technical communique semi global stabilization of linear time delay systems with control energy constraint this note is concerned with the problem of semi globally stabilizing a linear system with an input delay and a constraint on the energy of its input under the condition of null controllability with vanishing energy the parametric lyapunov equation based l 2 low gain feedback is adopted to solve the problem the proposed approach is applied to the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another spacecraft in a circular orbit around the earth to validate its effectiveness

saturated delayed controls for feedforward nonlinear systems the saturated delayed feedback is presented to globally stabilize a class of feedforward nonlinear systems whose nominal dynamics is the cascade of multiple oscillators and multiple integrators key strategies are stated as follows 1 to compensate the arbitrarily large input delay and to carry out the recursive analysis we transform the concerned system into a normal form 2 in the convergence analysis for multiple oscillators that are relatively difficult to treat we combine the saturated delayed terms define the composite lyapunov functions and use the cauchy formula 3 for ease of the analysis on nonlinear terms we employ saturation levels to restrict them as applications the usual feedforward nonlinear systems with multiple integrators as the nominal dynamics and the null controllable linear systems are dealt with in some new manners and a saturated delayed controller is presented for the well known tora system

linear systems subject to input saturation and time delay global asymptotic stabilization this note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay under standard necessary conditions we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large constant delay to validate the approach a third order integrator and oscillator with multiplicity two example is presented

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

l_p stabilization of integrator chains subject to input saturation using lyapunov based homogeneous design consider the n th integrator dot x j nx sigma u e n where x in mathbb r n u in mathbb r j n is the n th jordan block and e n 0 cdots 0 1 t in mathbb r n we provide easily implementable state feedback laws u k x which not only render the closed loop system globally asymptotically stable but also are finite gain l p stabilizing with arbitrarily small gain as in a saberi p hou and a stoorvogel ieee trans automat control 45 2000 pp 1042 1052 these l p stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite time stabilization of linear systems we also provide additional l infty stabilization results for the case of both internal and external disturbances of the n th integrator namely for the perturbed system dot x j nx e n sigma k x d d where d in mathbb r and d in mathbb r n

a relationship between equality relations and the t redundancy of fuzzy partitions and its application to sugeno controllers abstract the question whether a family of fuzzy subsets can be transformed by a multiplicative function is investigated in order to minimize its t l redundancy and in order to get a family of fuzzy points with respect to some equality relation

i fuzzy equivalence relations and i fuzzy partitions a t fuzzy equivalence relation is a fuzzy binary relation on a set x which is reflexive symmetric and t transitive for a t norm t recently mesiar et al r mesiar b reusch h thiele fuzzy equivalence relations and fuzzy partitions j multi valued logic soft comput 12 2006 167 181 have generalised the t norm t to any general conjunctor c and investigated the minimal assumptions required on such operations called duality fitting conjunctors such that the fuzzification of the equivalence relation admits any value from the unit interval and also the one one correspondence between the fuzzy equivalence relations and fuzzy partitions is preserved in this work we conduct a similar study by employing a related form of c transitivity viz i transitivity where i is an implicator we show that although every i fuzzy equivalence relation can be shown to be a c fuzzy equivalence relation there exist c fuzzy equivalence relations that are not i fuzzy equivalence relations and hence these concepts are not equivalent most importantly we show that the class of duality fitting implicators i is much richer than the residuals of the duality fitting conjunctors in the study of mesiar et al we also show that the i fuzzy partitions have a constant wise structure

output feedback regulation of a chain of integrators with unknown time varying delays in states and input we consider a problem of global asymptotic regulation of a chain of integrators that has unknown time varying delays in both states and input by output feedback the time varying delays are only known to be bounded and their bounds and time varying rates are unknown to solve the considered problem we introduce a newly designed adaptive output feedback controller for system analysis we give a new transformation and techniques in order to deal with new phenomena associated with unknown time varying delays in states

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

continuity issues of the implicational interpretation of fuzzy rules the implicational interpretation of fuzzy rules has received little attention in real world applications so far this is largely due to the fact that ensuring continuity of the resulting function is not a straightforward task this paper targets this subject departing from consistent linguistic descriptions rule bases we introduce sufficient conditions for the continuity of the implicational interpretation with mean of maximum defuzzification we demonstrate that continuity can be achieved under practically feasible conditions regardless of the dimensionality of the input

guaranteed cost synchronization of chaotic cellular neural networks with time varying delay synchronization of cellular neural networks with time varying delay is discussed in this letter based on razumikhin theorem a guaranteed cost synchronous controller is given unlike lyapunov krasovskii analysis process there is no constraint on the change rate of time delay the saturated terms emerging in the razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by lipschitz condition and vector inequality which will bring more conservatism then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form with the help of a sufficient and necessary transformation condition the minimization of the guaranteed cost is studied and a further criterion for getting the controller is presented finally the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time varying delay cellular neural networks

monoidal closed categories weak topoi and generalized logics abstract a weak topos can be considered as the categorical foundation of fuzzy set theory prominent examples of weak topoi are the category met1 the category of sheaves and the category cm set of complete m valued sets over a locally involutory monoid m

global stabilization of the multiple integrators system by delayed and bounded controls this note is concerned with global stabilization of multiple integrators by delayed and bounded controllers three types of new nonlinear control laws are proposed based on some special canonical forms and explicit conditions are proposed to guarantee the global stability of the closed loop systems differently from the existing canonical forms the new special canonical forms used in this note contain not only time delay in the input but also time delays in its state which are essential in the recursive design since they lead to natural cancellation moreover some free parameters are introduced into these controllers these advantages can help to improve the transient performance of the closed loop system significantly numerical simulations for the fourth order integrators illustrate that the proposed new controllers can indeed outperform the existing one

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

properties of the parametric lyapunov equation based low gain design with applications in stabilization of time delay systems this technical note studies some properties of the recently developed parametric lyapunov equation based low gain feedback design method as applications of these new properties alternative and simpler solutions are proposed to the global stabilization problem for a class of linear systems with input delay and the semi global stabilization problem when the systems are in addition subject to actuator saturation besides the simplicity in their construction the new solutions can also be easily scheduled online to achieve global result in the presence of input saturation

fuzzy controllers with conditionally firing rules mamdani 1975 controller was successfully used in many applications one of its interpretations is that it uses a fuzzy relation as an approximation of the desirable input output correspondence we analyze mathematical properties of mamdani controller and notice that it has lower computational complexity when compared to the residuum based controller however we show that in standard situations both these fuzzy controllers do not represent the rule base properly in the sense of finding a solution to the related system of fuzzy relational equations first we consider the premises and consequents as typical inputs and outputs and we want their correspondence to be kept next we require that each normal input produces an output that bears nontrivial information these two conditions appear to be almost contradictory to the previous controllers we suggest a generalization of mamdani controller which allows us to satisfy these requirements the theory and experiments suggest that it performs better without any change of rule base and without a substantial increase of complexity

truncated predictor feedback stabilization of polynomially unstable linear systems with multiple time varying input delays this technical note is concerned with stabilization of polynomially unstable linear systems with multiple time varying input delays a truncated predictor feedback tpf which is obtained by truncating the distributed terms in the traditional predictor feedback is proposed the proposed tpf is a linear static partial state feedback with a time varying feedback gain that is constructed from the steady solution to a class of parametric lyapunov differential equations under the assumption that the open loop system is only polynomially unstable and is uniformly controllable it is shown that for sufficiently small value of the design parameter the resulting closed loop system is exponentially stable no matter how large the time varying delays are as long as they are bounded simulation demonstrates these theoretical results

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

global asymptotic stabilization for chains of integrators with a delay in the input the problem of the global uniform asymptotic stabilization by bounded feedback of a chain of integrators with a delay in the input is solved no limitation on the size of the delay is imposed to validate the approach a third order example is presented

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

necessary and sufficient conditions for the existence of solution of generalized fuzzy relation equations a x b abstract in 2013 li and jin studied a particular type of fuzzy relational equations on finite sets where the introduced min bi implication composition is based on ukasiewicz equivalence in this paper such fuzzy relation equations are studied on a more general level namely complete residuated lattice valued fuzzy relation equations of type y y a x y x y b x are analyzed and the existence of solutions s is studied first a necessary condition for the existence of solution is established then conditions for lower and upper limits of solutions are given and finally sufficient conditions for the existence of the smallest and largest solutions respectively are characterized if such general or global solutions do not exist there might still be partial or point wise solutions this is a novel way to study fuzzy relation equations such point wise solutions are studied on ukasiewicz product and godel t norm based residuated lattices on the real unit interval

simple saturated designs for ancbc systems and extension to feedforward nonlinear systems this article re examines the robust stabilisation of the asymptotically null controllable with bounded controls ancbc systems and extends the established algorithm to a wide class of feedforward nonlinear systems whose nominal dynamics contains both multiple integrators and multiple oscillators based on the notion of converging input bounded state cibs rather than small input small state siss the computation burden in sussmann et al sussmann h j sontag e d and yang y 1994 a general result on the stabilization of linear systems using bounded controls ieee transactions on automatic control 39 2411 2425 is reduced and a class of simple saturated control laws is presented for the cibs stabilisation of ancbc systems then by combining the technique of dealing with higher order terms the algorithm for ancbc systems is extended to feedforward nonlinear systems

fuzzy control from the logical point of view abstract this paper is a discussion of the logical aspect in fuzzy control which is an application of the theory of approximate reasoning first we analyze approximate reasoning and show that it is a concise logical theory based on many valued logic integrated with some parts of linguistics then we demonstrate that fuzzy control based on equality relations can transparently be formulated as a result of the logical theory finally we demonstrate that fuzzy control can be seen as a repeated derivation in a continuously modified logical theory and propose a hypothesis on the role of linguistics in the controllability problem

weak properties and aggregated extension of fuzzy relations abstract this paper studies the conditions under which the relations extended by aggregation which act upon fuzzy subsets satisfy the conditions required to generate quasi uniformities and distances on the class of fuzzy subsets

stabilization analysis of time delay hamiltonian systems in the presence of saturation abstract the stabilization of a class of hamiltonian systems with state time delay and input saturation is addressed in this paper sufficient conditions are derived by using lyapunov krasovskii functional theorem to guarantee the systems as well as the resulted closed loop systems by output feedback to be asymptotically stable when input saturation effectively occurs a numerical example is presented to illustrate the effectiveness of the obtained results in this paper

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

dependable control of uncertain linear systems based on set theoretic methods this article concerns the feedback control of discrete time systems subject to disturbances and uncertainties in both model parameters and signal measurements the uncertainties are assumed to be unknown but bounded and thus characterised by closed intervals or sets the main result is a new approach to design a feedback controller keeping the system state in a target set first a method is proposed that computes minimal enclosures of the set of reachable states which are consistent with the uncertain input and output measurements and the system dynamics then a control method to keep the current state set in the target set is developed which extends control techniques based on invariant polyhedra the method is illustrated by a mobile robot experiment

robust controller design of uncertain discrete time delay systems with input saturation and disturbances this technical note deals with the problem of robust controller design of uncertain discrete time delay systems subject to control input saturation and bounded external disturbances a sufficient condition is obtained which guarantees the existence of state feedback controllers and an admissible initial condition domain such that the resulting closed loop system is uniformly exponentially convergent to a ball with certain exponential decay rate for every initial condition emanating from the admissible domain an iterative linear matrix inequality relaxation scheme can be used to construct desired state feedback controllers a simulation example is provided to demonstrate the effectiveness of the proposed method

global stabilization of oscillators with bounded delayed input the problem of globally asymptotically stabilizing by bounded feedback of an oscillator with an arbitrary large delay in the input is solved a first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term next it is shown through a lyapunov analysis that the stabilization can be achieved as well when neglecting the distributed terms it turns out that this main result is intimately related to the output feedback stabilization problem

linear systems subject to input saturation and time delay finite gain l lowercase p stabilization this paper deals with finite gain stabilization of linear systems by static feedbacks which are bounded and time delayed for neutrally stable continuous time linear systems we provide a saturated linear feedback law ensuring finite gain stability with respect to every l p norm p in 1 infty with an arbitrary small bound on the control and large constant delay moreover we provide upper bounds for the corresponding l p gains which are delay independent

foundations of fuzzy sets abstract this paper gives an overview of the origins of fuzzy set theory and the problems for the foundations of fuzzy sets arising from those origins and current practice it then gives detailed accounts of categorical approaches using a closed structure to capture the fuzzy and connective within these categories weak forms of subobject representations provide an internal second order logic an approach to fuzzy real numbers and fuzzy topology is included to illustrate the use of this internal second order theory

approximation of uncertain functional relationships in this paper we consider methods for the linguistic modelling of vague functional relationships where the linguistic model is supposed to be given as a set of rules two approaches for deriving a fuzzy valued function from such models are proposed it is argued that both approaches can be interpreted as a generalization of ordinary methods for the interpolation and approximation of functions mathematical properties of fuzzy functions associated with a set of rules are investigated particularly for the second approach a universal approximation property is shown