fault detection and isolation based on fuzzy automata fuzzy automata are proposed for fault diagnosis the output of the monitored system is partitioned into linear segments which in turn are assigned to pattern classes templates with the use of membership functions a sequence of templates is generated and becomes input to fuzzy automata which have transitions that correspond to the templates of the properly functioning system if the automata reach their final states i e the input sequence is accepted by the automata with a membership degree that exceeds a certain threshold then normal operation is deduced otherwise a failure is diagnosed fault diagnosis of a dc motor and detection of abnormalities in the ecg signal are used as case studies

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

differential identities of prime rings with involution main theorem let r be a prime ring with involution suppose that 0 x5 xa 0 is a differential identity for r where a are distinct regular words of derivations in a basis m with respect to a linear order u e w be such that vl vs is dindependent in v and ul ut is d independent in w then there exists a e sw v such that via v i 1 s and a uj u j 1 t if and only if v uj v u for i 1 s and j 1 t proposition 4 suppose that r is a prime ring with involution and that f is a generalized polynomial if f vanishes on a nonzero ideal of r than f vanishes on q the two sided quotient ring of r the objective of this paper is to prove the following generalization of kharchenko s theorem on differential identities to prime rings with involution the notation here is explained in i below main theorem let r be a prime ring with involution suppose that x ai xj 0 is a differential identity for r where a1 are distinct regular words of derivations in a basis m with respect to a linear order on m then 0 zi iz 0 is a generalized identity for r where zij are distinct indeterminates received by the editors april 18 1988 1980 mathematics subject classification 1985 revision primary 16a38 secondary 16a28 16a72 16a12 16a48

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

approximation to a class of non autonomous systems by dynamic fuzzy inference marginal linearization method in this paper a dynamic fuzzy inference marginal linearization dfiml method is proposed for modeling nonlinear dynamic systems this method can transfer a group of input output data into a time variant fuzzy system with variable coefficients it is shown that solutions of time variant fuzzy systems generalized by dfiml method are universal approximators to solutions of a class of non autonomous systems also the analytical solutions of these time variant fuzzy systems can be obtained finally a simulation example is provided to illustrate the validity and potential of the developed techniques

enlarging the domain of attraction and maximising convergence rate for delta operator systems with actuator saturation in this paper we present some new approaches to improve the feedback property of delta operator systems with actuator saturation both enlarging the domain of attraction and maximising the convergence rate are the desired feedback properties the lifting technique is used to enlarge the domain of attraction for the delta operator systems subject to actuator saturation the maximisation of convergence rate is realised by designing control gain inside a given ellipsoid a necessary and sufficient condition is proposed for the contractive invariance of the given ellipsoid simulation results are provided to demonstrate the effectiveness of the developed techniques

finiteness properties of differential polynomials abstract let r be a prime ring with extended centroid c and let x i j be a reduced differential polynomial with coefficients in q the symmetric martindale quotient ring of r and with zero constant term let a x i j x i r and b x ij x ij r we prove that the finiteness of a and the finite dimensionality of the c span of a are equivalent to that of b and that of the c span of b respectively hence some questions on differential polynomials are reduced to those on ordinary generalized polynomials let and d be two derivations of r l a lie ideal of r and a right ideal of r as applications of our theorems we obtain the necessary and sufficiency conditions for the finiteness of d d l and d l and for the finite dimensionality of the c spans of d d l and d l

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

preference for flexibility in a savage framework we study preferences over savage acts that map states to opportunity sets and satisfy the savage axioms preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies the main result of this paper characterizes maximization of the expected indirect utility in terms of an indirect stochastic dominance axiom that expresses a preference for more opportunities in expectation the key technical tool of the paper a version of mobius inversion has been imported from the theory of nonadditive belief functions it allows an alternative representation using choquet integration and yields a simple proof of kreps 1979 classic result

simulation of fuzzy random variables this work deals with the simulation of fuzzy random variables which can be used to model various realistic situations where uncertainty is not only present in form of randomness but also in form of imprecision described by means of fuzzy sets utilizing the common arithmetics in the space of all fuzzy sets only induces a conical structure as a consequence it is difficult to directly apply the usual simulation techniques for functional data in order to overcome this difficulty two different approaches based on the concept of support functions are presented the first one makes use of techniques for simulating hilbert space valued random elements and afterwards projects on the cone of all fuzzy sets it is shown by empirical results that the practicability of this approach is limited the second approach imitates the representation of every element of a separable hilbert space in terms of an orthonormal basis directly on the space of fuzzy sets in this way a new approximation of fuzzy sets useful to approximate and simulate fuzzy random variables is developed this second approach is adequate to model various realistic situations

identities ore extensions and character skew derivations following 17 a derivation is called quasi algebraic if there exist a ai q such that k x i 1k 1ai i x ax k x a 0 for x q let k be the minimal such integer and g0 g1 mutually outer automorphisms of q let f zij be a generalized polynomial in variables zij where i 0 and 0 j k it is shown in 6 that if f gi j x or f jgi x is an identity then so is f zij we generalize this to sets of skew derivations in theorems 1 and 2 in theorem 3 we apply these results to the ore extensions of several variables of 2 and in theorem 4 to the character hopf algebras of the character skew derivations of 12

h output feedback control of fuzzy system models under sampled measurements this paper studies the problem of control for a class of fuzzy system models by using a linear output controller the system under consideration is described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are assumed unmeasurable we develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models a design algorithm for constructing the linear output controller is given a numerical simulation example is given to show the potential of the proposed techniques

tabular method for determining root distribution of delta operator formulated real polynomials a tabular method for the investigation of real polynomial root distribution with respect to the circle spl verbar c 1 spl delta spl verbar 1 spl delta in the complex plane is presented such a procedure is useful in stability considerations of spl delta operator formulated discrete time systems with sampling time spl delta in particular when the characteristic polynomial contains literal coefficients we show that direct verification of stability may be preferable over techniques that utilize transformations when the sampling frequency is fast relative to the system bandwidth in addition as sampling frequency increases the relationship with the well known routh hurwitz table becomes apparent

identities with skew derivations abstract we solve affirmatively a problem raised by kharchenko on identities with compositions of skew derivations we define the notion of trivial identities with compositions of skew derivations which is unique in a certain sense it is proved that if a prime ring r satisfies a nontrivial identity with compositions of skew derivations then r also satisfies a generalized polynomial identity without skew derivations we actually work in a more general context in which higher skew derivations in the literature known to the author are all covered

dynamic output feedback h control synthesis for discrete time t s fuzzy systems via switching fuzzy controllers this paper studies the problem of dynamic output feedback h control of discrete time takagi sugeno t s fuzzy systems via a switched dynamic parallel distributed compensation dpdc scheme the considered switched dpdc control structure is determined based on the values of membership functions some new properties of membership functions are obtained and exploited to derive sufficient conditions for designing switching dpdc controllers that guarantee the stability and h performances of closed loop nonlinear systems the design conditions are given in terms of solvability of a set of linear matrix inequalities lmis it is shown that the new approach provides results at least as good as the corresponding dpdc methods a numerical example is given to illustrate the effectiveness of the proposed approach

robust h control for a class of discrete time fuzzy systems via delta operator approach in this paper we investigate a robust h control problem for a class of t s fuzzy systems with time delays by using delta operator approach it is known that a better control effect can be obtained by using delta operator approach than using shift operator approach for small sampling periods furthermore the delta operator can unify some previous related continuous and discrete fuzzy systems into fuzzy delta operator system framework based on lyapunov krasovskii functionals in delta domain a new fuzzy h state feedback controller is presented in terms of linear matrix inequalities some experiment results of an ball and beam model on a laboratory scale setup are presented to illustrate the effectiveness and potential for the developed techniques

robust stability of discrete time systems using delta operators the robust stability of discrete time systems formulated in terms of the delta delta operator is discussed that is given the nominal characteristic equation p delta of a discrete time system it is of interest to know how much the coefficients can be perturbed while preserving stability a procedure to obtain the maximum intervals for a perturbed polynomial p delta to still be stable is presented

identities with a single skew derivation abstract let r be a prime ring with extended centroid c and a continuous skew derivation of r we define the notion of k polynomials which in the case that is an ordinary derivation reduces to polynomials of the form x p n 1 x p n 1 n x where i c it is shown that all generalized identities with are consequences of gpis of r and an identity in the form x x m b b x where x is a k polynomial of minimal possible order m

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

stochastic finite time boundedness on switching dynamics markovian jump linear systems with saturated and stochastic nonlinearities in this paper problems of finite time boundedness are investigated for a class of discrete time switching dynamics markovian jump linear systems with saturated and stochastic nonlinearities the time varying transition probabilities are described by a piecewise constant matrix subject to a high level average dwell time adt switching sensor and actuator saturations are characterized by a vector valued decomposition method and the stochastic nonlinearities are approximated by a statistical method in general not all trajectories originating from the admissible initial states could be stabilized in the mean square sense or sufficient conditions are too restrictive to yield feasible solutions therefore the purpose of studying the problems addressed here is to design an output feedback controller via the adt approach such that the resulting closed loop systems are stochastically finite time bounded and have a guaranteed disturbance attenuation capability simulation results demonstrate the potential and effectiveness of the theoretical results

comparative study of finite wordlength effects in shift and delta operator parameterizations the sensitivity of the transfer function to finite wordlength effect errors in the implementation of the coefficients of both shift operator and delta operator parameterizations is analyzed the relationships between optimal realization sets in shift and delta operator are established it is shown that the optimal realization in delta operator parameterizations have better performance than those in their shift operator counterparts when the poles of the systems are clustered around z 1 a numerical example is given

robust h control for uncertain fuzzy systems with distributed delays via output feedback controllers this paper investigates the problem of robust h output feedback control for a class of uncertain fuzzy systems with distributed delays the system is described by a state space takagi sugeno fuzzy model with distributed delays and norm bounded parameter uncertainties the aim is to design a fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities a sufficient condition for the solvability of this problem is presented finally simulation examples are provided to illustrate the effectiveness of the proposed design approach

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

improved finite word length characteristics in digital control using delta operators this paper examines some of the consequences of finite word lengths in digital control it is shown that in many cases of practical importance the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach this latter approach is shown to give better coefficient representation and less roundoff noise in many cases we thus argue that the shift operator and its associated z transform can be replaced by delta operators and their associated transform which we designate a transform an added advantage of this approach is that discrete designs and transforms converge to their continuous time counterparts as the sampling rate is increased

an antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation the article considers linear systems subject to actuator saturation an antiwindup technique is used to enlarge the domain of attraction of the closed loop system under an a priori designed linear dynamic feedback law the design of the antiwindup compensation gain is formulated and solved as an iterative optimization problem with lmi constraints numerical examples are used to demonstrate the effectiveness of the proposed design technique

a non minimal but very weak axiomatization of common belief the paper introduces a modal logic system of individual and common belief which is shown to be sound and complete with respect to a version of neighbourhood semantics this axiomatization of common belief is the weakest of all those currently available it dispenses with even the monotonicity rule of individual belief it is non minimal in that it does not use just the equivalence rule but the conjunction of the latter with the specially devised rule of c restricted monotonicity

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

stability analysis for high frequency networked control systems this note generalizes the stability analysis for a high frequency networked control system the high frequency networked control system is described by a delta operator system with a high frequency constraint stability conditions are given for the high frequency delta operator system furthermore by developing the generalized kalman yakubovic popov lemma improved stability conditions are also presented in terms of linear matrix inequalities some experiment results are presented to illustrate the effectiveness of the developed techniques

new results on delay dependent robust stability criteria of uncertain fuzzy systems with state and input delays this paper focuses on the delay dependent stability analysis and stabilization for uncertain t s fuzzy control systems with state and input delays the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology in fact these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis finally some examples are included to show that the proposed criteria improve the existing results significantly

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

robust anti windup controller design of time delay fuzzy systems with actuator saturations this study presents a robust anti windup fuzzy control approach for uncertain nonlinear time delay systems with actuator saturations the discussed system dynamics is presented by the takagi sugeno t s fuzzy model to facilitate the design process the nonlinearity of input saturation is characterized by a specific sector condition given a stabilizing dynamic output feedback fuzzy controller an anti windup control approach is then developed to maximize the size of estimate of the domain of attraction significantly the convergence of all admissible initial states within this region could be ensured based on the lyapunov krasovskii delay independent and delay dependent analyses sufficient conditions for the robust stabilization are derived these conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities allowing the fuzzy controller to be synthesized more efficiently finally numeric simulations are given to validate the proposed approach

an anti windup design for linear systems with input saturation abstract an anti windup design problem is posed and it is shown that all observer based anti windup modifications solve this problem at least locally sufficient conditions for an observer based anti windup modification to solve the global version of this problem are presented a novel observer based anti windup design is then proposed such that the anti windup problem can be interpreted in terms of a reduced order system in particular the proposed anti windup design induces an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed loops the dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function the second part of the paper shows how the original dynamic compensator can be modified while retaining those dynamic features that produce a desirable closed loop steady state response to ensure that the requisite invariant subspace exists and it is reasonably tuned for input saturation two case studies are carried out on systems that have been investigated in the literature

adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash like hysteresis in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain nonlinear systems with unknown backlash like hysteresis and unmeasured states the fuzzy logic systems are used to approximate the nonlinear system functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are semi globally uniformly ultimately bounded suub and both observer error and tracking error can converge to a small neighborhood of the origin two simulations are included to illustrate the effectiveness of the proposed approach

stability analysis and controller synthesis for discrete time delayed fuzzy systems via small gain theorem this paper investigates the problems of stability analysis and controller synthesis of discrete time takagi sugeno t s fuzzy systems with time varying delay via an input output approach the original system is reformulated as a feedback subsystem and a forward subsystem with two constant time delays and a delay uncertainty satisfying the scaled small gain theorem the lifting method is employed to convert the forward subsystem to a delay free system where the main result concerning the stability analysis of the system is obtained based on the scaled small gain theorem the merit of the new stability condition lies in its reduced conservatism which is made possible by a more precise estimation of the time varying delay additionally a state feedback controller is designed through the lyapunov krasovskii functional approach combined with the utilization of the scaled small gain theorem two illustrative examples are given to demonstrate the less conservatism of the stability condition and the effectiveness of the controller design method

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

null controllable region of delta operator systems subject to actuator saturation abstractin this paper we give exact description of null controllable regions for delta operator systems subject to actuator saturation the null controllable region is in terms of a set of extremal trajectories of anti stable subsystems for the delta operator system with real eigenvalues or complex eigenvalues the description is simplified to an explicit formula which is used to characterise the boundary of a null controllable region the relations of null controllable regions are shown separately for continuous time systems discrete time systems and delta operator systems two numerical examples are given to illustrate the effectiveness of the proposed techniques on null controllable regions

standard state space models preclude unawareness we show that a very broad class of models including possibility correspondences necessarily fail to capture very simple and intuitive implications of unawareness we explain why standard state space formulations suffer from this problem illustrating the point with an example of a nonstandard state space model which avoids the difficulty

new approach on robust delay dependent h _ infty control for uncertain t s fuzzy systems with interval time varying delay this paper investigates the robust h infin control for takagi sugeno t s fuzzy systems with interval time varying delay by employing a new and tighter integral inequality and constructing an appropriate type of lyapunov functional delay dependent stability criteria are derived for the control problem because neither any model transformation nor free weighting matrices are employed in our theoretical derivation the developed stability criteria significantly improve and simplify the existing stability conditions also the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem numerical examples are given to demonstrate the effectiveness of the proposed methods

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

lie ideals and derivations of prime rings in this paper we shall consider the relationship between the derivations and lie ideals of a prime ring some of the results we obtain have been obtained earlier even for rings more general than prime rings in the case of inner derivations we shall also look at the action of derivations on lie ideals the results we obtain extend some that had been proved earlier only for the action of derivations on the ring itself let r be a ring and d 0 a derivation of r if u is a lie ideal of r we shall be concerned about the size of d c how does one measure this size one way is to look at the centralizer of d u in r the bigger d u the smaller this centralizer should be this explains our interest in the centralizer of d u the result we obtain generalizes the principal theorem of 11 we may also measure the size of d u by looking at how large d u the subring generated by d u turns out to be we view d u as large if it contains a non zero ideal of r for our special setting we will obtain a result which generalizes one in 2 finally a well known and often used result states that if d is a derivation of r which is semi prime and 2 torsion free such that dz 0 then d 0 see the proof of lemma 1 1 9 in 3 if r is prime of characteristic not 2 and d i 0 for a non zero ideal 1 of r it also follows that d 0 what can one say if d u 0 for some non central lie ideal of r for inner derivations this was studied and answered in 4 for prime rings and for any derivation d 0 we answer the question of when d u 0 completely in our theorem 1 we shall be working in the context of prime rings of characteristic not 2 in all that we do here however many of the results have some suitable analog for semi prime 2 torsion free rings in the presence of 2 torsion most of our results are not valid as stated but something non trivial can be said in

h state feedback controller design for continuous time t s fuzzy systems in finite frequency domain this paper is concerned with finite frequency h state feedback controller designs for continuous time takagi sugeno t s fuzzy systems a parallel distributed compensation pdc controller is designed in finite frequency domain with the aid of the generalized kalman yakubovich popov gkyp lemma the design problem is formulated as solving a set of linear matrix inequalities lmis simulation examples illustrate that the finite frequency design approach proposed in this paper receives better results than those of existing full frequency approaches

brief paper adaptive sliding mode controller design based on t s fuzzy system models an adaptive sliding mode control asmc technique based on t s fuzzy system models is proposed in this paper for a class of perturbed nonlinear mimo dynamic systems in order to solve tracking problems a t s fuzzy model is firstly formed by utilizing fuzzy theorem to amalgamate a set of linearized dynamic equations the adaptive sliding mode controller is then designed based on this fuzzy model with perturbations the proposed control scheme can drive the dynamics of controlled system into a designated sliding surface in finite time and guarantee the property of asymptotical stability it is also shown that the information of upper bound of modeling errors as well as perturbations except the information of upper bound of input uncertainty is not required when using the proposed controller

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

robust stability functionals of state delayed systems with polytopic type uncertainties via parameterdependent lyapunov functions this paper considers the problem of robust stability for linear systems with a constant time delay in the state and subject to real convex polytopic uncertainty both delay independent and delay dependent stability conditions are characterized by linear matrix inequalities which allow the use of parameter dependent lyapunov functionals to analyse the system stability against parameter perturbations and therefore improve the conservativeness resulting from the single lyapunov functional in order to determine the maximum of time delay within which the system remains stable the problem can be cast into a generalized eigenvalue problem and solved by standard lmi solvers two examples are included to illustrate the proposed method

h control design for fuzzy discrete time singularly perturbed systems via slow state variables feedback an lmi based approach this paper addresses the h control problem via slow state variables feedback for discrete time fuzzy singularly perturbed systems at first a method of evaluating the upper bound of singular perturbation parameter e with meeting a prescribed h performance bound requirement is given subsequently two methods for designing h controllers via slow state variables feedback are presented in terms of solutions to a set of linear matrix inequalities lmis in particular one of them can be used to improve the upper bound of the singular perturbation parameter e finally two numerical examples are given to illustrate the effectiveness of the proposed methods

nonlinear identities with skew derivations abstract let r be a prime ring with the extended centroid c suppose that r is acted by a pointed coalgebra with group like elements acting as automorphisms of r a generalized polynomial with variables acted by the coalgebra is called an identity if it vanishes on r we prove the following 1 if c is a perfect field then any such identity is a consequence of simple basic identities defined in 6 and gpis of r with variables acted by frobenius automorphisms 2 if c is not a perfect field then any such identity is a consequence of simple basic identities defined in 6 and gpis of r with this we extend yanai s result 25 to nonlinear identities these are actually special instances of our theorems 1 and 2 below respectively which extend kharchenko s theory of differential identities 14 15 to the context of expansion closed word sets introduced in 6

further studies on relaxed stabilization conditions for discrete time two dimension takagi sugeno fuzzy systems this paper investigates the stabilization problem of discrete time two dimension 2 d takagi sugeno t s fuzzy systems based on a novel non parallel distributed compensation non pdc control scheme combined with a new non quadratic lyapunov function less conservative stabilization conditions are developed the proposed non quadratic lyapunov function is homogeneous polynomially parameter dependent on membership functions as the degree of the lyapunov function increases the conservatism of the obtained stabilization conditions is gradually reduced by exploiting the algebraic property of membership functions the stabilization conditions approach to exactness in the sense of convergence compared with the existing methods no slack variables are introduced in control synthesis and hence the same or less conservative results can be obtained with a lower computational cost a numerical example is given to illustrate the effectiveness of the proposed method

output feedback stabilization of linear systems with actuator saturation the note presents a method for designing an output feedback law that stabilizes a linear system subject to actuator saturation with a large domain of attraction this method applies to general linear systems including strictly unstable ones a nonlinear output feedback controller is first expressed in the form of a quasi lpv system conditions under which the closed loop system is locally asymptotically stable are then established in terms of the coefficient matrices of the controller the design of the controller coefficient matrices that maximizes an estimate of the domain of attraction is then formulated and solved as an optimization problem with lmi constraints

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

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

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

piecewise fuzzy anti windup dynamic output feedback control of nonlinear processes with amplitude and rate actuator saturations in this paper a novel anti windup dynamic output compensator is developed to deal with the robust h infin output feedback control problem of nonlinear processes with amplitude and rate actuator saturations and external disturbances via fuzzy modeling of nonlinear systems the proposed piecewise fuzzy anti windup dynamic output feedback controller is designed based on piecewise quadratic lyapunov functions it is shown that with sector conditions robust output feedback stabilization of an input constrained nonlinear process can be formulated as a convex optimization problem subject to linear matrix inequalities simulation study on a strongly nonlinear continuously stirred tank reactor cstr benchmark plant is given to show the performance of the proposed anti windup dynamic compensator

technical communique robust stabilization of uncertain systems with unknown input delay this paper is concerned with the robust controller design for uncertain input delayed systems the time delay is assumed to be an unknown constant a controller with delay feedback for the robust stabilization of the system is proposed the stability criterion of the closed loop system is derived in terms of linear matrix inequalities lmis examples show that in many cases our method can give less conservative results than those by the existing methods moreover for the same cases our controllers have lower feedback gains than the existing ones

left annihilators characterized by gpis let r be a semiprime ring with extended centroid c u the right utumi quotient ring of r s a subring of u containing r and pi p2 two right ideals of r in the paper we show that 1s pi 1s p2 if and only if pi and p2 satisfy the same generalized polynomial identities gpis with coefficients in sc where ls pi denotes the left annihilator of pi in s as a consequence of the result if p is a right ideal of r such that ir p 0 then p and u satisfy the same gpis with coefficients in the two sided utumi quotient ring of r this paper is motivated by chuang s paper 3 and beidar s paper 2 recall that a ring r is said to be a left faithful ring if for a e r ar 0 implies a 0 for a left faithful ring r the right utumi quotient ring of r can be characterized as a ring u satisfying the following axioms 1 r is a subring of u 2 for each a e u there exists a dense right ideal p of r such that ap c r 3 if a e u and ap 0 for some dense right ideal p of r then a 0 4 for any dense right ideal p of r and for any right r module homomorphism q pr rr there exists a e u such that q x ax for all x e p let r be a left faithful ring and p be a dense right ideal of r we note that p itself is a left faithful ring furthermore p and r have the same right utumi quotient ring more precisely denote by u r u p resp the right utumi quotient ring of r p resp then there exists a ring isomorphism h from u p onto u r such that h x x for all x e p in 3 chuang proved the theorem let r be a prime ring u its right utumi quotient ring and nr a dense r submodule of ur then n and u satisfy the same generalized polynomial identities gpis with coefficients in u in this theorem we note that n n r is always a dense right ideal of r since n n r and r have the same right utumi quotient ring chuang s theorem just says that r and u satisfy the same gpis with coefficients in u also in an earlier paper 2 beidar proved that the same result remains true for semiprime rings for a semiprime ring r we observe that n n r is a dense right ideal of r for any dense r submodule nr of ur also lu n n r the left annihilator of n n r received by the editors april 11 1994 and in revised form july 8 1994 originally communicated to the proceedings of the ams by ken goodearl 1991 mathematics subject classification primary 1 6r50

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

on design of dynamic output feedback controller for gcs of large scale systems with delays in interconnections lmi optimization approach this paper considers the dynamic output feedback controller design problem for decentralized guaranteed cost stabilization gcs of large scale systems with time delays in subsystem interconnections based on the lyapunov method a linear matrix inequality lmi convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function

technical communique observer based h fuzzy control design for t s fuzzy systems with state delays this paper is concerned with the problem of observer based h fuzzy control design for takagi sugeno t s fuzzy systems with time delay the main contribution is that an effective matrix decoupling technique is developed to derive a single step lmi condition for observer based h control design this overcomes the drawback of two step lmi approach in the literature when restricted to delay free fuzzy systems the present result is shown less conservative than existing ones an illustrative example is given to show the effectiveness of our results

differential identities with automorphisms and antiautomorphisms i abstract let r be a prime ring with the extended centroid c an anti automorphism g of r is said to be frobenius if in the case of char r g for all c or in the case of char r p 0 g p n for all c where n is a fixed integer which may be zero positive or negative anti automorphisms g 1 g 2 are said to be strongly independent if for any i j g i g 1 j is not frobenius the following is proved main theorem let z ijk be a polynomial with frobenius anti automorphisms assume that x jgk i 0 holds on a nonzero two sided ideal of r where x i are distinct indeterminates j are distinct regular derivation words with respect to a linearly ordered basis of outer derivations and g k are strongly independent anti automorphisms of r then z ijk 0 holds on the two sided utumi quotient ring of r if z ijk does not involve antiautomorphisms then z ijk 0 also holds on the left utumi quotient ring of r

on distributed delay in linear control laws part ii rational implementations inspired from the spl delta operator this note proposes rational implementations for distributed delay in linear control laws the main benefit of doing so is the easy implementation of rational transfer functions the proposed approach was inspired from the spl delta operator the resulting rational implementation has an elegant structure of chained low pass filters the stability of each node can be guaranteed by the choice of the number n of the nodes the stability of the closed loop system can also be guaranteed since the h sup spl infin norm of the implementation error approaches 0 when n goes to spl infin moreover the steady state performance of the system is retained without the need to change the control structure

synthesis of controllers for continuous time delay systems with saturating controls via lmis the stabilization of linear continuous time systems with time delay in the state and subject to saturating controls is addressed sufficient conditions obtained via a linear matrix inequality lmi formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements the method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed loop system is guaranteed when control saturations effectively occur

fuzzy approximation relations on fuzzy n cell number space and their applications in classification in this paper the problems of fuzzy binary relations on fuzzy n cell number space and their applications are investigated firstly we have defined some fuzzy approximation relations on fuzzy n cell number space and studied their properties secondly as application we have developed an algorithmic version of classification in an imprecise or uncertain environment by using the fuzzy approximation relations practical examples are provided to show the application and rationality of the proposed techniques

model reference adaptive control using the delta operator reference is made to a recent paper by g c goodwin r lozano leal d q mayne and r h middleton automatica vol 22 p 199 207 1986 where it is shown that a cancellation of nonminimum phase zeros appearing in discrete time model reference adaptive control mrac at a fast sampling rate can be easily avoided if the model to be identified is expressed in terms of the delta operator a new proof of stability of the mrac is given using the delta operator which in contrast to the proof given in the above paper does not require an assumption that a system consisting of a model determined by estimated parameters and a control law based on certainty equivalence principle is exponentially stable a simple parameterization is proposed for the discrete time mrac using the delta operator which allows application of the usual i e without dead zone estimation algorithms

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

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

new results on h_ infty filtering for fuzzy time delay systems this paper is concerned with the h infin fuzzy filtering problem for a class of continuous time fuzzy systems with time varying delays the objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed h infin performance of the filtering error system motivated by the parallel distributed compensation technique we design a new filter model in this paper filter parameter matrices can be obtained from the solution of a convex optimization problem in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired h infin fuzzy filter is given two numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed design approach

robust fuzzy scheduling control for nonlinear systems subject to actuator saturation via delta operator approach this paper focuses on robust fuzzy scheduling control for nonlinear systems with actuation saturation via delta operator approach a class of t s fuzzy delta operator systems is extended to describe nonlinear systems subject to actuator saturation and linear fractional uncertainty moreover a set invariance condition is established for t s fuzzy delta operator systems based on the set invariance condition an optimization approach is proposed to estimate the domain of attraction for the t s fuzzy delta operator systems the domain of attraction is arbitrarily close to a null controllable region by the designed pdc control law or non pdc control law furthermore the non pdc control law is proposed by using fuzzy weighting dependent lyapunov function the effectiveness of the developed techniques is shown through a numerical example

a novel approach for static anti windup compensation of one sided lipschitz systems under input saturation abstract this paper illustrates a new strategy for designing the local static anti windup aw compensator for nonlinear systems with one sided lipschitz osl nonlinearities under saturating actuators and exogenous disturbances the static aw strategy is designed such that the resulting closed loop system with osl nonlinearity actuator saturation and exogenous disturbance is stable and the region of attraction can be maximized inequalities based conditions are formulated for the static aw gain design by using lyapunov stability theory sector condition l2 gain reduction osl inequality and quadratic inner bounded qib condition the proposed aw technique is simpler to design straightforward to implement and deals with a broader class of systems in contrast to conventional methods an application example demonstrates that the proposed static aw can successfully mitigate the saturation consequences in osl nonlinear systems