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

disturbance observer based control for semi markovian jump systems with generally uncertain transition rate and saturation nonlinearity abstract this paper deals with the problem of disturbance observer based control dobc for semi markovian jump systems s mjss with generally uncertain transition rate tr and saturation nonlinearity unlike the existing theories the proposed method considers the external disturbance and saturation nonlinearity in s mjss with more general tr first of all to study this dobc problem the sufficient condition for stochastic stability of the system is derived by the use of lyapunov krasovskii functional then the design methods of the anti disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed loop system furthermore the maximum domain of attraction is estimated by solving an optimization iterative algorithm finally two numerical examples are given to prove the correctness of the proposed results

stochastic stability and l1 gain analysis for positive nonlinear semi markov jump systems with time varying delay via t s fuzzy model approach abstract this paper treats the issues of stochastic stability and l 1 gain analysis for continuous time positive fuzzy semi markov jump systems pfsmjss with time varying delay the system under consideration involves semi markov stochastic process related to weibull distribution the practical systems such as lotka volterra population model described by pfsmjss always need to consider the sudden change in the operating process to deal with these problems a sufficient condition for stochastic stability of pfsmjss is established which is dependent of the bound of time varying delay then based on the obtained results l 1 gain performance is analyzed in standard linear programming lp finally lotka volterra population model shows the validity of the conclusions

convergent finite difference solvers for viscosity solutions of the elliptic monge ampere equation in dimensions two and higher the elliptic monge ampere equation is a fully nonlinear partial differential equation that originated in geometric surface theory and has been applied in dynamic meteorology elasticity geometric optics image processing and image registration solutions can be singular in which case standard numerical approaches fail novel solution methods are required for stability and convergence to the weak viscosity solution in this article we build a wide stencil finite difference discretization for the monge ampere equation the scheme is monotone so the barles souganidis theory allows us to prove that the solution of the scheme converges to the unique viscosity solution of the equation solutions of the scheme are found using a damped newton s method we prove convergence of newton s method and provide a systematic method to determine a starting point for the newton iteration computational results are presented in two and three dimensions which demonstrates the speed and accuracy of the method on a number of exact solutions which range in regularity from smooth to nondifferentiable

on a splitting type algorithm for the numerical realization of contact problems with coulomb friction this paper presents and analyses an iterative process for the numerical realization of contact problems with coulomb friction which is based on the method of successive approximations combined with a splitting type approach numerical examples illustrate the efficiency of this method

a partial differential equation for the rank one convex envelope a partial differential equation pde for the rank one convex envelope is introduced the existence and uniqueness of viscosity solutions to the pde is established elliptic finite difference schemes are constructed and convergence of finite difference solutions to the viscosity solution of the pde is proven computational results are presented and laminates are computed from the envelopes results include the kohn strang example the classical four gradient example and an example with eight gradients which produces nontrivial laminates

a numerically scalable domain decomposition method for the solution of frictionless contact problems we present a domain decomposition method with lagrange multipliers for solving iteratively frictionless contact problems this method which is based on the feti method and therefore is named here the feti c method incorporates a coarse contact system that guides the iterative prediction of the active zone of contact we demonstrate numerically that this method is numerically scalable with respect to both the problem size and the number of subdomains copyright 2001 john wiley sons ltd

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

on the inequality f x d 2u ge f u g u du q we consider fully nonlinear degenerate elliptic equations with zero and first order terms we provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which extend the classical keller osserman condition for semilinear equations

h sub spl infin state feedback controller design for discrete time fuzzy systems using fuzzy weighting dependent lyapunov functions for discrete time takagi sugeno ts fuzzy systems we propose an h sub spl infin state feedback fuzzy controller associated with a fuzzy weighting dependent lyapunov function the controller which is designed via parameterized linear matrix inequalities plmis employs not only the current time but also the one step past information on the time varying fuzzy weighting functions appropriately selecting the structures of variables in the plmis allows us to find an lmi formulation as a special case

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

robust stabilization for uncertain markovian jump fuzzy systems based on free weighting matrix method this paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain markovian jump nonlinear systems the class of systems under consideration is represented by the t s fuzzy model with partly known transition probability matrix the free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain markovian jump fuzzy systems mjfss in terms of linear matrix inequalities lmis furthermore a sufficient condition for the mode dependent state feedback fuzzy controller is derived for the mjfss for all admissible parameter uncertainties finally a simulation example is provided to illustrate the effectiveness of the proposed methodology

regularity for an obstacle problem of hessian equations on riemannian manifolds abstract in this paper we study the regularity for solutions to an obstacle problem of hessian type fully nonlinear equations on riemannian manifolds as an application the existence of a c 1 1 solution is proved

observer based robust h sub spl infin control for fuzzy systems using two step procedure this paper investigates both robust h sub spl infin analysis and synthesis problems involving observer based fuzzy control via linear matrix inequality methods for which efficient optimization techniques are available the observer and controller are capable of disturbance rejection in the presence of unknown but bounded disturbance we present results in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are demonstrated by examples

on the smoothness of convex envelopes we examine differentiability properties of the convex envelope conv e of a given function e rn cc cc in terms of properties of e it is shown that c1 as well as optimal c1 a regularity results 0 a 1 can be obtained under general conditions

a tour of the theory of absolutely minimizing functions a detailed analysis of the class of absolutely minimizing functions in euclidean spaces and the relationship to the infinity laplace equation

reliable mixed h passive control for t s fuzzy delayed systems based on a semi markov jump model approach abstract this paper investigates the problem of the reliable mixed h passive control for takagi sugeno t s fuzzy delayed systems based on a semi markov jump model smjm approach the focus is to design a fuzzy fault tolerant controller such that the resulting closed loop system is stochastically stable with a prescribed mixed h passive performance level even if the actuator failures appear a semi markov process is employed to describe the encountered failures of the actuator by applying the lyapunov krasovskii method in combination with some novel inequalities some conditions on the performance analysis are established where some negative quadratic terms are fully considered to reduce the conservatism based on the conditions an explicit expression for the desired controller is given three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method

on positive solutions of fully nonlinear degenerate lane emden type equations abstract we prove existence and uniqueness results of positive viscosity solutions of fully nonlinear degenerate elliptic equations with power like zero order perturbations in bounded domains the principal part of such equations is either p k d 2 u or p k d 2 u some sort of truncated laplacians given respectively by the smallest and the largest partial sum of k eigenvalues of the hessian matrix new phenomena with respect to the semilinear case occur moreover for p k we explicitly find the critical exponent p of the power nonlinearity that separates the existence and nonexistence range of nontrivial solutions with zero dirichlet boundary condition

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

finite time h control for t s fuzzy descriptor semi markov jump systems via static output feedback abstract this paper is concerned with the finite time static output feedback h controller design problem for a type of nonlinear continuous time descriptor semi markov jump systems s mjss via takagi sugeno t s fuzzy model where the transition rates are time varying and dependent on sojourn time firstly based on the stochastic lyapunov functional sufficient conditions on singular stochastic h finite time boundedness ss h ftb for continuous time t s fuzzy descriptor s mjss are given then in order to design the static output feedback controller easily the closed loop system is represented in an augmented form furthermore based on the lower and upper bounds of the time varying transition rates and by using the matrix inequality decoupling technique a novel linear matrix inequality lmi condition on ss h ftb of closed loop system is presented meanwhile the static output feedback controller is developed in terms of lmis the proposed design method doesn t impose any constraints on system matrices or slack variables which shows less conservative results lastly numerical examples are given to demonstrate the effectiveness of the obtained methods

new passivity analysis for neural networks with discrete and distributed delays in this brief the problem of passivity analysis is investigated for a class of uncertain neural networks nns with both discrete and distributed time varying delays by constructing a novel lyapunov functional and utilizing some advanced techniques new delay dependent passivity criteria are established to guarantee the passivity performance of nns essentially different from the available results when estimating the upper bound of the derivative of lyapunov functionals we consider and best utilize the additional useful terms about the distributed delays which leads to less conservative results these criteria are expressed in the form of convex optimization problems which can be efficiently solved via standard numerical software numerical examples are provided to illustrate the effectiveness and less conservatism of the proposed results

existence through convexity for the truncated laplacians we study the dirichlet problem on a bounded convex domain of mathbb r n with zero boundary data for truncated laplacians mathcal p k pm which are degenerate elliptic operators for k n defined by the upper and respectively lower partial sum of k eigenvalues of the hessian matrix we establish a necessary and sufficient condition theorem 1 in terms of the flatness of domains for existence of a solution for general inhomogeneous term this result in particular shows that the strict convexity of the domain is sufficient for the solvability of the dirichlet problem the result and related ideas are applied to the solvability of the dirichlet problem for the operator mathcal p k with lower order term when the domain is strictly convex and the existence of principal eigenfunctions for the operator mathcal p 1 an existence theorem is presented with regard to the principal eigenvalue for the dirichlet problem with zero th order term for the operator mathcal p 1 a nonexistence result is established for the operator mathcal p k with first order term when the domain has a boundary portion which is nearly flat furthermore when the domain is a ball we study the dirichlet problem with a constant inhomogeneous term and a possibly sign changing first order term and the associated eigenvalue problem

the dirichlet problem for the convex envelope the convex envelope of a given function was recently characterized as the solution of a fully nonlinear partial differential equation pde in this article we study a modified problem the dirichlet problem for the underlying pde the main result is an optimal regularity result differentiability c1 regularity of the boundary data implies the corresponding result for the solution in the interior despite the fact that the solution need not be continuous up to the boundary secondary results are the characterization of the convex envelope as i the value function of a stochastic control problem and ii the optimal underestimator for a class of nonlinear elliptic pdes

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

adaptive t s fuzzy control design for fractional order systems with parametric uncertainty and input constraint abstract thanks to the superiority of fractional differential equations in modeling high technology dynamical real world systems the design and control of fractional order systems have been widely investigated in recent decades on the other hand supposing that dynamic equations of the fractional order systems usually include various parameters and nonlinear terms takagi sugeno t s fuzzy models with if then rules can used to characterize the systems dynamics also the control community knows that there are usually some nonlinearities such as dead zone backlash hysteresis and saturation in control actuators which can decrease the ideal prescribed performance of the fractional systems the saturation nonlinearity is perhaps the most commonly existed one in control applications of fractional nonlinear systems that should be compensated by a proper method so this article proposes a novel adaptive t s fuzzy variable structure control technique for nonlinear fractional order systems in spite of the saturating input and control fluctuations the parameters of the fractional system as well as those of the saturation function are presumed to be unknown accordingly update rules are extracted to estimate such fluctuations then simple adaptive linear like control rules are developed according to the t s fuzzy control theory the stability of the origin equilibrium point of the final closed loop system is assured by lyapunov stability theory at last comparative computer simulations are presented to highlight the accuracy and applicability of the proposed adaptive fuzzy saturated control methodology

filtering based robust fault detection of fuzzy jump systems this paper studies the robust fault detection filter rfdf design problems for uncertain nonlinear markov jump systems with state delays and parameter uncertainties by means of takagi sugeno fuzzy models the dynamics of filtering error generator and the fuzzy rfdf system are constructed with the aid of the selected weighting matrix function the design objective is to find an optimal rfdf which results in a minimal difference between the reference model ideal solution and the rfdf real solution to be designed a sufficient condition is firstly established on the stochastic stability by using stochastic lyapunov krasovskii functional approach then in terms of linear matrix inequalities techniques sufficient conditions on the existence of fuzzy rfdf are presented and proved finally the design problem is formulated as an optimization algorithm simulation results illustrate that the proposed rfdf can detect the faults shortly after the occurrences

new criteria of stability analysis for generalized neural networks subject to time varying delayed signals abstract this paper focuses on the new criteria of stability analysis for generalized neural networks gnns subject to time varying delayed signals a new methodology is employed with the aids of slack variables by constructing an augmented lyapunov krasovskii functional lkf involving newton leibniz enumerating and triple integral term some less conservative conditions are achieved in terms of linear matrix inequality lmi numerical examples including real time application are given to illustrate the superiority and effectiveness of proposed approach

adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements this paper investigates the adaptive fuzzy backstepping control and h infty performance analysis for a class of nonlinear systems with sampled and delayed measurements in the control scheme a fuzzy estimator fe model is used to estimate the states of the controlled plant while the fuzzy logic systems are used to approximate the unknown nonlinear functions in the nonlinear system the controller is obtained based on the fe model by combining the backstepping technique with the classic adaptive fuzzy control method in the stability analysis all the signals in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded suub and the outputs of the system are proven to converge to a small neighborhood of origin furthermore the h infty performance is investigated and the outputs of the closed loop system are bounded in the h infty sense two examples are given to illustrate the effectiveness of the proposed control scheme

technical communique dissipative analysis and control of state space symmetric systems the paper addresses the problem of analysis and static output feedback control synthesis for strict quadratic dissipativity of linear time invariant systems with state space symmetry as a particular case of dissipative systems we consider the mixed h and positive real performance criterion and we develop an explicit expression for calculating the h norm of these systems subsequently an explicit parametrization of the static output feedback control gains that solve the mixed h and positive real performance problem is obtained numerical examples demonstrate the use and computational advantages of the proposed explicit solutions

static output feedback h control of a class of nonlinear discrete time systems this paper is concerned with the problem of designing robust h static output feedback sof controllers for a class of discrete time nonlinear systems which are represented by t s fuzzy models by considering the properties of system output matrices a method for h sof control synthesis is developed in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing techniques for designing sof controllers the new proposed method can give less conservative results by removing the constraint that the considered lyapunov matrix is diagonal numerical examples are given to illustrate the effectiveness of the proposed design method

fault estimation and tolerant control for fuzzy stochastic systems this paper deals with the problem of fault estimation and fault tolerant control for takagi sugeno t s fuzzy stochastic systems with sensor failures where the system under consideration contains ito type stochastic disturbances a new robust observer technique is presented to obtain the estimates of the system states and the sensor faults simultaneously and a fuzzy fault tolerant control scheme is developed to guarantee the closed loop system to be exponentially stable in mean square sufficient conditions are obtained for the existence of admissible controllers and it is shown that the reachability of the sliding mode dynamics can be guaranteed under the proposed control techniques finally a numerical example is provided to illustrate the effectiveness and applicability of the theoretic results obtained

distributed cooperative learning over time varying random networks using a gossip based communication protocol abstract motivated by applications of distributed estimation and distributed decision making in wireless sensor networks wsns and unmanned aerial vehicle uav networks we study a distributed learning problem over time varying undirected random networks using a gossip based communication protocol a novel distributed cooperative learning dcl algorithm termed the gossip based dcl gbdcl algorithm is presented to solve the problem by training the raw data distributed and blocked throughout different nodes exploiting the robustness of the gossip based protocol each node is guaranteed to build the same learning model in theory against random disconnections and communication route variations in the network topology it is proved that the gbdcl algorithm converges to the optimal consensus asymptotically the correctness and effectiveness of the presented gbdcl algorithm are verified in the theoretical analysis and simulations

fuzzy semi markov migration process in credit risk we explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory we prove that a fuzzy market is viable if and only if an equivalent martingale measure exists from which we construct the forward probability measure and under which the discounted price of a default free bond is a martingale we model the evolution of credit migration of a defaultable bond as an inhomogeneous semi markov process with fuzzy states we study the effects of changing the real probability measure to a forward probability measure in addition we investigate the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default finally we discuss parameter estimation and calibration of the inhomogeneous markov chain with fuzzy states

improved fuzzy control design for nonlinear markovian jump systems with incomplete transition descriptions this paper addresses the state feedback control of nonlinear continuous time markovian jump systems the nonlinearity is represented by takagi sugeno fuzzy models and the transition probability matrix is assumed to be partly known some elements in the matrix are known some are unknown but with known lower and upper bounds and some are completely unknown by making full use of the continuous property of the transition probability matrix new sufficient conditions for the stochastic stability of the system are obtained in terms of linear matrix inequalities we show that the conditions given are less conservative than or at least the same as those for existing results moreover using the conditions obtained we establish a method for design of a h state feedback controller numerical examples illustrate the effectiveness of the proposed method

improved delay dependent robust stabilization conditions of uncertain t s fuzzy systems with time varying delay this paper aims to develop simplified yet improved delay dependent robust control for uncertain t s fuzzy systems with time varying delay this is achieved through constructing new lyapunov krasovskii functionals and improving jensen s inequality unlike existing work in this area the approach developed in this paper employs neither free weighing matrices nor model transformations as a result simplified yet improved stability conditions are obtained for t s fuzzy systems with norm bounded type uncertainties for controller synthesis of the fuzzy systems the stabilization problem with memoryless state feedback control is solved via utilizing a cone complementarity minimization algorithm numerical examples are given to demonstrate the effectiveness of the proposed approach

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

numerical implementation of two nonconforming finite element methods for unilateral contact we consider the finite element approximation of the unilateral contact problem between elastic bodies we are interested in a practical problem which often occurs in finite element computations concerning two independently discretized bodies in unilateral contact it follows that the nodes of both bodies located on the contact surface do not fit together we present two different approaches in order to define unilateral contact on nonmatching meshes the first is an extension of the mortar finite element method to variational inequalities that defines the contact in a global way on the contrary the second one expresses local node on segment contact conditions in both cases the theoretical approximation properties are given then we implement and compare the two methods

analysis of frictional contact problem using boundary element method and domain decomposition method in this paper we study the bilateral or unilateral contact with coulomb friction between two elastic solids using a domain decomposition method coupled with the boundary element method the decomposition method we have selected is the schur complement method a non overlapping technique it enables to reduce the solution of the global problem to the solution of a problem defined only on the contact surface moreover its principal advantage is that computing is done separately on each solid we have chosen to associate it with the boundary element method indeed it only requires the discretization of the boundaries of solids this technique of coupling reduces the number of unknowns and the time of computing we have applied it to the study of indentation of an elastic foundation by an elastic flat punch and a sphere in this last case our results are in conformity with the hertz theory and the analytical solution of spence moreover we have shown the influence of friction on the size of the contact radius and on the normal pressure at centre copyright 1999 john wiley sons ltd

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

a novel approach to stability and stabilization of fuzzy sampled data markovian chaotic systems abstract this paper studies the problems of stability and stabilization of a class of markovian chaotic systems via fuzzy sampled data control different from some existing results the markovian jumping with general uncertain transition rates is considered for such systems a novel approach i e input delay dependent vector approach is proposed for the first time based on this approach an input delay dependent lyapunov krasovskii functional lkf with cubic function of input delay is successfully constructed and the convex combination technique is used with ease to derive stability and stabilization criteria compared with some existing stability and stabilization criteria for chaotic systems our results are not only less conservative but also with reduced calculation complexity finally the superiorities of proposed results are illustrated by two numerical examples

solution of contact problems by feti domain decomposition with natural coarse space projections abstract an efficient non overlapping domain decomposition algorithm of the neumann neumann type for solving both coercive and semicoercive contact problems is presented the discretized problem is first turned by the duality theory of convex programming to the quadratic programming problem with bound and equality constraints and the latter is further modified by means of orthogonal projectors to the natural coarse space introduced by farhat and roux in the framework of their feti method the resulting problem is then solved by an augmented lagrangian type algorithm with an outer loop for the lagrange multipliers for the equality constraints and an inner loop for the solution of the bound constrained quadratic programming problems the projectors are shown to guarantee fast convergence of iterative solution of auxiliary linear problems and to comply with efficient quadratic programming algorithms proposed earlier reported theoretical results and numerical experiments indicate high numerical scalability of the algorithm which preserves the parallelism of the feti methods

optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations in this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients more precisely we deal with coefficients and right hand sides rhs in lq with q geq n this extends the result of caffarelli on the c loc 1 1 regularity of the convex envelope of supersolutions of fully nonlinear elliptic equations with bounded rhs moreover we also provide a regularity result with estimates for omega semiconvex functions that are supersolutions to the same type of equations with unbounded rhs i e rhs in l q q geq n by a completely different method our results here extend the recent regularity results obtained by braga et al adv math 334 184 242 2018 for q n as far as fully nonlinear pdes are concerned these results include in particular the apriori estimate obtained by caffarelli et al commun pure appl math 38 2 209 252 1985 on the modulus of continuity of the gradient of omega semiconvex supersolutions for linear equations and bounded rhs that have a holder modulus of semiconvexity

further robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delay via relaxed integral inequality abstract this paper focuses on robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delays two delay product type terms are introduced for constructing a new lyapunov krasovskii functional which contains more information of time varying delay and a novel relaxed integral inequality is applied to estimate the derivative of lkf for achieving reduction of estimation gap as a result several further robust stability criteria with less conservativeness are proposed finally three numerical examples and an application to control of a truck trailer are provided to show the effectiveness and advantages of the presented methods

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

robust h fuzzy control for uncertain nonlinear markovian jump systems with time varying delay this paper investigates the problem of robust h fuzzy control for a class of uncertain nonlinear markovian jump systems with time varying delay the class of systems under consideration is described by the takagi sugeno fuzzy model the goal of the paper is to design a mode dependent fuzzy state feedback controller such that the closed loop system is stochastically stable with a prescribed h performance of disturbance attenuation for all admissible parameter uncertainties in order to obtain a less conservative control design a new stochastic lyapunov krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals then by employing this functional a delay decomposition approach to the design of robust h fuzzy controllers is developed in terms of linear matrix inequalities finally two examples are given to illustrate the merit and usability of the proposed design method

the augmented lagrangian method for equality and inequality constraints in hilbert spaces in this paper we consider an augmented lagrangian method for the minimization of a nonlinear functional in the presence of an equality constraint whose image space is in a hilbert space an inequality constraint whose image space is finite dimensional and an affine inequality constraint whose image space is in an infinite dimensional hilbert space we obtain local convergence of this method without imposing strict complementarity conditions when the equality as well as the inequality constraint with finite dimensional image space are augmented to the author s knowledge this result even generalizes the convergence results which are known when all spaces are finite dimensional

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

passivity analysis and passive control of fuzzy systems with time varying delays this paper is concerned with the passive controller design problem for a class of continuous time takagi sugeno t s fuzzy systems with both state and input delays the delays are assumed to be time varying and differentiable a notion of very strict passivity is adopted the purpose is to design a state feedback fuzzy controller such that the resulting closed loop system is very strictly passive vsp delay dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time delay systems and fuzzy systems these conditions are expressed by means of strict linear matrix inequalities lmis that can be easily solved a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method

local stabilization for discrete time t s fuzzy time delay systems with sensor fault abstract this paper focuses on a local stabilization problem for discrete time t s fuzzy time delay systems with sensor fault and external disturbances the main purpose is to synthesize a controller such that the state can be restricted into a pre specified region even when the system is subject to sensor fault and external disturbance first by restricting the reachable set into an ellipsoid set which is contained in the objective domain the system state is restricted into the objective area such that the local stabilization can be achieved second the differential mean value theorem is used to determine the bound of the deviation between the membership function of the system and that of the controller then the information of the deviation is employed for designing the controller different from some existing methods in the proposed method the influence of the sensor fault on the membership function of the controller has been fully considered and the information of aforementioned deviation is made full use of such that a less conservative stability criterion can be derived meanwhile due to the use of the differential mean value theorem the deviation bound can be calculated then the requirement where the deviation bound of is assumed to be previously known is removed finally an example is presented to verify the effectiveness of the proposed method

uzawa block relaxation domain decomposition method for the two body contact problem with tresca friction we propose a uzawa block relaxation domain decomposition method for a two body contact problem with tresca friction we introduce auxiliary interface unknowns to transform the variational problem into a saddle point problem applying a uzawa block relaxation algorithm to the corresponding augmented lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two uncoupled linear elasticity subproblems in each iteration the auxiliary unknowns are computed explicitly using kuhn tucker conditions and fenchel duality theory numerical experiments show the scalability of the domain decomposition algorithm on matching or nonmatching meshes for two or three dimensional contact problems

implementation of the fixed point method in contact problems with coulomb friction based on a dual splitting type technique the paper deals with the numerical solution of the quasi variational inequality describing the equilibrium of an elastic body in contact with a rigid foundation under coulomb friction after a discretization of the problem by mixed finite elements the duality approach is exploited to reduce the problem to a sequence of quadratic programming problems with box constraints so that efficient recently proposed algorithms may be applied a new variant of this method is presented it combines fixed point with block gauss seidel iterations the method may be also considered as a new implementation of fixed point iterations for a sequence of problems with given friction results of numerical experiments are given showing that the resulting algorithm may be much faster than the original fixed point method and its efficiency is comparable with the solution of frictionless contact problems

conditions of output stabilization for nonlinear models in the takagi sugeno s form this paper deals with the control law design with an observer for models in the takagi sugeno s ts form in the general case where the nonlinearities and the variables involved are not measurable the results presented in this paper give sufficient conditions of stabilization for the global loop i e ts model stabilized with a state feedback and a fuzzy observer conditions are given in the form of linear matrix inequalities lmi problem

finite time h reliable control for t s fuzzy systems with variable sampling abstract this work mainly concentrates on the finite time h reliable control for t s fuzzy systems with aperiodic sampling by considering the information of the state an improved lyapunov krasovskii functional lkf is structured moreover based on free weighted method and aperiodic sampling techniques further criteria are proposed to guarantee that the t s fuzzy systems is finite time stabilization with h performance meanwhile the h reliable controller is designed with larger sampling interval finally the advantages of the obtained results are affirmed by a truck trailer system

a numerical approach to variational problems subject to convexity constraint we describe an algorithm to approximate the minimizer of an elliptic functional in the form int omega j x u nabla u on the set cal c of convex functions u in an appropriate functional space x such problems arise for instance in mathematical economics 4 a special case gives the convex envelope u 0 of a given function u 0 let t n be any quasiuniform sequence of meshes whose diameter goes to zero and i n the corresponding affine interpolation operators we prove that the minimizer over cal c is the limit of the sequence u n where u n minimizes the functional over i n cal c we give an implementable characterization of i n cal c then the finite dimensional problem turns out to be a minimization problem with linear constraints

observer design for takagi sugeno descriptor models this paper considers observer design for nonlinear descriptor systems we propose approaches based on takagi sugeno ts models an extended estimation vector is used in order to keep the descriptor structure of the observer the design conditions are expressed as linear matrix inequalities the proposed observer structure via an intermediate variable as estimated variable is able to recover the previous observer results for ts descriptors moreover through a direct extension via so called finsler s lemma relaxed conditions are obtained numerical examples show the effectiveness of the proposed approaches

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

stability and dissipativity analysis of distributed delay cellular neural networks in this brief the problems of delay dependent stability analysis and strict q s dissipativity analysis are investigated for cellular neural networks cnns with distributed delay first by introducing an integral partitioning technique two new forms of lyapunov krasovskii functionals are constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities based on this criterion a new sufficient delay and dependent condition is given to guarantee that the cnns with distributed delay are strictly q s dissipative the results developed in this brief can tolerate larger allowable delay than existing ones in the literature which is demonstrated by several examples

fast finite difference solvers for singular solutions of the elliptic monge ampere equation the elliptic monge ampere equation is a fully nonlinear partial differential equation which originated in geometric surface theory and has been applied in dynamic meteorology elasticity geometric optics image processing and image registration solutions can be singular in which case standard numerical approaches fail in this article we build a finite difference solver for the monge ampere equation which converges even for singular solutions regularity results are used to select a priori between a stable provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain this allows singular solutions to be computed using a stable method and regular solutions to be computed more accurately the resulting nonlinear equations are then solved by newton s method computational results in two and three dimensions validate the claims of accuracy and solution speed a computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

fault detection for discrete time markov jump linear systems with partially known transition probabilities in this article the fault detection fd problem for a class of discrete time markov jump linear system mjls with partially known transition probabilities is investigated the proposed systems are more general which relax the traditional assumption in markov jump systems that all the transition probabilities must be completely known a residual generator is constructed and the corresponding fd is formulated as an h filtering problem by which the error between residual and fault are minimised in the h sense the linear matrix inequality based sufficient conditions for the existence of fd filter are derived a numerical example on a multiplier accelerator model economic system is given to illustrate the potential of the developed theoretical results

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 consensus control for a class of multi agent systems via distributed pid algorithm and weighted edge dynamics abstract this paper studies the robust proportional integral derivative pid consensus control for a class of linear multi agent systems mass with external disturbances different from the existing results both the consensus analysis and the transient performance characteristics for high order linear mass are considered based on a factorization of laplacian matrix the initial mas is firstly transformed into the so called weighted edge dynamics and then a design equivalence between the proposed pid consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results furthermore by combining lyapunov theory and barbalat s lemma it is proved that both the stabilization of weighted edge dynamics and the consensus of mas can be guaranteed even in the presence of external disturbances in particular some relationships between the transient time performance of weighted edge dynamics and the pid design parameters are given finally some numerical examples on lc oscillator network are provided to illustrate the validity of theoretical results

mixed h infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays in this brief the problems of the mixed h infinity and passivity performance analysis and design are investigated for discrete time delay neural networks with markovian jump parameters represented by takagi sugeno fuzzy model the main purpose of this brief is to design a filter to guarantee that the augmented markovian jump fuzzy neural networks are stable in mean square sense and satisfy a prescribed passivity performance index by employing the lyapunov method and the stochastic analysis technique applying the matrix decomposition techniques sufficient conditions are provided for the solvability of the problems which can be formulated in terms of linear matrix inequalities a numerical example is also presented to illustrate the effectiveness of the proposed techniques

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem