characterizations of classes of stable matrices abstract this paper extends some results on the structure of subsets of the set of stable matrices for these subsets different characterizations are obtained using the set product defined in this paper as well as inertia and algebraic characterizations for low dimensions 2 2 and 3 3 matrices some inclusion relations that hold for these classes of matrices are proved and some open questions mentioned

finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information this paper studies the problem of finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information the partly usable model information is considered following a certain bernoulli distributed white noise sequence the objective of the study is to design a state feedback controller such that the augmented closed loop system is mean square stochastically finite time bounded and a tracking performance level is achieved over a finite time interval by using the mode dependent diagonally dominant lyapunov function approach some sufficient conditions are established for the existence of an admissible state feedback controller based on these a state feedback controller can be constructed by using a simple matrix decoupling approach two numerical examples and a modified general economic model are presented to demonstrate the effectiveness of our proposed approach

finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

fuzzy stability criterion of a class of nonlinear systems abstract a fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of lyapunov first a sufficient condition that guarantees stability of a fuzzy system is given in terms of lyapunov s direct method two concepts for stability of fuzzy systems are defined locally stable and globally table second a construction procedure for lyapunov functions is presented finally the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems

purely infinite simple c algebras that are principal groupoid c algebras abstract from a suitable groupoid g we show how to construct an amenable principal groupoid whose c algebra is a kirchberg algebra which is kk equivalent to c g using this construction we show by example that many uct kirchberg algebras can be realised as the c algebras of amenable principal groupoids

partially mode dependent l2 l filtering for discrete time nonhomogeneous markov jump systems with repeated scalar nonlinearities abstract this paper is concerned with the problem of partially mode dependent l 2 l filtering for discrete time nonhomogeneous markov jump systems mjss with repeated scalar nonlinearities our main purpose is to design a partially mode dependent l 2 l filter such that the filtering error system is stochastically stable with l 2 l performance the time varying transition probabilities tps are depicted as a polytope by adopting the diagonally dominant lyapunov functional and based on linear matrix inequalities lmis sufficient conditions are presented for the existence of the filter three examples are given to validate the effectiveness of our results

asymptotic properties of solutions of third order nonlinear differential equations with deviating argument abstract the aim of this paper is to establish comparison principles on property a between a nonlinear differential equation of the third order with deviating argument with delay advanced or mixed argument and the corresponding linear equation without deviating argument on the basis of these comparison principles the sufficient conditions for delay advanced and mixed equations to have property a are presented the results obtained are compared with existing ones in the framework of the papers

h_ bm infty fuzzy control for systems with repeated scalar nonlinearities and random packet losses this paper is concerned with the h infin fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses a modified takagi sugeno t s fuzzy model is proposed in which the consequent parts are composed of a set of discrete time state equations containing a repeated scalar nonlinearity such a model can describe some well known nonlinear systems such as recurrent neural networks the measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses attention is focused on the analysis and design of h infin fuzzy controllers with the same repeated scalar nonlinearities such that the closed loop t s fuzzy control system is stochastically stable and preserves a guaranteed h infin performance sufficient conditions are obtained for the existence of admissible controllers and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities which can be readily solved by using standard numerical software two examples are given to illustrate the effectiveness of the proposed design method

a galerkin neural network based design of guaranteed cost control for nonlinear distributed parameter systems this paper presents a galerkin neural network based guaranteed cost control gcc design for a class of parabolic partial differential equation pde systems with unknown nonlinearities a parabolic pde system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement motivated by this in the proposed control scheme galerkin method is initially applied to the pde system to derive an ordinary differential equation ode system with unknown nonlinearities which accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently parameterized by a multilayer neural network mnn with one hidden layer and zero bias terms then based on the neural model and a lure type lyapunov function a linear modal feedback controller is developed to stabilize the closed loop pde system and provide an upper bound for the quadratic cost function associated with the finite dimensional slow system for all admissible approximation errors of the network the outcome of the gcc problem is formulated as a linear matrix inequality lmi problem moreover by using the existing lmi optimization technique a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained finally the proposed design method is applied to the control of the temperature profile of a catalytic rod

finite time boundedness for switched systems with sector bounded nonlinearity and constant time delay finite time boundedness and finite time stability of switched systems with sector bounded nonlinearity and constant time delay are investigated sufficient conditions which guarantee finite time stability or finite time boundedness of the switched nonlinear system are presented respectively average dwell time of switching signals is also given moreover finite time weighted l2 gain of the switched nonlinear system is addressed to measure its disturbance tolerance capability in the fixed time interval detail proofs are accomplished by using multiple lyapunov like functions an example is employed to verify the efficiency of the proposed method

the c algebras of finitely aligned higher rank graphs we generalise the theory of cuntz krieger families and graph algebras to the class of finitely aligned k graphs this class contains in particular all row finite k graphs the cuntz krieger relations for non row finite k graphs look significantly different from the usual ones and this substantially complicates the analysis of the graph algebra we prove a gauge invariant uniqueness theorem and a cuntz krieger uniqueness theorem for the c algebras of finitely aligned k graphs

brief new results for analysis of systems with repeated nonlinearities this work presents new results for analysis of systems with repeated monotonic or slope restricted nonlinearities we first give new integral quadratic constraints iqcs that are satisfied by the inputs and outputs of diagonal operators with equal monotonic or slope restricted diagonal entries then we present new analysis results for systems with repeated nonlinearities obtained using the new iqcs for the type of nonlinearities considered in this work the new results are less conservative than previously known results the computation of the new conditions is discussed the results in this paper apply also to problems with nonrepeated nonlinearities whenever these are representable as the interconnection of multiple repeated nonlinearities and a constant matrix

stability of discrete time systems joined with a saturation operator on the state space this note studies the stability of discrete time dynamical systems acted upon by a saturation process in the state space a finite procedure is proposed to focus on the asymptotic behavior of systems which produces linear constraints imposed on lyapunov stein matrix inequalities to be solved a little linear algebra broadens the scope of stability test from that of the earlier liu michel s criterion

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

stability analysis of neural net controllers using fuzzy neural networks neural networks can only be trained with a crisp and finite data set therefore the approximation quality of a trained network is hard to verify so a common way in proving stability of a trained neural net controller is to demonstrate the existence of a lyapunov function in this article we propose a new method how stability of a neural net controller used as a closed loop feedback controller can be proven instead of finding a lyapunov function conditions for a fuzzy training set are developed if a fuzzy neural net is trained using this training set special properties of fuzzy neural nets can be used for estimating the generalization error after defuzzification of the fuzzy net finite stability of the process can be concluded

further results for systems with repeated scalar nonlinearities a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity is considered this paper sharpens several previous results on the performance synthesis and model reduction for such systems extensions to the case that the nonlinearity is not an odd function are also discussed

higher dimensional generalizations of the thompson groups abstract motivated by the goal of generalizing the cuntz krieger algebras and making heavy use of the pioneering work of robertson and steger kumjian and pask generalized the notion of a directed graph to what they termed a higher rank graph the c algebras constructed from such higher rank graphs have proved to be highly interesting higher rank graphs are in fact a class of cancellative categories and so the one vertex higher rank graphs are therefore a class of cancellative monoids in this paper we call them k monoids finite direct products of free monoids belong to this family but there are many examples not of this form it is well known that the classical thompson groups arise from the free monoids and it is easy to show that brin s higher dimensional thompson groups arise from finite direct products of free monoids in this paper we generalize these constructions and show how to construct a family of new groups with simple commutator subgroups from arbitrary aperiodic k monoids thereby subsuming all the above examples although we give simple direct constructions of our groups a key feature of our paper is that we also show that they arise as topological full groups of the usual etale groupoids associated with k monoids in this way our groups are naturally associated with c algebras the question of the mutual isomorphisms amongst this family of groups appears to be a delicate one and is not handled here

a new method for stability analysis of nonlinear discrete time systems we address the problem of global lyapunov stability of discrete time systems with known coefficients we develop a method for reduction of dissipativity domain effectively testing if the system has a convex lyapunov function our implementation is immediately applicable to differentiable systems with bounded nonlinearities but the method proposed is more general and applicable to nondifferentiable systems with bounded right hand sides our main application emphasis is on stability analysis of recurrent neural networks we illustrate how to use our approach with examples

an h sub spl infin design approach for neural net based control schemes presents an h sub spl infin design approach for a neural net based control scheme in this scheme a class of nonlinear systems is approximated by two multilayer perceptrons the neural networks are piecewisely interpolated to generate a linear differential inclusion model based on this model a state feedback control law is designed the h sub spl infin control is specified to eliminate the effect of approximation errors and external disturbances to achieve the desired performance it is shown that finding the permissible control gain matrices can be transformed to a standard linear matrix inequality problem and solved using the convex optimization method

semigroupoid c algebras abstract a semigroupoid is a set equipped with a partially defined associative operation given a semigroupoid we construct a c algebra o from it we then present two main examples of semigroupoids namely the markov semigroupoid associated to an infinite 0 1 matrix and the semigroupoid associated to a row finite higher rank graph without sources in both cases the semigroupoid c algebra is shown to be isomorphic to the algebras usually attached to the corresponding combinatorial object namely the cuntz krieger algebras and the higher rank graph c algebras respectively in the case of a higher rank graph d it follows that the dimension function d is superfluous for defining the corresponding c algebra

sliding mode control of discrete time switched systems with repeated scalar nonlinearities this note studies the design of sliding mode control smc for discrete time hybrid stochastic switched systems with repeated scalar nonlinearities the weighed mathcal h infty gain performance is considered for the system dynamics to optimize its transient state performance first sufficient conditions are given to guarantee the corresponding system is exponentially stable while achieving a desired weighed mathcal h infty performance a new switching surface function is constructed by the average dwell time technique and the positive diagonally dominant lyapunov functional method to further reduce the conservativeness induced by the repeated scalar nonlinearity then the corresponding sliding mode dynamics are obtained and the solvability condition for the desired switching surface function is derived furthermore the synthesis of the proposed smc law is proposed to force the resulting closed loop system trajectories onto the pre specified sliding mode region with a desired level of accuracy finally the feasibility and the effectiveness of the presented new design techniques are illustrated by examples and simulations

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

quantitative characterizations of exponential convergence property of nonlinear discrete dynamical systems in this technical note we consider the exponential convergence property of the trajectories of nonlinear discrete dynamical systems with exponential stability based on an invariant quantity derived from lyapunov functions of the systems the essential and quantitative relationship between exponential convergence property of trajectories and the lyapunov functions is revealed

the tight groupoid of the inverse semigroups of left cancellative small categories the second named author was partially supported by pai iii grant fqm 298 of the junta de andalucia and by the dgi mineco and european regional development fund jointly through grant mtm2017 83487 p

chaotic synchronization cryptosystems combined with rsa encryption algorithm abstract chaotic synchronization has suffered from demodulating information by hackers via the public channel different methods have been developed to hide the contents of a message using chaotic signals nevertheless many studies have shown that most of the existing methods are unreliable in the aspect of security according to the above in order to enhance the strength of the cryptosystem and provide greater security we carry out double encryption which combines chaotic synchronization with rsa algorithm in this study a design methodology for neural network nn based secure communications in multiple time delay chaotic mtdc systems is proposed to obtain double encryption via rsa algorithm and chaotic synchronization rsa algorithm is an asymmetric encryption and its strength is based on the tremendous difficulty of factorizing two large prime numbers accordingly it takes much more time to process rsa algorithm if the length of the key is much longer a shorter key is used to decrease the processing time of rsa algorithm in this work nevertheless it will result in a lower security of the cryptosystem in order to enhance the strength of the cryptosystem we carry out double encryption which combines chaotic synchronization with rsa algorithm moreover an iga is proposed in this study to effectively overcome the weakness of the traditional ga on the basis of the iga a fuzzy controller is synthesized to not only realize the exponential synchronization but also achieve optimal h performance by minimizing the disturbances attenuation level finally a numerical example with simulations is given to illustrate the effectiveness of our approach

all multipliers for repeated monotone nonlinearities we have derived the largest class of bounded linear time invariant operators that preserve positivity of repeated monotone nonlinearities it reduces conservativeness of integral quadratic constraint iqc stability analysis of systems having repeated monotone nonlinearities to the minimum possible utility of this characterization stems from the fact that such nonlinearities are typically encountered in stability analysis of anti windup schemes among other applications we have also derived the time varying counterpart of this class of operators

a new approach to fuzzy modeling and control of discrete time systems we present a new approach to fuzzy modeling and control of discrete time systems which is based on the formulation of a novel state space representation using the hyperbolic tangent function the new representation designated the hyperbolic model combines the advantages of fuzzy system theory and classical control theory on the one hand the hyperbolic model is easily derived from a set of mamdani type fuzzy rules on the other hand classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of mamdani type fuzzy rules thus this new approach combines the best of two worlds it enables linguistic interpretability of both the model and the controller and guarantees closed loop stability and robustness

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

amenability of groupoids arising from partial semigroup actions and topological higher rank graphs we consider the amenability of groupoids g equipped with a group valued cocycle c g q with amenable kernel c 1 e we prove a general result which implies in particular that g is amenable whenever q is amenable and if there is countable set d g such that c g u d q for all u g 0 we show that our result is applicable to groupoids arising from partial semigroup actions we explore these actions in detail and show that these groupoids include those arising from directed graphs higher rank graphs and even topological higher rank graphs we believe our methods yield a nice alternative groupoid approach to these important constructions

bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant lyapunov functions or storage functions satisfying appropriate linear matrix inequalities results are also presented for model reduction errors for such systems

an approach to stability criteria of neural network control systems this paper discusses stability of neural network nn based control systems using lyapunov approach first it is pointed out that the dynamics of nn systems can be represented by a class of nonlinear systems treated as linear differential inclusions ldi next stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single nn systems and feedback nn control systems furthermore a method of parameter region pr representation which graphically shows the location of parameters of nonlinear systems is proposed by introducing new concepts of vertex point and minimum representation from these concepts an important theorem which is useful for effectively finding a lyapunov function is derived stability criteria of single nn systems are illustrated in terms of pr representation finally stability of feedback nn control systems which consist of a plant represented by an nn and an nn controller is analyzed

event triggered h control for networked discrete time markov jump systems with repeated scalar nonlinearities this paper investigates the event triggered h control problem for networked discrete time markov jump systems subject to repeated scalar nonlinearities an event triggered communication transmission scheme is adopted and an event generator is presented between the controller and sensor our aim is to design a controller such that although the unavoidable phenomenon of network induced delays is fully considered the resulting closed loop system is stochastically stable with a prescribed h performance level by employing a diagonally dominant type lyapunov functional a co design method is established for the existence of an admissible controller and some available mode dependent event triggered parameters finally the effectiveness of our proposed control design method is shown by a numerical example

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

delayed standard neural network models for control systems in order to conveniently analyze the stability of recurrent neural networks rnns and successfully synthesize the controllers for nonlinear systems similar to the nominal model in linear robust control theory the novel neural network model named delayed standard neural network model dsnnm is presented which is the interconnection of a linear dynamic system and a bounded static delayed or nondelayed nonlinear operator by combining a number of different lyapunov functionals with s procedure some useful criteria of global asymptotic stability and global exponential stability for the continuous time dsnnms cdsnnms and discrete time dsnnms ddsnnms are derived whose conditions are formulated as linear matrix inequalities lmis based on the stability analysis some state feedback control laws for the dsnnm with input and output are designed to stabilize the closed loop systems most rnns and neurocontrol nonlinear systems with or without time delays can be transformed into the dsnnms to be stability analyzed or stabilization synthesized in a unified way in this paper the dsnnms are applied to analyzing the stability of the continuous time and discrete time rnns with or without time delays and synthesizing the state feedback controllers for the chaotic neural network system and discrete time nonlinear system it turns out that the dsnnm makes the stability conditions of the rnns easily verified and provides a new idea for the synthesis of the controllers for the nonlinear systems

stability of systems with several monotone nonlinearities this paper is devoted to stability problems of automatic control systems frequency domain criteria for global asymptotic stability of equilibrium sets for new classes of nonlinearities are derived results are illustrated by examples

stability analysis of discrete time recurrent neural networks we address the problem of global lyapunov stability of discrete time recurrent neural networks rnns in the unforced unperturbed setting it is assumed that network weights are fixed to some values for example those attained after training based on classical results of the theory of absolute stability we propose a new approach for the stability analysis of rnns with sector type monotone nonlinearities and nonzero biases we devise a simple state space transformation to convert the original rnn equations to a form suitable for our stability analysis we then present appropriate linear matrix inequalities lmis to be solved to determine whether the system under study is globally exponentially stable unlike previous treatments our approach readily permits one to account for non zero biases usually present in rnns for improved approximation capabilities we show how recent results of others on the stability analysis of rnns can be interpreted as special cases within our approach we illustrate how to use our approach with examples though illustrated on the stability analysis of recurrent multilayer perceptrons the approach proposed can also be applied to other forms of time lagged rnns

generalised morphisms of k graphs k morphs in a number of recent papers k l graphs have been constructed from k graphs by inserting new edges in the last l dimensions these constructions have been motivated by c algebraic considerations so they have not been treated systematically at the level of higher rank graphs themselves here we introduce k morphs which provide a systematic unifying framework for these various constructions we think of k morphs as the analogue at the level of k graphs of c correspondences between c algebras to make this analogy explicit we introduce a category whose objects are k graphs and whose morphisms are isomorphism classes of k morphs we show how to extend the assignment c to a functor from this category to the category whose objects are c algebras and whose morphisms are isomorphism classes of c correspondences

forward and converse lyapunov theorems for discrete dynamical systems this technical note addresses the stability analysis of nonlinear dynamic systems three main contributions are made first we show that the standard assumption of a continuous lyapunov function can be and in some cases must be relaxed we introduce the concept of the weak lyapunov function which requires that an annulus condition be satisfied we believe that this annulus condition is a more natural construct because it is precisely what is needed to make the forward lyapunov theorem true second we provide an example of a nonlinear system with stable equilibrium point that cannot be shown to be stable with a continuous lyapunov function finally we demonstrate a simpler and less restrictive proof of the converse lyapunov theorem

establishing convexity of polynomial lyapunov functions and their sublevel sets there has been renewed interest in the use of polynomial and homogeneous polynomial lyapunov functions for addressing stability and performance issues in systems and control theory however no condition is yet available to establish the convexity of these functions and the convexity of their sublevel sets properties that can be useful in many applications in this paper new conditions for establishing these convexity properties are proposed which can be handled through convex linear matrix inequalities optimizations by means of sum of squares relaxations

adjoint differential equations and oscillation abstract the paper offers effective oscillation criteria for the equation formula where pi and q are positive continuous functions on an interval a in the case n 4 is even and the operator formula is not in canonical form the technique is established on properties of adjoint equations of an equation rn t rn 1 t r1 t r0 t y cy 0 with 0 c r and ri i 0 1 n positive continuous functions the conception of adjoint equations is stated in the paper

robust control of dynamical systems using neural networks with input output feedback linearization this paper presents a control algorithm that combines three valuable features in robust and non linear control namely modelling using neural networks input output feedback linearization and lmi based robust controller design in the first step of the algorithm an affine description of a feedforward neural network model is derived by performing an input output feedback iof linearization an uncertainty description of the iof linearized system is derived based on the parametric uncertainties of the affine model then the lmi based robust controller is designed by means of an optimization procedure a key step in this procedure is the derivation of a polytopic boundary for the state space matrices of the iof linearized system based on the estimated parameters of the neural network and their uncertainty bounds

stabilization and performance synthesis for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered given a plant of this form sufficient conditions are derived for 1 the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant lyapunov function and 2 the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level several of these conditions can be written into linear matrix inequalities

a class of c algebras generalizing both graph algebras and homeomorphism c algebras iv pure infiniteness this is the final one in the series of papers where we introduce and study the c algebras associated with topological graphs in this paper we get a sufficient condition on topological graphs so that the associated c algebras are simple and purely infinite using this result we give one method to construct all kirchberg algebras as c algebras associated with topological graphs

boundary quotients and ideals of toeplitz c algebras of artin groups abstract we study the quotients of the toeplitz c algebra of a quasi lattice ordered group g p which we view as crossed products by a partial actions of g on closed invariant subsets of a totally disconnected compact hausdorff space the nica spectrum of g p our original motivation and our main examples are drawn from right angled artin groups but many of our results are valid for more general quasi lattice ordered groups we show that the nica spectrum has a unique minimal closed invariant subset which we call the boundary spectrum and we define the boundary quotient to be the crossed product of the corresponding restricted partial action the main technical tools used are the results of exel laca and quigg on simplicity and ideal structure of partial crossed products which depend on amenability and topological freeness of the partial action and its restriction to closed invariant subsets when there exists a generalised length function or controlled map defined on g and taking values in an amenable group we prove that the partial action is amenable on arbitrary closed invariant subsets the topological freeness of the boundary action depends on topological freeness of the restriction to a certain lattice subgroup of g the core of g p which often turns out to be trivial our main results are obtained for right angled artin groups with trivial centre that is those with no cyclic direct factor they include a presentation of the boundary quotient in terms of generators and relations that generalises cuntz s presentation of o n a proof that the boundary quotient is purely infinite and simple and a parametrisation of the ideals of the toeplitz c algebra in terms of subsets of the standard generators of the artin group

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

on the balanced truncation and coprime factors reduction of markovian jump linear systems abstract the paper deals with the balanced truncation and coprime factors reduction of markovian jump linear mjl systems which can have mode varying state input and output dimensions we develop machinery for balancing mean square stable mjl system realizations using generalized gramians and strict lyapunov inequalities and provide an improved a priori upper bound on the error induced in the balanced truncation process we also generalize the coprime factors reduction method and in doing so extend the applicability of the balanced truncation technique to the class of mean square stabilizable and detectable mjl systems we provide tools to establish mean square stabilizability and detectability of the considered mjl systems in addition a notion of right coprime factorization of mjl systems and methods to construct such factorizations are given the error measure in the coprime factors reduction approach while still norm based does not directly capture the mismatch between the nominal system and the reduced order model as is the case in the balanced truncation approach where mean square stable models are considered instead the error measure is given in terms of the distance between the coprime factors realizations and thus has an interpretation in terms of robust feedback stability the paper concludes with an illustrative example which demonstrates how to apply the coprime factors model reduction approach

stability analysis of neural network interconnected systems this paper is concerned with the stability problem of a neural network nn interconnected system which consists of a set of nn models first a linear difference inclusion ldi state space representation is established for the dynamics of each nn model subsequently based on the ldi state space representation a stability criterion in terms of lyapunov s direct method is derived to guarantee the asymptotic stability of nn interconnected systems finally a numerical example with simulations is given to demonstrate the results

on characterizations of exponential stability of nonlinear discrete dynamical systems on bounded regions in this paper we discuss the quantitative characterization problems of the exponential stability and trajectory convergence property of nonlinear discrete dynamical systems on a bounded set of the state space through introducing two new concepts the lip constant of a nonlinear operator and strongly equivalent metrics of a norm we show that the nonlinear discrete dynamical systems are exponentially stable on the bounded set if and only if the corresponding nonlinear operator is contractive under some strongly equivalent metrics or if and only if the lip constant of the nonlinear operator is less than one in the latter case we further show that the infimum of the exponential bounds of trajectories of the system equals exactly to the lip constant based on the obtained results we clearly explain how trajectory convergence properties of the systems are determined quantitatively by the lip constant and strongly equivalent metrics the obtained results not only are of importance in understanding the essence of exponential stability and trajectory convergence properties of nonlinear discrete dynamical systems on bounded sets of the state space but also provide some new useful criteria of testing exponential stability and estimating convergence speed of trajectories of the systems

stability and stabilizability of fuzzy neural linear control systems this paper discusses stability analysis of fuzzy neural linear fnl control systems which consist of combinations of fuzzy models neural network nn models and linear models the authors consider a relation among the dynamics of nn models those of fuzzy models and those of linear models it is pointed out that the dynamics of linear models and nn models can be perfectly represented by takagi sugeno t s fuzzy models whose consequent parts are described by linear equations in particular the authors present a procedure for representing the dynamics of nn models via t s fuzzy models next the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of lyapunov the stability criteria is reduced to the problem of finding a common lyapunov function for a set of lyapunov inequalities the stability conditions are employed to analyze stability of fnl control systems finally stability analysis for four types of fnl control systems is demonstrated

neural network based control design an lmi approach we address a neural network based control design for a discrete time nonlinear system our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin a linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state feedback control law for the nonlinear system based on the certainty equivalence principle the control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal further the stability of the closed loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed loop system converges finally a simple example is presented so as to illustrate our control design procedure

sliding mode control for markovian jump repeated scalar nonlinear systems with packet dropouts the uncertain occurrence probabilities case abstract this paper studies the sliding mode based control problem for a class of delayed markovian jump repeated scalar nonlinear systems rsnss subject to packet dropouts pds and randomly occurring uncertainties rous here the phenomenon of the markovian pds is modeled by utilizing a random variable obeying markov process by using the bernoulli distributed random variables the rous under uncertain occurrence probabilities uops are characterized from the mathematical perspective in addition the time delay considered is bounded time varying with known upper and lower bounds the attention is on designing a sliding mode based control method for markovian jump rsnss in the simultaneous presence of markovian pds rous and time varying delays specifically the robustly asymptotically mean square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion moreover the reachability in discrete setting is analyzed i e the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre designed sliding surface in mean square sense by synthesizing a robust sliding mode control smc law finally the effectiveness of developed control method is verified by some simulations

on the rank minimization problem over a positive semidefinite linear matrix inequality we consider the problem of minimizing the rank of a positive semidefinite matrix subject to the constraint that an affine transformation of it is also positive semidefinite our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice this problem is of importance in many contexts for example in feedback synthesis problems and such an example is also provided

quantitative studies on asymptotic growth behaviors of trajectories of nonlinear discrete dynamical systems this technical note studies quantitatively asymptotic growth behaviors of trajectories agbt of nonlinear autonomous discrete dynamical system that has unbounded domain non lipschitz continuous nonlinear operator and stable or unstable equilibrium point we explain how trajectory motion speed is quantitatively determined in the system and study exact computation and sharp estimation of the smallest exponential bound of trajectories we characterize exponential stability and asymptotic stability of the system from a new point of view and provide a simple condition to distinguish them from each other these results extend existing results that were obtained in some special cases of the system and are helpful for quantitative analysis and understanding of agbt of the system