adaptive multilevel methods in space and time for parabolic problems the periodic case the aim of this paper is to display numerical results that show the interest of some multilevel methods for problems of parabolic type these schemes are based on multilevel spatial splittings and the use of dierent time steps for the various spatial components the spatial discretization we investigate is of spectral fourier type so the approximate solution naturally splits into the sum of a low frequency compo nent and a high frequency one the time discretization is of implicit explicit euler type for each spatial component based on a posteriori estimates we introduce adaptive one level and mul tilevel algorithms two problems are considered the heat equation and a nonlinear problem numerical experiments are conducted for both problems using the one level and the multilevel algorithms the multilevel method is up to 70 faster than the one level method

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

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

novel stability criteria for t s fuzzy systems in this paper novel stability conditions for takagi sugeno t s fuzzy systems are presented the so called nonquadratic membership dependent lyapunov function is first proposed which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature then new membership dependent stability conditions are developed by the new lyapunov function approach it is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical results

modeling and controller design for complex flexible nonlinear systems via a fuzzy singularly perturbed approach this paper investigates the problems of modeling and controller design for complex flexible nonlinear systems cfnss based on a fuzzy singularly perturbed model a standard discrete time fuzzy singularly perturbed model fspm is firstly constructed to estimate cfnss based on a matrix spectral norm approach a static output feedback controller is designed which guarantees the resulting closed loop system is asymptotically stable the gains of controllers are obtained by solving a set of e independent linear matrix inequalities lmis so the ill conditioned problems caused by e can be easily avoided finally the proposed approach is applied to modeling and attitude control of flexible satellites in contrast to the existing results the proposed method has the following advantages i flexible vibrations can be effectively suppressed and ii the control performance is greatly improved as well as iii the control inputs do not need to be limited in controller design two practical examples are provided to illustrate the effectiveness of the presented approach from the simulation results it can be seen that the proposed approach can also effectively overcome the external disturbances and noises

stabilization of networked stochastic time delay fuzzy systems with data dropout this paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout the plant in the networked control system ncs under consideration is a discrete stochastic time delay nonlinear system represented by a takagi sugeno fuzzy model exponential stability criteria of the ncs are developed by using a common quadratic lyapunov function and a fuzzy lyapunov function respectively a stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software three numerical examples are presented to demonstrate the effectiveness of the proposed methods

stabilisation of polytopic singularly perturbed linear systems this article deals with two time scale polytopic linear systems in the singular perturbation form and in discrete time the aim is to propose well conditioned convex conditions for stability analysis and control design as the classical lti time scale separation based approach is not successful in the case of polytopic singularly perturbed systems our method leads to linear matrix inequality conditions independent of the singular perturbation parameter and offers an interesting solution from a numerical point of view in addition the conservatism of the proposed approach is limited as it is based on parameter dependent lyapunov functions a numerical example taken from the literature illustrates the effectiveness of the given stabilisation conditions

brief robust output feedback control of nonlinear singularly perturbed systems in this work we consider nonlinear singularly perturbed systems with time varying uncertain variables for which the fast subsystem is asymptotically stable and the slow subsystem is input output linearizable and possesses input to state stable iss inverse dynamics for these systems we synthesize a robust output feedback controller that ensures boundedness of the state and enforces robust asymptotic output tracking with attenuation of the effect of the uncertain variables on the output of the closed loop system the controller is constructed through combination of a high gain observer with a robust state feedback controller synthesized via lyapunov s direct method the proposed controller enforces the aforementioned properties in the closed loop system for initial conditions uncertainty and rate of change of uncertainty in arbitrarily large compact sets provided that the singular perturbation parameter is sufficiently small and the observer gain is sufficiently large

stability analysis and synthesis of fuzzy singularly perturbed systems in this paper we investigate the stability analysis and synthesis problems for both continuous time and discrete time fuzzy singularly perturbed systems for continuous time case both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities lmis for discrete time case only the analysis problem can be cast in lmis while the derived stability conditions for controller design are nonlinear matrix inequalities nmis furthermore a two stage algorithm based on lmi and iterative lmi ilmi techniques is developed to solve the resulting nmis and the stabilizing feedback controller gains can be obtained for both continuous time and discrete time cases the reduced control law which is only dependent on the slow variables is also discussed finally an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures

galerkin and subspace decomposition methods in space and time for the navier stokes equations abstract the galerkin method and the subspace decomposition method in space and time for the two dimensional incompressible navier stokes equations with the h 2 initial data are considered the subspace decomposition method consists of splitting the approximate solution as the sum of a low frequency component discretized by the small time step t and a high frequency one discretized by the large time step p t with p 1 the h 2 stability and l 2 error analysis for the subspace decomposition method are obtained finally some numerical tests to confirm the theoretical results are provided

new results on h filtering for fuzzy systems with interval time varying delays this paper investigates the problem of h filtering for continuous takagi sugeno t s fuzzy systems with an interval time varying delay in the state based on the delay partitioning idea a new approach is proposed for solving this problem which can achieve much less conservative feasibility conditions the attention is focused on the design of an h filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the h attenuation level from disturbance to estimation error is below a prescribed scalar the constructed lyapunov krasovskii functional by applying the delay partitioning method can potentially guarantee the obtained delay dependent conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software finally an example is illustrated to show the reduction in conservatism of the proposed filter design method

adaptive sliding mode control design for a class of uncertain singularly perturbed nonlinear systems this paper addresses adaptive sliding mode control asmc of uncertain singularly perturbed nonlinear uspn systems with guaranteed h control performance first we use takagi sugeno t s fuzzy model to construct the uspn systems then the sliding surface can be determined via linear matrix inequality lmi design procedure second we propose neural network nn based asmc design to stabilise the uspn systems the proposed methods are based on the lyapunov stability theorem the adaptive law can reduce the effect of uncertainty the proposed nn based asmc will stabilise the uspn systems for all 0 simulation result reveals that the proposed nn based asmc scheme has better convergence time compared with the fuzzy control scheme li t h s lin k j 2004 stabilization of singularly perturbed fuzzy systems ieee transactions on fuzzy systems 12 579 595

distributed quantized multi modal h fusion filtering for two time scale systems abstract in this paper we deal with the distributed h fusion filtering problem for a class of discrete time system with significant modal difference in the time scale the nonstandard singularly perturbed model spm is employed to describe the addressed two time scale system where the small perturbation parameter e reflects the discrepancies in the time scale some sufficient conditions are provided to guarantee the existence of the parameters of the local filters for the spm where o e 2 the second order correction terms in e is eliminated and an upper bound of e is calculated to enhance the filtering accuracy and scalability the estimates provided by the local filter are transmitted to the fusion centre via the communication network in the presence of the bandwidth constraint a quantized fusion scheme is developed and the design of the fusion parameters is cast into a convex optimization problem finally an example on the f 8 airplane is provided to verify the validity and applicability of the proposed methodology

a descriptor system approach to singular perturbation of linear regulators the relationship between the regulator problem for a singularly perturbed system and the analogous one for a descriptor system is investigated meanwhile a decomposition approach is provided for solution of the linear quadratic regulator problem for singularly perturbed systems this approach is a significant advance over the two stage method

fuzzy model based nonfragile control for nonlinear singularly perturbed systems with semi markov jump parameters this paper is concerned with the fuzzy model based nonfragile control problem for discrete time nonlinear singularly perturbed systems with stochastic jumping parameters the stochastic parameters are generated from the semi markov process the memory property of the transition probabilities among subsystems is fully considered in the investigated systems consequently the restriction that the transition probabilities are memoryless in widely used discrete time markov jump model can be removed based on the t s fuzzy model approach and semi markov kernel concept several criteria ensuring delta error mean square stability of the underlying closed loop system are established with the help of those criteria the designed procedures which could well deal with the fragility problem in the implementation of the proposed fuzzy model based controller are presented a technique is developed to estimate the permissible maximum value of singularly perturbed parameter for discrete time nonlinear semi markov jump singularly perturbed systems finally the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit model

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

multilevel methods in space and time for the navier stokes equations we investigate the discretization in time of numerical schemes based on multilevel spatial splittings for the two dimensional periodic navier stokes equations the approximate solution is computed as the sum of a low frequency component and a high frequency one these two terms are advanced in time using different stepsizes we show improved stability conditions with respect to the classical galerkin method we derive error estimates that indicate that the high frequency term can be integrated less often we address implementation issues and show that the method should yield a significant gain in computing time

lur e lyapunov function and absolute stability criterion for lur e singularly perturbed systems this technical note investigates the absolute stability problem for lur e singularly perturbed systems with multiple nonlinearities the objective is to determine if the system is absolutely stable for any e 0 e0 where e denotes the perturbation parameter and e0 is a pre defined positive scalar first an e dependent lur e lyapunov function is constructed that facilitates the stability analysis of the singularly perturbed system then a stability criterion expressed in terms of e independent linear matrix inequalities lmis is derived based on the stability criterion an algorithm is proposed to compute the stability bound that is shown to be less conservative than those computed using other existing methods finally examples are given to show the feasibility and effectiveness of the obtained method

numerics and hydrodynamic stability toward error control in computational fluid dynamics we critically review the available error analysis in computational fluid dynamics cfd and come to the conclusion that the existing error estimates are meaningless in most cases of interest we propose a new approach to error analysis in cfd aiming at reliable and efficient adaptive quantitative error control this is based on a precise analysis of hydrodynamic stability coupled with galerkin orthogonality we prove a priori and a posteriori type error estimates in a model case for pipe flow formulate corresponding adaptive algorithms and discuss the potential of this approach for adaptive error control in cfd

static output feedback simultaneous stabilization ilmi approach in this note the static output feedback simultaneous stabilization problem is addressed using a matrix inequality approach a necessary and sufficient condition for simultaneous stabilizability of r proper mimo plants via static output feedback is obtained it is proven that the existence of a stabilizing feedback gain which simultaneously stabilizes this set of plants is equivalent to that of the solution of a set of coupled quadratic matrix inequalities an iterative lmi ilmi algorithm based on the linear matrix inequality technique is proposed to obtain the feedback gain illustrated examples show its effectiveness

h_ bm infty fuzzy filtering of nonlinear systems with intermittent measurements this paper is concerned with the problem of h infin fuzzy filtering of nonlinear systems with intermittent measurements the nonlinear plant is represented by a takagi sugeno t s fuzzy model the measurements transmission from the plant to the filter is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements attention is focused on the design of an h infin filter such that the filter error system is stochastically stable and preserves a guaranteed h infin performance a basis dependent lyapunov function approach is developed to design the h infin filter by introducing some slack matrix variables the coupling between the lyapunov matrix and the system matrices is eliminated which greatly facilitates the filter design procedure the developed theoretical results are in the form of linear matrix inequalities lmis finally an illustrative example is provided to show the effectiveness of the proposed approach

error estimates on a new nonlinear galerkin method based on two grid finite elements a new nonlinear galerkin method based on finite element discretization is presented in this paper for semilinear parabolic equations the new scheme is based on two different finite element spaces defined respectively on one coarse grid with grid size h and one fine grid with grid size h ll h nonlinearity and time dependence are both treated on the coarse space and only a fixed stationary equation needs to be solved on the fine space at each time with linear finite element discretizations it is proved that the difference between the new nonlinear galerkin solution and the standard galerkin solution in h 1 omega norm is of the order of h 3

h control for fuzzy singularly perturbed systems in this paper both the state feedback and static output feedback h controllers for fuzzy singularly perturbed systems are investigated we give sufficient conditions for the existence of h controller such that the closed loop fuzzy control system is globally stable and achieves a prescribed level of disturbance attenuation for sufficiently small perturbation parameters the linear matrix inequality lmi approach is proposed to obtain the state feedback gains and a homotopy based iterative lmi algorithm is developed to get the static output feedback gains simulation results for two examples are included to demonstrate the effectiveness of the proposed approaches

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

control synthesis of singularly perturbed fuzzy systems this paper considers the problem of designing stabilizing and hinfin controllers for nonlinear singularly perturbed systems described by takagi sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e for the synthesis problem of simultaneously designing the bound of e and stabilizing or hinfin controllers linear matrix inequalities lmi based methods are presented for evaluating the upper bound of e subject to stability or a prescribed hinfin performance bound constraint for the resulting closed loop system sufficient conditions are developed respectively for the stabilizing and hinfin control synthesis without the consideration of improving the bound of e new design methods are also given in terms of solutions to a set of lmis examples are given to illustrate the efficiency of the proposed methods

brief the infinite time near optimal decentralized regulator problem for singularly perturbed systems a convex optimization approach this paper presents lq decentralized pole location for singularly perturbed systems the poles are located in a sector included in the left half complex plane the singular perturbation method is used to define reduced and well behaved problems it is shown that the lq control problem with pole location in a sector can be solved using the lmi tool the associated parametrical optimization problem involves a linear cost objective under lmi constraints the decentralized control problem is then solved in the reduced slow system by just introducing structure constraints on the matrix variables constraints that do not destroy the linearity and then the convexity of the problem

on the exponential stability of singularly perturbed systems this paper establishes some results and properties related to the exponential stability of general dynamical systems and in particular singularly perturbed systems for singularly perturbed systems it is shown that if both the reduced order system and the boundary layer system are exponentially stable then provided that some further regularity conditions are satisfied the full order system is exponentially stable for sufficiently small values of the perturbation parameter mu and its rate of convergence approaches that of the reduced order system mu 0 as mu approaches zero exponentially decaying norm bounds are given for the slow and fast components of the full order system trajectories to achieve this result a new converse lyapunov result for exponentially stable systems is presented

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

gerbershiu analysis with two sided acceptable levels in this paper insurers surplus process moved within upper and lower levels is analyzed to this end a truncated type of gerbershiu function is proposed by further incorporating the minimum and the maximum surplus before ruin into the existing ones e g gerber and shiu 1998 cheung et al 2010a a key component in our analysis of this proposed gerbershiu function is the so called transition kernel explicit expressions of the transition function under two different risk models are obtained these two models are both generalizations of the classical poisson risk model i the first model provides flexibility in the net premium rate which is dependent on the surplus such as linear or step function and ii the second model assumes that claims arrive according to a markovian arrival process map finally we discuss some applications of the truncated gerbershiu function with numerical examples under various scenarios

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

a robust h_ infty non pdc design scheme for singularly perturbed t s fuzzy systems with immeasurable state variables this paper addresses an observer based robust h infty fuzzy controller design method for singularly perturbed nonlinear systems with external disturbances which are represented by uncertain takagi sugeno t s fuzzy models for a practical output feedback design the premise variables of the fuzzy controller and the fuzzy observer are considered unknown in general a fuzzy lyapunov function is utilized for the synthesis of the nonparallel distributed compensation based controller the closed loop singularly perturbed t s fuzzy system is asymptotically robustly stable in the absence of disturbances and satisfies an h infty norm condition in the presence of disturbances for all positive values of the singular perturbation parameter within the given desired bound using the descriptor redundancy approach some strict linear matrix inequality lmi conditions are derived for the h infty robustness of the closed loop system when uncertainties are simultaneously considered in all state space matrices of each fuzzy subsystem the main disadvantage of a fuzzy lyapunov function based design is that the bounds on the derivatives of the membership functions must be known a priori inspired by a recent work that provides the bounds of the membership derivatives for a given arbitrary compact set on the state space a new method is proposed that guarantees that the closed loop observer based uncertain singularly perturbed t s fuzzy system remains robustly stable in the compact set using finsler s lemma the resulting design conditions are converted to lmis two numerical examples are provided to show the effectiveness of the proposed method

stability analysis and synthesis for an affine fuzzy control system via lmi and ilmi a continuous case a new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper the method suggested is based on the numerical convex optimization techniques in analysis the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities lmis the emphasis of this paper however is on the synthesis of fuzzy controller based on the derived stability condition in the synthesis the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains continuous iterative lmi ilmi approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system

brief a descriptor system approach to nonlinear singularly perturbed optimal control problem this paper considers the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system which is nonlinear in both the slow and the fast variables the relationship between this problem and the analogous one for a descriptor system is investigated parameter independent controllers are constructed that solve the problem for the descriptor system and lead the full order system to the near optimal performance estimates on the closeness of the cost under near optimal controllers to the optimal one are obtained

adaptive finite element methods for parabolic problems iv nonlinear problems we extend our program on adaptive finite element methods for parabolic problems to a class of nonlinear scalar problems we prove a posteriori error estimates design corresponding adaptive algorithms and present some numerical results

adaptive finite element methods for parabolic problems ii optimal error estimates in l l 2 and l l optimal error estimates are derived for a complete discretization of linear parabolic problems using space time finite elements the discretization is done first in time using the discontinuous galerkin method and then in space using the standard galerkin method the underlying partitions in time and space need not be quasi uniform and the partition in space may be changed from time step to time step the error bounds show in particular that the error may be controlled globally in time on a given tolerance level by controlling the discretization error on each individual time step on the same given level i e without error accumulation effects the derivation of the estimates is based on the orthogonality of the galerkin procedure and the use of strong stability estimates the particular and precise form of these error estimates makes it possible to design efficient adaptive methods with reliable automatic error control for parabolic problems in the norms under consideration

infinite time regulators for singularly perturbed difference equations linear quadratic regulators for singularly perturbed difference equations are considered asymptotic behaviour of the optimal solution as the perturbation parameter tends to zero is studied the composite feedback control strategy of continuous time singularly perturbed systems is extended to the new problem

multiobjective control for t s fuzzy singularly perturbed systems this paper investigates the problem of multiobjective control for a class of takagi sugeno t s fuzzy singularly perturbed systems based on a linear matrix inequality lmi approach a state feedback controller that depends on the singular perturbation parameter epsiv is developed such that 1 the h infin performance of the resulting closed loop system is less than or equal to some prescribed value 2 the closed loop poles of each local system are within a prespecified lmi stability region and 3 for a given upper bound epsivmacr for the singular perturbation parameter epsiv both 1 and 2 are guaranteed for all epsiv isin 0 epsivmacr it is shown that the epsiv dependent controller is well defined for any epsiv isin 0 epsivmacr and can be reduced to an epsiv independent one if epsiv is sufficiently small finally a practical example is given to show the feasibility and effectiveness of the obtained method

approaches to robust filtering design of discrete time fuzzy dynamic systems this paper presents two filter design methods for discrete time fuzzy dynamic systems based on a piecewise quadratic lyapunov function it is shown that the resulting filtering error system is globally stable with guaranteed hinfin or generalized h2 performance and the filter gains can be obtained by solving a set of linear matrix inequalities two simulation examples are also given to illustrate the performance of the proposed approaches

stability constraints of active magnetic bearing control systems direct lyapunov stability method is employed to analyse the closed loop stability of an electromagnetically suspended rotor system in which non linearity and singular perturbation nature are embedded five explicit sets of stability constraints are proposed so that the state feedback loop is not over designed under impact of modeling inaccuracy due to neglected higher order terms stability conditions for equilibrium point slow mode manifold and boundary layer are studied in addition the singular perturbation order reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller the stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available the proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness rise time and overshoot is illustrated in comparison to output feedback law and deadbeat control the reported st

fuzzy singularly perturbed modeling and composite controller design for nonlinear multiple time scale systems with time delay abstract this paper investigates the problems of modeling and robust controller design for nonlinear multiple time scale systems mtsss with time delay an uncertain standard discrete time fuzzy singularly perturbed model fspm with time delay is firstly constructed to estimate the considered system based on a matrix spectral norm approach robust composite controllers with or without time delay are designed respectively they are composed by a slow state variables feedback controller and an output integrator the controller s gains are obtained by solving a set of e independent linear matrix inequalities lmis such that the ill conditioned problems caused by e can be easily avoided the designed control laws not only can stabilize resulting closed loop systems but also can overcome external disturbances finally simulation results for ce150 helicopter system illustrate the effectiveness of the proposed approaches in contrast to the existing results the proposed methods have the following advantages i they have better practical value since parameter uncertainty external disturbances and the problem that the state variables are not fully measurable are considered ii a high accurate control performance can be achieved iii external disturbances can be effectively reduced