disc the following theorem is proved a weierstrass point of a hyperellitic surface of constant curvature is always a vortex equilibrium

a height gap theorem for finite subsets of mathrm gl _ d overline bbb q and nonamenable subgroups we introduce a conjugation invariant normalized heightb f on nite subsets of matrices f in gld q and describe its properties in particular we prove an analogue of the lehmer problem for this height by showing that b f whenever f generates a nonvirtually solvable subgroup of gld q where d 0 is an absolute constant this can be seen as a global adelic analog of the classical margulis lemma from hyperbolic geometry as an application we prove a uniform version of the classical burnside schur theorem on torsion linear groups in a companion paper we will apply these results to prove a strong uniform version of the tits alternative

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

thomson s heptagon a case of bifurcation at infinity abstract vortex modeling has a long history descartes 1644 used it as a model for the solar systems j j thomsom 1883 used it as a model for the atom we consider point vortex systems which can be regarded as discrete solutions of the euler equation their dynamics is described by a hamiltonian system of equations we are interested in polygonal configurations and how their stability depends upon various dynamical variables in the plane a polygon with seven vortices has been shown to be a special boundary case polygons with n 7 vortices are linearly and nonlinearly stable while polygons with n 7 vortices are unstable why should n 7 be special celestial mechanics helped us to simplify a problem that has been studied for over a century and to show that the case of thomson s heptagon is actually a case of bifurcation at infinity this becomes particularly clear when considering the corresponding problem of a ring on a sphere with two polar vortices of variable intensities n and s at the north and south pole respectively

the motion of point vortices on closed surfaces we develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere when the sum of the vortex circulations is non ze

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

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

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

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

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

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

on the dimension of furstenberg measure for sl _ 2 mathbb r random matrix products let mu be a measure on sl 2 mathbb r generating a non compact and totally irreducible subgroup and let nu be the associated stationary furstenberg measure for the action on the projective line we prove that if mu is supported on finitely many matrices with algebraic entries then begin aligned dim nu min big 1 frac h mathrm mathrm rw mu 2 chi mu big end aligned where h mathrm mathrm rw mu is the random walk entropy of mu chi mu is the lyapunov exponent for the random matrix product associated with mu and dim denotes pointwise dimension in particular for every delta 0 there is a neighborhood u of the identity in sl 2 mathbb r such that if a measure mu in mathcal p u is supported on algebraic matrices with all atoms of size at least delta and generates a group which is non compact and totally irreducible then its stationary measure nu satisfies dim nu 1

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

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

bertrand s postulate and subgroup growth abstract in this article we investigate the l 1 norm of certain functions on groups called divisibility functions using these functions their connection to residual finiteness and integration theory on profinite groups we define the residual average of a finitely generated group one of the main results in this article is the finiteness of residual averages on finitely generated linear groups whether or not the residual average is finite depends on growth rates of indices of finite index subgroups our results on index growth rates are analogous to results on gaps between primes and provide a variant of the subgroup growth function which may be of independent interest

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

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

n body dynamics on closed surfaces the axioms of mechanics a major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of n body and n vortex dynamics on riemann surfaces in this paper we show how the two problems are in fact closely related when considering the role played by the intrinsic geometry of the surface this enables a straightforward deduction of the dynamics of point masses using recently derived results for point vortices on general closed differentiable surfaces m endowed with a metric g we find generally that kepler s laws do not hold what is more even newton s first law the law of inertia fails on closed surfaces with variable curvature e g the ellipsoid

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

nonlinear stability of a latitudinal ring of point vortices on a nonrotating sphere we study the nonlinear stability of relative equilibria of configurations of identical point vortices on the surface of a sphere in particular we study how the stability changes as a function of the colatitude theta and of the number of vortices n by using the integrals of motion we view the system in asuitable corotating frame where the polygonal vortex configuration is at rest then after a sufficient criterion due to dirichlet the stability ranges are the theta intervals for which the hessian of the hamiltonian evaluated at the equilibrium configuration is positive or negative definite we find that the stability intervals coincide with those for linear stability determined by polvani and dritschel j fluid mech 255 1993 pp 35 64 for n 3 we recover the result previously established by pekarsky and marsden j math phys 39 1998 pp 5894 5907

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

statistics of point vortex turbulence in non neutral flows and in flows with translational and rotational symmetries a theory esler and ashbee in j fluid mech 779 275 308 2015 describing the statistics of n freely evolving point vortices in a bounded two dimensional domain is extended first the case of a non neutral vortex gas is addressed and it is shown that the density of states function can be identified with the probability density function of an infinite sum of independent non central chi squared random variables the details of which depend only on the shape of the domain equations for the equilibrium energy spectrum and other statistical quantities follow the validity of which are verified against direct numerical simulations of the equations of motion second domains with additional conserved quantities associated with a symmetry e g circle periodic channel are investigated and it is shown that the treatment of the non neutral case can be modified to account for the additional constraint

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

a topological tits alternative let k be a local eld and gln k a linear group over k we prove that either contains a relatively open solvable subgroup or it contains a relatively dense free subgroup this result has applications in dynamics riemannian foliations and pronite groups

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

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

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

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

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

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

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

uniform non amenability abstract for any finitely generated group g an invariant fol g 0 is introduced which measures the amount of non amenability of g if g is amenable then fol g 0 if fol g 0 we call g uniformly non amenable we study the basic properties of this invariant for example its behaviour when passing to subgroups and quotients of g we prove that the following classes of groups are uniformly non amenable non abelian free groups non elementary word hyperbolic groups large groups free burnside groups of large enough odd exponent and groups acting acylindrically on a tree uniform non amenability implies uniform exponential growth we also exhibit a family of non amenable groups in particular including all non solvable baumslag solitar groups which are not uniformly non amenable that is they satisfy fol g 0 finally we derive a relation between our uniform folner constant and the uniform kazhdan constant with respect to the left regular representation of g

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

vortex dynamics in complex domains on a spherical surface we consider the motion of both point vortices and uniform vortex patches in arbitrary possibly multiply connected regions bounded by impenetrable walls on the surface of a sphere by exploiting knowledge of the functional form of the relevant green s function in a pre image circular domain that is conformally equivalent to a stereographic projection of the fluid domain on the spherical surface we first generalize kirchhoff routh theory for point vortex motion in the plane to point vortex motion on a spherical shell next we study vortex patch motion and show that there is a contour dynamics formulation for the evolution of uniform vortex patches in any finitely connected domain on a spherical shell bounded by impenetrable walls we describe a novel numerical scheme whereby this motion can be computed some illustrative calculations are shown

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

uniform independence in linear groups we show that for any non virtually solvable finitely generated group of matrices over any field there is an integer m such that given an arbitrary finite generating set for the group one may find two elements a and b that are both products of at most m generators such that a and b are free generators of a free subgroup this uniformity result improves the original statement of the tits alternative

vortex motion on surfaces with constant curvature vortex motion on two dimensional riemannian surfaces with constant curvature is formulated by way of the stereographic projection the relation and difference between the vortex motion on a sphere s 2 and on a hyperbolic plane h 2 can be clearly analysed the hamiltonian formalism is presented for the motion of point vortices on s 2 and h 2 the set of first integrals for each hamiltonian shows a corresponding algebraic property in terms of the poisson bracket defined respectively for s 2 and h 2 as an example of analytic solutions the motion of a vortex pair dipole is considered it is shown that a dipole draws a geodesic curve as its trajectory on s 2 and h 2

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

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

kazhdan quotients of golod shafarevich groups the main goal of this paper is to prove that every golod shafarevich group has an infinite quotient with kazhdan s property t in particular this gives an affirmative answer to the well known question about non amenability of golod shafarevich groups

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

on dense free subgroups of lie groups abstract we give a method for constructing dense and free subgroups in real lie groups in particular we show that any dense subgroup of a connected semisimple real lie group g contains a free group on two generators which is still dense in g and that any finitely generated dense subgroup in a connected non solvable lie group h contains a dense free subgroup of rank 2 dim h this answers a question of carriere and ghys and it gives an elementary proof to a conjecture of connes and sullivan on amenable actions which was first proved by zimmer

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

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

point vortex dynamics a classical mathematics playground the idealization of a two dimensional ideal flow as a collection of point vortices embedded in otherwise irrotational flow yields a surprisingly large number of mathematical insights and connects to a large number of areas of classical mathematics several examples are given including the integrability of the three vortex problem the interplay of relative equilibria of identical vortices and the roots of certain polynomials addition formulas for the cotangent and the weierstras function projective geometry and other topics the hope and intent of the article is to garner further participation in the exploration of this intriguing dynamical system from the mathematical physics community

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

a combination theorem for anosov subgroups we prove an analogue of klein combination theorem for anosov subgroups by using a local to global principle for morse quasigeodesics

approximate subgroups of residually nilpotent groups we show that a k approximate subgroup a of a residually nilpotent group g is contained in boundedly many cosets of a finite by nilpotent subgroup the nilpotent factor of which is of bounded step combined with an earlier result of the author this implies that a is contained in boundedly many translates of a coset nilprogression of bounded rank and step the bounds are effective and depend only on k in particular if g is nilpotent they do not depend on the step of g as an application we show that there is some absolute constant c such that if g is a residually nilpotent group and if there is an integer n 1 such that the ball of radius n in some cayley graph of g has cardinality bounded by n c log log n then g is virtually log n step nilpotent

on uniform exponential growth for linear groups let be a finitely generated group given a finite set of generators s of the word length ls for an element is defined to be the smallest positive integer for which there exist s1 sn s s 1 such that s1 sn for each n n denote by bs n the set of elements in whose word length with respect to s is at most n it follows from the subadditive property of ls that limn bs n 1 n exists which we denote by s a finitely generated group is said to be of exponential growth if s 1 of polynomial growth if for some c 0 and d n bs n c n d for all n 1 and of intermediate growth otherwise for some finite generating set s of observe that the growth type of does not depend on the choice of generating set s if a finitely generated group is linear it is known that is either of polynomial growth in which case is virtually nilpotent or of exponential growth otherwise tit72 mil68 wol68