poles and zeros at infinity of linear time varying systems the notions of poles and zeros at infinity and their relations are extended to the case of linear continuous time varying systems this study is based on the notion of a newborn systems which is in a mathematical point of view a graded module extension over the noncommutative ring of differential operators it is proved to be a relevant generalization to the time varying case of the equivalence class for the so called restricted equivalence of rosenbrock s polynomial matrix descriptions the authors approach is intrinsic and unifies the definitions previously given in the literature in the time invariant case

stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

robust static output feedback stabilization for nonlinear discrete time systems with time delay via fuzzy control approach this paper addresses the problem of designing robust static output feedback controllers for nonlinear discrete time interval systems with time delays both in states and in control input in the approach we do not directly employ the lyapunov approach as do in most of traditional fuzzy control design approaches instead sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed loop fuzzy system the stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the matlab linear matrix inequality lmi toolbox finally an example is provided to illustrate the effectiveness of the proposed approach

improved h control of discrete time fuzzy systems a cone complementarity linearization approach in this paper new results are presented for h analysis and synthesis problems of discrete time takagi sugeno ts fuzzy systems by defining a multiple lyapunov function a new sufficient condition guaranteeing the h performance of the ts fuzzy systems is first derived which is expressed by a set of linear matrix inequalities lmis both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework based on this new condition for h performance the corresponding h controller design problem is then investigated different from the traditional quadratic framework the synthesis problem is solved by exploiting the cone complementarity linearization ccl method together with a sequential minimization problem subject to lmi constraints obtained for the existence of admissible controllers which can be readily solved by using standard numerical software

polynomial matrix linearization and strongly irreducible realization for singular systems abstract a scheme for polynomial matrix linearization is proposed by using the linearization we propose a realization for singular systems the properties of the realization are studied and then a strongly irreducible realization is presented

transformations of matrix pencils and implications in linear systems theory a new transformation of matrix pencils is proposed and its theory formally developed its restriction to generalized state space system matrix pencils is shown to be an appropriate generalization of the usual state space transformation and to represent a closed form expression in system matrix terms of verghese s concept of strong equivalence of such pencils

generalized proper inverse of polynomial matrices and the existence of infinite decoupling zeros a necessary and sufficient condition is presented for the existence of a generalized proper rational inverse for nonsquare polynomial matrices the condition is then proved to be equivalent to the absence of infinite decoupling zeros this condition provides a simple test for the absence of infinite decoupling zeros in the polynomial fraction form it can also be used to remove the infinite decoupling zeros in order to achieve a strongly irreducible system and to provide a new look of the unimodular matrix operation effect at infinity for the left and right polynomial fraction forms

infinite frequency structure and a certain matrix laurent expansion abstract a method for determining the smith mcmillan form at infinity of a rational matrix is derived by considering the laurent expansion at infinity of the matrix this method is used to provide a new test for the absence of infinite zeros in a rational matrix and a new formula for calculating the highest degree among the largest minors of a polynomial matrix

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

stability of fuzzy control systems with bounded uncertain delays global exponential stability of fuzzy control systems with delays is studied these delays in the fuzzy control systems are assumed to be any uncertain bounded continuous functions stability of systems with uncertain delays is interesting since in practical applications it is not easy to know the delays exactly conditions for global exponential stability of free fuzzy systems with uncertain delays are derived criteria for design of nonlinear fuzzy controllers to feedback control the stability of global nonlinear fuzzy systems are given theorems are proved via the method of functional differential inequalities analysis

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

aggregation kinetics for a one dimensional zero degree kelvin model of spinodal decomposition we study analytically the approach to equilibrium in a simple zero temperature model for phase separation in a binary alloy in which nearest neighbor interchange can occur only if the portion of ab bonds is thereby decreased the approach to equilibrium is found analytically because of the existence of infinitely many possible stationary states the asymptotic distribution of ab pairs depends on the details of the initial state and must be obtained by a recursion method

on conditions guaranteeing two polynomial matrices possess identical zero structures some sufficient conditions for two polynomial matrices to simultaneously possess identical finite and infinite zero structures are developed a special case of this problem that of obtaining conditions under which a polynomial matrix has no infinite zeros is also considered and certain connections with previous work are established

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

a new general state space representation for discrete time systems abstract a new general state space representation for causal and anticausal discrete time systems is introduced some of its properties related to systems and network theory concepts are developed the relation to the descriptor form state space representation is also explained applications are given to show the usefulness of the new representation

critical differentiability of maps and canceling operators for a first order homogeneous linear differential operator mathbb a and 1 q infty we show that l n n 1 q differentiability of bv mathbb a text loc maps is equivalent to van schaftingen s elliptic and canceling ec condition for mathbb a for higher order ec operators we give a generalization of dorronsoro s theorem on critical l p taylor expansions for bv k maps here bv mathbb a text loc is the space of u in l 1 text loc such that mathbb a u is a radon measure these results can be formulated as sharp pointwise regularity results for elliptic systems mathbb a u mu where mu is a radon measure thereby covering the limiting case p 1 of a theorem of calder on and zygmund which was open so far

domain number distribution in the nonequilibrium ising model we study domain distributions in the one dimensional ising model subject to zero temperature glauber and kawasaki dynamics the survival probability of a domain s t t and an unreacted domain q1 t t are characterized by two independent nontrivial exponents we develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents

realization algorithm for determining generalized state space representations a realization algorithm is presented that determines a generalized state space representation from a so called column pseudoproper right mfd this algorithm is a generalization of the realization algorithm given by wolovich and is proved to be controllable in the rosenbrock sense moreover the dimension of the realization is equal to the determinantal degree of the given right mfd in a generalized sense

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

infinite frequency structure preserving transformations for general polynomial system matrices a recent transformation proposed for polynomial matrices is extended to the systems theory case of general polynomial system matrices two such extensions are proposed depending on whether the system matrix or its normalized form is used the relationship between both these transformations is established and under them all finite and infinite frequency system zero and pole structure is shown to be invariant

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

surface to bulk crossover in directed compact percolation for directed compact percolation in two dimensions the authors conjecture the exact analytical expressions for the percolation probability near a non conducting wall the initial wet site is at a varying distance from the wall which is along the oriented time direction their results allow an explicit evaluation of the surface to bulk crossover in the percolation probability

low and high dimension limits of a phase separation model we study a simple zero temperature model for phase separation of a binary alloy in which nearest neighbor interchange can occur if the fraction of ab pairs is not thereby increased we present analytic results for the one dimensional case and numerical results for the infinite dimensionality limit on a cayley tree in neither limit does the final fraction of ab pairs agree with the dimension independent result found previously ind 3 4 5

a nine fold canonical decomposition for linear systems the zero structure for non minimal proper systems in state space form is investigated the approach is geometric and a complete characterization in geometric terms is given of the invariant decoupling system and transmission zeros as defined by rosenbrock the first main result is a formula for the transmission zeros second a canonical lattice diagram is presented of a decomposition of the state space which can be viewed as the product of the kalman canonical decomposition and the morse canonical decomposition this decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings via this diagram a number of equivalent formulae for the transmission zeros are derived the freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials finally the relation is demonstrated be

matrix pencil equivalents of a general 2 d polynomial matrix a two level algorithm which reduces a general 2 d polynomial matrix to an equivalent matrix pencil form is presented the exact nature of the equivalence transformation connecting the matrix with its associated pencil is established

delay dependent lmi conditions for stability and stabilization of t s fuzzy systems with bounded time delay this paper studies the stability and stabilization problems for time delay nonlinear systems through takagi sugeno t s fuzzy model approach the time delays are assumed to be bounded but perhaps non smooth delay dependent conditions are presented in terms of lmis illustrative examples are given to show the effectiveness and merits of the present results

fast kawasaki spin exchange limit of spin facilitated kinetic ising models we study a fock space operator technique for describing the stochastic kinetics of a spin facilitated kinetic ising model we focus in particular on the diffusion fast kawasaki exchange limit in which the kinetics can be described by a single mean field evolution equation we derive some general criteria for the approximative validity of mean field theory for the case of a nondiverging diffusion coefficient of the local spin states

infinite elementary divisors of a matrix polynomial and implications a new characterization of infinite poles and zeros in terms of a natural extension of the idea of infinite elementary divisors of a matrix pencil to matrix polynomials is developed it is used to show that two previous descriptions of infinite frequency structure are equivalent subsequently a polynomial matrix transformation which simultaneously preserves the finite and infinite zero structure is presented

generalized functional observer a functional observer and state feedback are proposed for singular systems in the polynomial fraction form that requires no impulsive mode elimination the order of the compensator is determined by the newly defined generalized observability index that is associated with the mcmillan degree of the system a new generalized lyapunov equation is also proposed through a realization scheme that can be applied to both ordinary and singular systems the solution to the equation provides an algebraic approach to the observer of singular systems in the generalized state space form

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

model reference output feedback fuzzy tracking control design for nonlinear discrete time systems with time delay in this study a model reference fuzzy tracking control design for nonlinear discrete time systems with time delay is introduced first the takagi and sugeno ts fuzzy model is employed to approximate a nonlinear discrete time system with time delay next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs the advantage of proposed tracking control design is that only a simple fuzzy observer based controller is used in our approach without feedback linearization technique and complicated adaptive scheme by the proposed method the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem lmip the lmip can be efficiently solved using the convex optimization techniques simulation example is given to illustrate the design procedures and tracking performance of the proposed method

h2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities abstract this paper deals with h2 guaranteed cost gc fuzzy control problem for uncertain continuous time nonlinear systems the state feedback case and observer based output feedback case are considered the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system with parametric uncertainties sufficient conditions for the existence of h2 gc fuzzy controllers are given in terms of linear matrix inequalities lmis the suboptimal h2 gc fuzzy controllers are given by means of the lmi optimization procedures which cannot only guarantee that the closed loop overall fuzzy systems are globally asymptotically stable but also provide an optimized upper bound on the quadratic performance cost finally an example is presented to illustrate the effectiveness of the proposed fuzzy controllers

two spin majority cellular automaton as a model of 2d cluster and interface growth a new probabilistic cellular automaton model is introduced to simulate cluster and interface growth in two dimensions the dynamics of this model is an extension to higher dimensions of the compact directed percolation studied by essam numerical results indicate that the two dimensional cluster coarsening and growth can be described only approximately by the conventional cluster size scaling due to a crossover in the growth mode the spreading of the initially flat interface follows a purely diffusional t1 2 law

delay dependent h fuzzy observer based control for discrete time nonlinear systems with state delay this paper studies the h fuzzy observer based control problem for discrete time nonlinear systems with state delay via a fuzzy lyapunov krasovskii functional lkf approach the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with state delay based on a non parallel distributed compensation pdc scheme a new fuzzy lkf is first constructed to derive a delay dependent condition such that the closed loop fuzzy system is asymptotically stable and satisfies a prescribed level of h disturbance attenuation in the derivation process two free fuzzy weighting matrices are introduced to express the relationship between the present state and delay state then a novel linear matrix inequality lmi approach is proposed for the design of a delay dependent h fuzzy observer based controller the control and observer matrices can be solved directly by using the existing lmi optimization techniques finally a numerical example is given to illustrate the effectiveness of the proposed design method

the eigenstructure of an arbitrary polynomial matrix computational aspects we give a new numerical method to compute the eigenstructure i e the zero structure the polar structure and the left and right null space structure of a polynomial matrix p these structural elements are of fundamental importance in several systems and control problems involving polynomial matrices the approach is more general than previous numerical methods because it can be applied to an arbitrary m n polynomial matrix p with normal rank r smaller than m and or n the algorithm is then shown to compute the structure of the left and right null spaces of p as well the speed and accuracy of this new approach are also discussed

realization and partial fractions abstract we discuss the relation between two intrinsically different proposals that have been made in the literature concerning the representation by constant matrices of rational matrices given in fractional form it turns out that the relation is most naturally studied in the framework of partial fraction decompositions we develop the realization theory for decompositions with respect to arbitrary complementary parts of the extended complex plane which may for instance correspond to stability and instability an isomorphism is obtained which connects the spaces used in the two methods and several identities relating to the mcmillan degree are derived in a direct way finally a new computational procedure is given to obtain the partial fraction decomposition of a rational matrix given in fractional form

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

design of h control for fuzzy time delay systems abstract in this paper the design problems of h output feedback controllers for takagi sugeno fuzzy time delay systems are considered we first introduce takagi sugeno fuzzy time delay systems and the h performance norm for stable fuzzy time delay systems we consider systems with multiple time delays in state we give a sufficient condition for the norm being less than a given number we then consider the h problems with output feedback controllers both memoryless controller and controller with memory are considered in the design of output feedback controllers the selection of the premise variables in the if then rules is important as for the premise variable we consider three cases where the premise variable is a given function the output and the state of the underlying system in the first two cases we give a design method of h controllers and sufficient conditions which guarantee the required h performance of the closed loop system in the last case we give an h controller for an approximation of the original system two examples are given to illustrate the theory