control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

complexity of stability and controllability of elementary hybrid systems in this paper we consider simple classes of nonlinear systems and prove that basic questions related to their stability and controllability are either undecidable or computationally intractable np hard as a special case we consider a class of hybrid systems in which the state space is partitioned into two halfspaces and the dynamics in each halfspace correspond to a different linear system

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

analysis and design of discrete time linear systems with nested actuator saturations abstract this paper is concerned with the analysis and design of discrete time linear systems subject to nested saturation functions by utilizing a new compact convex hull representation of the saturation nonlinearity a linear matrix inequalities lmis based condition is obtained for testing the local and global stability of the considered nonlinear system the estimation of the domain of attraction and the design of feedback gains such that the estimation of the domain of attraction for the resulting closed loop system is maximized are then converted into some lmis based optimization problems compared with the existing results on the same problems the proposed solutions are less conservative as more slack variables are introduced into the conditions a couple of numerical examples are worked out to validate the effectiveness of the proposed approach

global stability and finite l 2 m gain of saturated uncertain systems via piecewise polynomial lyapunov functions in this technical note we provide sufficient conditions for global asymptotic stability and global l2m gain estimation of linear systems subject to saturations and or deadzones with structured parametric uncertainties based on piecewise polynomial lyapunov functions by using sum of squares relaxations these conditions are formulated in terms of linear matrix inequalities example studies are used to comparatively illustrate the proposed techniques

an improved lmi based approach for stability of piecewise affine time delay systems with uncertainty the stability problem for uncertain piecewise affine pwa time delay systems is investigated in this article it is assumed that there exists a known constant time delay in the system and the uncertainly is norm bounded sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the lyapunov krasovskii functional with a triple integration term this approach handles switching based on the delayed states in addition to the states for a pwa time delay system considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches the effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples

distributivity inequalities of monotonic operations the aim of this work is to complement recent results about distributive binary operations our investigation was motivated by non distributive logical connectives and their generalizations in fuzzy set theory in spite of the title we neither solve the concerned functional inequalities nor look for characterization of the solutions of such inequalities we only lay bare conditions for their fulfilment for monotonic operations with neutral or zero element we present the sufficient conditions to obtain the subdistributivity or superdistributivity in the case of the lack of distributivity for the considered pairs of operations in particular we describe families of increasing binary operations subdistributive or superdistributive with respect to idempotent uninorms and nullnorms

lyapunov functions and l 2 gain bounds for systems with slope restricted nonlinearities abstract the stability and l 2 performance analysis of systems consisting of an interconnection of a linear time invariant lti system and a static nonlinear element which is lipschitz slope restricted and sector bounded is revisited the main thrust of the paper is to improve and extend an existing result in the literature to enable i concise and correct conditions for asymptotic stability of the interconnection and ii reasonably tight bounds on the l 2 gain between an exogenous input and a given output to be obtained numerical examples indicate that the proposed algorithm performs well compared to competing results in the literature

a unified lyapunov approach to analysis of oscillations and stability for systems with piecewise linear elements this technical note develops a unified lyapunov approach to analysis of self induced oscillations and stability for systems with piecewise linear elements for self induced oscillation within a global or regional attractor invariant level sets of a piecewise quadratic lyapunov function are obtained to bound the attractor via linear matrix inequality based optimization the analysis results for self induced oscillations are easily adapted to global or regional stability analysis

robust exponential stability of uncertain systems with time varying delays focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time varying delays the uncertainties are assumed to be continuous time varying nonlinear and norm bounded sufficient conditions for robust exponential stability are given for both single and multiple delays cases

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

common quadratic lyapunov like functions with associated switching regions for two unstable second order lti systems in this paper we establish quadratic lyapunov like functions for qualitative analysis of switched systems specifically for a class of switched systems consisting of two unstable second order lti linear time invariant subsystems we explore in detail some necessary and sufficient conditions for the existence of common weakly quadratic lyapunov like functions with associated switching regions in r 2 plane the existence conditions and the construction of such quadratic lyapunov like functions are established by using the conic switching laws

some new characterizations and properties of quasi copulas in this paper we characterize the concept of quasi copula in three different ways as a special subclass of aggregation operators in terms of its associated volume and for the bivariate case in terms of non increasing tracks on 0 1 2 we also provide sufficient conditions and new properties for quasi copulas

an lmi approach to stability of systems with severe time delay this note describes the stability problems of uncertain systems with arbitrarily time varying and severe time delay using new lyapunov krasovskii functionals less conservative stability conditions are obtained for such systems the results are illustrated using the numerical examples based on simple linear matrix inequalities

the distributivity property of increasing binary operations abstract this paper is mainly devoted to solving the functional equations of distributivity and conditional distributivity of increasing binary operations with the unit our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory in particular some assumptions namely associativity and commutativity and results about conditional distributivity of uninorms and triangular norms and triangular conorms were simplified moreover some other properties e g componentwise convexity concavity for special operations from the class of quasi copulas is considered

modularity conditions between overlap grouping function and uni nullnorm or null uninorm abstract overlap and grouping functions as two kinds of special continuous commutative aggregation functions have wide applications in image processing and classification modularity conditions between the class of overlap grouping functions satisfying o 1 e e g 0 e e and special classes of uninorms and those of another special class of overlap grouping functions over nullnorms have been studied in 49 in this paper we extend these results to any overlap grouping function moreover we study the modularity conditions between overlap grouping functions and uni nullnorms null uninorms which are the generalization of uninorms nullnorms

parametric classes of generalized conjunction and disjunction operations for fuzzy modeling it is argued that inference procedures of fuzzy models do not always require commutativity and associativity of the operations used this raises the possibility of considering nonassociative and noncommutative conjunction and disjunction operations such operations are investigated in this paper and different methods for their generation are proposed a number of new types of conjunction operations that are simpler than the known parametric classes of t norms are given and as an application example the approximation of a function by a fuzzy inference system is considered

a new boundary spectral strip method for non periodical geometrical entities based on analytical integrations abstract a method based on expanding the boundary integral equation into a trigonometric series or a high order polynom is proposed depending on the domain geometry it is a non element method which yields solutions to elastostatic and potential problems using a small computer memory yet obtaining more precise results as compared with other common numerical methods when the geometry of the problem contains circles and straight lines all the integrations required for solution of the boundary integral are solved analytically some elastostatic problems are solved here and compared with the boundary element method bem which shows some remarkable advantages of the boundary strip method over the bem

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

distributivity and conditional distributivity for uni nullnorms abstract the distributivity and conditional distributivity of a uninorm over a continuous t conorm is an open problem posed by klement in the linz seminar 2000 closing session after this the study of distributivity and conditional distributivity between two aggregation operators become specially interesting in this work we continue investigating the same topic for uni nullnorms then the full characterization of all pairs f g satisfying distributivity and conditional distributivity is given where f is a uni nullnorm g is a t norm or a t conorm or a uninorm from u min and u max

the dominance relation in some families of continuous archimedean t norms and copulas the dominance relation in several families of continuous archimedean t norms and copulas is investigated on the one hand the contribution provides a comprehensive overview on recent conditions and properties of dominance as well as known results for particular cases of families on the other hand it contains new results clarifying the dominance relationship in five additional families of continuous archimedean t norms and copulas

a complete characterization of the maximal contractively invariant ellipsoids of linear systems under saturated linear feedback as level sets of quadratic lyapunov functions ellipsoids have been extensively used as estimates of the domain of attraction of a linear system under saturated linear feedback for a linear system with a single input subject to actuator saturation based on a convex hull representation of saturation functions a necessary and sufficient condition for an ellipsoid to be contractively invariant was previously established which through the solution of an lmi problem leads to the maximal ellipsoidal invariant set in this technical note for a linear system with multiple inputs subject to actuator saturation we develop a complete characterization of the maximal ellipsoidal invariant set by algebraic computation simulation results demonstrate the effectiveness of our results

distributivity and conditional distributivity for s uninorms abstract the distributivity condition plays an essential role in the framework of fuzzy connectives this paper studies both regular and conditional distributivity equations for s uninorms and gives the characterizations of distributivity equations between some binary aggregation operators and s uninorms in u min moreover we describe t norms t uninorms and semi t operators that are conditional distributive over s uninorms

brief paper anti windup synthesis for linear control systems with input saturation achieving regional nonlinear performance in this paper we present lmi based synthesis tools for regional stability and performance of linear anti windup compensators for linear control systems we consider both static and dynamic compensators algorithms are developed that minimize the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and that minimize this upper bound with a guaranteed reachable set or domain of attraction based on the structure of the optimization problems it is shown that for systems whose plants have poles in the closed left half plane plant order dynamic anti windup can achieve semiglobal exponential stability and finite l 2 gain for exogenous inputs with l 2 norm bounded by any finite value the problems are studied in a general setting where the only requirement on the linear control system is well posedness and internal stability the effectiveness of the proposed techniques is illustrated with an example

augmented lyapunov function approach to l2 gain analysis for discrete time systems with saturation nonlinearities abstract this paper presents a method for l 2 gain analysis of discrete time systems with saturation nonlinearity by using an augmented lyapunov functional by using sector and slope properties of the saturation nonlinearity the l 2 gain performance criterion is obtained via lmi formulation the proposed lyapunov function have augmented quadratic form with states as well as the sector bounded nonlinear function numerical examples show that the proposed method is less conservative than the existing ones

corrigendum corrigendum to the distributivity condition for uninorms and t operators fuzzy sets and systems 128 2002 209 225 in this paper the study of the distributivity equation involving uninorms in u given in fuzzy sets and systems 128 2002 209 225 is revised two wrong propositions in the mentioned reference are corrected and their right versions are proved

on the distributivity between t norms and t conorms the main result presented here concerns the distributivity between triangular norms and conorms understood in an extended meaning that is maps defined on an interval a b instead of the classical interval 0 1 as a secondary result the bidistributivity has been used to characterize the union and the intersection of fuzzy sets by means of algebraic conditions

on a family of connectives for fuzzy sets abstract in this paper we find the general solution of the functional equation s t x y t x n y x where s is a t conorm t is a t norm and n is a strong negation on the unit interval in particular the result yields a family of connectives for fuzzy sets

on the conditional distributivity of nullnorms over uninorms conditional distributivity of nullnorm over uninorm with continuous operators is discussed the structure of uninorms with idempotent operators is discussed the problem of conditional distributivity for different two aggregation operators plays an important role in many different fields such as utility theory and integration theory this paper deals with the conditional distributivity of a continuous nullnorm with respect to a uninorm with the continuous underlying t norm and t conorm

piecewise affine state feedback for piecewise affine slab systems using convex optimization abstract this paper shows that lyapunov based state feedback controller synthesis for piecewise affine pwa slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities lmis analytically parameterized by a vector furthermore it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem without affecting its parameterization structure finally it is shown that piecewise affine state feedback controller synthesis for piecewise affine slab systems to maximize the decay rate of a quadratic control lyapunov function can be cast as a set of quasi concave optimization problems analytically parameterized by a vector before casting the synthesis in the format presented in this paper lyapunov based piecewise affine state feedback controller synthesis could only be formulated as a bi convex optimization program which is very expensive to solve globally thus the fundamental importance of the contributions of the paper relies on the fact that for the first time the piecewise affine state feedback synthesis problem has been formulated as a convex problem with a parameterized set of lmis that can be relaxed to a finite set of lmis and solved efficiently to a point near the global optimum using available software furthermore it is shown for the first time that in some situations the global can be exactly found by solving only one concave problem

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t conorm this paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms in particular the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict from the obtained results it is deduced that distributivity and conditional distributivity are equivalent moreover we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict

stability and performance analysis of saturated systems via partitioning of the virtual input space this paper revisits the problem of estimating the domain of attraction and the nonlinear l 2 gain for systems with saturation nonlinearities we construct a virtual input space from the algebraic loop contained in systems and divide this virtual input space into several regions in one of these regions none of the virtual inputs saturate in each of the remaining regions there is a unique virtual input that saturates everywhere with the time derivative of its saturated signal being zero these special properties of the virtual inputs in different regions of the virtual input space are combined with an existing piecewise quadratic lyapunov function that contains the information of virtual input saturation to arrive at a set of less conservative stability and performance conditions from which we can obtain a larger level set of the piecewise quadratic lyapunov function as an estimate of the domain of attraction and a tighter scalar function of the bound on the l 2 norm of the exogenous input as an estimate of the local nonlinear l 2 gain simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction and a significantly tighter estimate of the nonlinear l 2 gain than the existing methods

the distributivity condition for uninorms and t operators in this work we study the functional equation given by the distributivity condition f x g y z g f x y f x z for all x y z 0 1 where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

computation of the constrained infinite time linear quadratic regulator this paper presents an efficient algorithm for computing the solution to the constrained infinite time linear quadratic regulator clqr problem for discrete time systems the algorithm combines multi parametric quadratic programming with reachability analysis to obtain the optimal piecewise affine pwa feedback law the algorithm reduces the time necessary to compute the pwa solution for the clqr when compared to other approaches it also determines the minimal finite horizon email protected s such that the constrained finite horizon lqr problem equals the clqr problem for a compact set of states s the on line computational effort for the implementation of the clqr can be significantly reduced as well either by evaluating the pwa solution or by solving the finite dimensional quadratic program associated with the clqr for a horizon of email protected s

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

a switching anti windup design based on partitioning of the input space abstract this paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti windup compensator the closed loop system consisting of the plant the controller and the anti windup compensator is first equivalently formulated as a linear system with input deadzone we then partition the input space into several regions in one of these regions all inputs saturate with the time derivative of the saturated input being zero in each of the remaining regions there is a unique input that does not saturate the time derivative of the deadzone function associated with the unsaturating input is zero by utilizing these special properties of the inputs on an existing piecewise lyapunov function of the augmented state vector containing the deadzone function of inputs we design a separate anti windup gain for each region of the input space the switching from one anti windup gain to another is activated when the input signals leave one region for another which can be implemented online since only the measurement of the input signals is required simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

subdistributivity and superdistributivity of binary operations recently the property of distributivity of binary operations on 0 1 is of great interest both for practical as well as fundamental reasons in this paper we summarize some facts connected with distributivity and non distributivity of binary operations on 0 1 motivated by non distributive logical connectives in fuzzy set theory we show some new results concerning the above property a new direction of investigations mainly concerns the distributivity inequalities for triangular norms and conorms and their diverse generalizations in particular we look for examples of binary operations fulfilling the distributivity inequalities

piecewise quadratic lyapunov functions for systems with deadzones or saturations a piecewise quadratic lyapunov function is developed for the analysis of the global and regional performances for systems with saturation deadzone in a general feedback configuration with an algebraic loop this piecewise quadratic lyapunov function effectively incorporates the structure of the saturation deadzone nonlinearity several sector like conditions are derived to describe the complex nonlinear algebraic loop these conditions transform several performance analysis problems into optimization problems with linear or bilinear matrix inequalities the effectiveness of the results is demonstrated with numerical examples

observer based control of piecewise affine systems this paper presents a new synthesis method for both state and dynamic output feedback control of a class of hybrid systems called piecewise affine pwa systems the synthesis procedure delivers stabilizing controllers that can be proven to give either asymptotic or exponential convergence rates the synthesis method builds on existing pwa stability analysis tools by transforming the design into a closed loop analysis problem wherein the controller parameters are unknown more specifically the proposed technique formulates the search for a piecewise quadratic control lyapunov function and a piecewise affine control law as an optimization problem subject to linear constraints and a bilinear matrix inequality the linear constraints in the synthesis guarantee that sliding modes are not generated at the switching the resulting optimization problem is known to be hard but suboptimal solutions can be obtained using the three iterative algorithms presented in the paper the new synthesis technique allows con

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

spectral methods for high order equations abstract solving navier stokes equations by means of scalar potentials leads to higher order equations with low order boundary conditions this approach usually involves numerical instabilities that do not appear using the primitive navier stokes equations such difficulties can be avoided with an explicit evaluation of some of the high order derivatives at the boundary we present three numerical techniques based on this method and on spectral expansions we apply them to the linear stability analysis of thermal convection in a cylinder

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

distributivity and conditional distributivity of semi uninorms over continuous t conorms and t norms the distributivity and conditional distributivity of a uninorm and a continuous t conorm present an open problem recalled by klement in the linz2000 closing session in 2006 ruiz and torrens 14 solved this problem for the most usual known classes of uninorms recently rak 13 solved the same problem for several classes of semi uninorms i e a special class of conjunctive semi uninorms a special class of disjunctive semi uninorms and the class of idempotent semi uninorms in this work we continue to investigate the same topic as the above by focusing on two other classes of semi uninorms i e representable semi uninorms and continuous semi uninorms the obtained results are different from the case of representable uninorms and also different from the cases of other known classes of semi uninorms moreover the dual case of distributivity and conditional distributivity of the above two classes of semi uninorms over continuous t norms is also investigated and similar results are obtained

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback ellipsoids as level sets of quadratic lyapunov functions and the convex hull of ellipsoids as a level set of a certain composite quadratic lyapunov function have both been extensively used as estimates of the domain of attraction of a linear system under saturated linear feedback by expressing the saturated linear feedback law on the convex hull of a group of linear feedback laws which in turn expresses the linear system under this saturated linear feedback in a linear differential inclusion conditions have been established under which an ellipsoid or the convex hull of a group of ellipsoids are contractively invariant sets and are thus estimates of the domain of attraction these conditions are usually less conservative for single input systems than for multiple input systems in this paper we consider multiple input systems and establish conditions for contractive invariance of the convex hull of ellipsoids that are less conservative than the existing conditions

the maximal contractively invariant ellipsoids for discrete time linear systems under saturated linear feedback abstract in this paper we consider the problem of determining the maximal contractively invariant ellipsoids for discrete time linear systems with multiple inputs under saturated linear feedback we propose an algebraic computational approach to determining such maximal contractively invariant ellipsoids we divide the state space into several regions according to the saturation status of each input and compute the possible maximal contractively invariant ellipsoids on each region except the region where none of inputs saturate and on their intersections the minimal one among these possible maximal contractively invariant ellipsoids is the maximal contractively invariant ellipsoids of the system simulation results demonstrate the effectiveness of our methods

regional analysis of slope restricted lurie systems this paper considers the stability analysis of nonlinear lurie type systems where the nonlinearity is both locally sector and slope restricted convex conditions for verifying stability computing outer estimates of reachable sets and upper bounds on the induced mathcal l 2 gain in a local or global domain are proposed the conditions use a lyapunov function that is quadratic on both the states and the nonlinearity and has an integral term on the nonlinearity numerical examples outline the benefits of the proposed approach

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

flipping and cyclic shifting of binary aggregation functions we introduce two types of transformations of random variables called flipping and cyclic shifting as these transformations preserve monotonicity at the level of univariate cumulative distribution functions they can be used to develop corresponding coordinate wise transformations of binary aggregation functions we lay bare the admissibility of these transformations i e the necessary and sufficient conditions under which they result in a binary aggregation function we investigate which additional properties such as the 1 lipschitz property and 2 increasingness entail these admissibility conditions moreover we point out which of these properties are preserved under flipping and or cyclic shifting interestingly quasi copulas remain quasi copulas under flipping while copulas remain copulas under flipping as well as under cyclic shifting

contribution to free boundary problems using boundary elements trefftz approach abstract there are two main approaches to the formulation of boundary methods these are boundary integral equations and approximations by complete systems of solutions trefftz method the latter has been the subject of extensive studies by one of the authors oriented to clarifying the foundations of the method and increasing its versatility the present paper is devoted to explain the application of this procedure to free boundary problems such as signorini and friction problems in elasticity

brief paper ultimate bounded stability and stabilization of linear systems interconnected with generalized saturated functions this paper proposes some ultimate bounded stability analysis and stabilization conditions for systems involving actuators with different nonlinear elements like for instance both saturation and dead zone or both saturation and stick slip results are based on the use of a convex differential inclusion approach indeed an adequate property allowing to upper bound some product terms related to the nonlinearity is provided thus constructive conditions associated to convex optimization schemes are developed to determine suitable regions of the state space in which the closed loop trajectories can be captured

stability of uncertain piecewise affine systems with time delay delay dependent lyapunov approach this article addresses the problem of robust stability of piecewise affine pwa uncertain systems with unknown time varying delay in the state it is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available a set of linear matrix inequalities lmis is derived providing sufficient conditions for the stability of the system these conditions depend on the upper bound of the delay the main contributions of the article are as follows first new delay dependent lmi conditions are derived for the stability of pwa time delay systems second the stability conditions are extended to the case of uncertain pwa time delay systems numerical examples are presented to show the effectiveness of the approach

binary survival aggregation functions we introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas a well studied class of binary aggregation functions with a profound probabilistic interpretation to their associated survival copulas the new transformation called double flipping is the composition of two elementary flipping transformations introduced earlier each operating on one of the arguments of the aggregation function we lay bare the relationships between these elementary flipping operations and double flipping we study invariants under these transformations furthermore we characterize the transformations that preserve flippability most importantly we characterize different subclasses of flippable aggregation functions in particular aggregation functions that have an absorbing element or that have a neutral element in this investigation the key role played by quasi copulas and their dual operations is highlighted these findings support the introduction of the term survival aggregation function

distributivity between uninorms and nullnorms recently the distributivity equation was investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms generally the assumption of associativity is not necessary in consideration of distributivity equation moreover if we omit commutativity assumption consideration of the left and right distributivity conditions is reasonable previous results about distributivity between uninorms and nullnorms can be obtained as simple corollaries

regional l 2m gain analysis for linear saturating systems sufficient conditions are presented for regional stability and nonlinear l2m gain analysis of linear systems subject to saturation based on piecewise polynomial lyapunov functions the proposed conditions are formulated in terms of convex optimization problems and improve existing results both for the quadratic l2 gain and the polynomial l2m gain cases