reduced order h filtering for linear systems with markovian jump parameters this paper addresses the reduced order h filtering problem for continuous time makovian jump linear systems where the jump parameters are modelled by a discrete time markov process sufficient conditions for the existence of the reduced order h filter are proposed in terms of linear matrix inequalities lmis and a coupling non convex matrix rank constraint in particular the sufficient conditions for the existence of the zero order h filter can be expressed in terms of a set of strict lmis the explicit parameterization of the desired filter is also given finally a numerical example is given to illustrate the proposed approach

optimal h model reduction via linear matrix inequalities continuous and discrete time cases necessary and sufficient conditions are derived for the existence of a solution to the continuous time and discrete time h model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set in addition an explicit parametrization of all reduced order models that correspond to a feasible solution is provided in terms of a contractive matrix these results follow from the recent solution of the h control design problem using lmis particularly simple conditions and a simple parametrization of all solutions are obtained for the zeroth order h approximation problem and the convexity of this problem is demonstrated computational issues are discussed and an iterative procedure is proposed to solve the h model reduction problem using alternating projections although global convergence of the algorithm is not guaranteed

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

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

fault estimation observer design for discrete time takagi sugeno fuzzy systems based on piecewise lyapunov functions this paper studies the problem of robust fault estimation fe observer design for discrete time takagi sugeno t s fuzzy systems via piecewise lyapunov functions both the full order fe observer ffeo and the reduced order fe observer rfeo are presented the objective of this paper is to establish a novel framework of the fe observer with less conservatism first under the multiconstrained design an ffeo is proposed to achieve fe for discrete time t s fuzzy models then using a specific coordinate transformation an rfeo is constructed which results in a new fault estimator to realize fe using current output information furthermore by the piecewise lyapunov function approach less conservative results on both ffeo and rfeo are derived by introducing slack variables simulation results are presented to illustrate the advantages of the theoretic results that are obtained in this paper

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis in this paper new descriptor observer design approaches are presented for multivariable systems with measurement noises if the system matrix is stable the proposed modified proportional and derivative observer technique allows us not only to decouple the measurement noise in any forms completely but also obtain accurate estimations of both system states and measurement noises if the system is detectable and the noise is bounded it has been shown that two design parameters can provide more degrees of freedom in this context the derivative gain parameter is chosen to reduce the amplification of the noise and the proportional gain is then selected to guarantee the stability of the error dynamics for systems with both measurement output noises and input disturbances a modified proportional derivative and integral observer is constructed to asymptotically estimate states input disturbances and output noises at the same time the applications of the proposed observers for systems with actuator and sensor faults are also discussed numerical examples are given to illustrate the design procedures and the simulation results show the satisfactory tracking performance

the lagrange multiplier rule in set valued optimization the known lagrange multiplier rule is extended to set valued constrained optimization problems using the contingent epiderivative as differentiability notion a necessary optimality condition for weak minimizers is derived which is also a sufficient condition under generalized convexity assumptions

functional observer and state feedback in this paper relations between the designs of functional observers and state feedback in the state space and transfer function approaches are presented if the state space description of the plan can be written in a controllable canonical form we show that the state space approach of the functional observer and state feedback design can be transformed in the transfer function approach form once the equations in the transfer function approach are solved all unknown elements in the equations of the state space approach can be computed by an iterative algorithm thus the relationship between the two approaches is established we shall also show that the transfer function approach has fewer restrictions

filtering for stochastic systems driven by poisson processes this paper investigates the filtering problem for stochastic systems driven by poisson processes by utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator this paper transforms the expectation of stochastic integral with respect to the poisson process into the expectation of lebesgue integral then based on this this paper designs an filter such that the filtering error system is mean square asymptotically stable and satisfies a prescribed performance level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

interpolation approach to h estimation and its interconnection to loop transfer recovery abstract this paper proposes to solve the h optimal estimation problem via interpolation theory the advantages of this approach are the following i direct and simple solutions can be obtained for the optimal estimators ii frequency weightings on estimation error and disturbance can be easily incorporated and iii unnecessary high observer gains can be avoided we also show the interconnection between the h optimal estimation problem and the optimal loop transfer recovery problem the interpolation approach applies to both continuous time and discrete time systems

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems this paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network rbfnn after a nonparametric approximate model of the system is constructed from a priori experiments or simulations a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations the procedures for both training and state estimation are described along with discussions on approximation error nonlinear systems with linear output equations are considered as a special case of the general formulation finally applications of the proposed rbfnn to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method

robust h filtering for discrete nonlinear stochastic systems with time varying delay this is the postprint version of the article the official published version can be accessed from the link below 2007 elsevier inc

improved robust h2 and h filtering for uncertain discrete time systems this paper is concerned with the robust h 2 and h filtering problems for linear discrete time systems with polytopic parameter uncertainty we aim to derive a less conservative design than existing linear matrix inequality lmi based sufficient conditions it is shown that a more efficient evaluation of robust h 2 or h performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations when applying this new matrix inequality condition to the robust filter design these parameters provide extra degrees of freedom in optimizing the guaranteed h 2 or h performance and lead to a less conservative design

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

fault detection for t s fuzzy systems with unknown membership functions this paper is concerned with the fault detection fd problem for takagi sugeno t s fuzzy systems with unknown membership functions if the membership functions are unknown the linear fd filter designs with fixed gains have been considered in the literature to reduce the conservatism of the existing results a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an fd filter with varying gains it is shown that the switching type fd filter with varying gains can achieve a better fd performance than the linear fd filter with fixed gains in addition based on some time domain inequalities a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an h constraint finally two examples are given to show the advantages of the proposed fd method

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

brief filtering on nonlinear time delay stochastic systems in this paper we address the filtering problem for a general class of nonlinear time delay stochastic systems the purpose of this problem is to design a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square both filter analysis and synthesis problems are considered sufficient conditions are proposed for the existence of desired exponential filters which are expressed in terms of the solutions to algebraic riccati inequalities involving scalar parameters the explicit characterization of the desired filters is also derived a simulation example is given to illustrate the design procedures and performances of the proposed method

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

output feedback fault tolerant control by a set theoretic description of ts fuzzy systems this paper is concerned with the observer based output feedback fault tolerant control problem for ts fuzzy systems by constructing a set theoretic description of fuzzy systems the equivalence class theory in set theory is applied for designing observer and controller for less conservative results firstly we designed the observer to get the information of the actuator faults in the system then we use this information to design the fault tolerant controller to compensate for the effect of faults and guarantee stability of the system finally a simple nonlinear massspringdamper system is presented to illustrate the effectiveness of the proposed approach

robustness with real parametric and structured complex uncertainty the problem of robust stability and performance in feedback control systems with n real possibly repeated uncertain parameters and structured unmodelled dynamics the latter taking the form of m complex blocks dynamic uncertainties is considered a robustness margin rm is defined with respect to such model uncertainty structure and an algorithm is developed to compute it robust stability and performance is characterized in terms of rm in much the same way as with the multivariate stability margin km or the structured singular value an iterative procedure employing the above algorithm is given to compute tight bounds on km and these bounds are exact for the case m 3

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

robust h filtering for a class of discrete time nonlinear systems abstract in this paper a robust h filtering problem is considered for a class of discrete time nonlinear systems based on the lyapunov method a design criterion of the robust h filter guarantee not only the stability but also the prespecified upper bound of h norm from the disturbance inputs to error state outputs the design condition can be solved easily by efficient convex optimization algorithms numerical examples show the effectiveness of the proposed method

delay dependent stabilization for stochastic fuzzy systems with time delays this paper is concerned with the delay dependent stabilization problem for a class of time delay stochastic fuzzy systems the time delays are assumed to appear in both the state and the control input the purpose is the design of a state feedback fuzzy controller such that the resulting closed loop system is asymptotically stable in the mean square a delay dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities lmis by solving these lmis a desired controller can be obtained finally a numerical example is given to demonstrate the effectiveness of the present results

stochastic input to state stability and h filtering for a class of stochastic nonlinear systems in this paper an h filtering problem is considered for a class of stochastic nonlinear systems with time delay and exogenous disturbances sufficient conditions for stochastic input to state stability siss of the stochastic nonlinear systems are developed via lyapunov function method and linear matrix inequalities lmis technique the purpose of this work is to design a nonlinear filter to ensure both the siss and a prescribed h attenuation level for the corresponding filtering error system by using the siss results a set of sufficient conditions for the existence of h filter is given in the form of lmi when the lmi is feasible an explicit expression of a desired filter is presented finally some numerical and practical examples are employed to demonstrate the effectiveness of the proposed approaches

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

h filtering via convex optimization this paper reformulates the suboptimal or level gamma h filtering problem into a linear matrix inequality lmi problem by applying a bounded real lemma to the closed loop transfer function this formulation not only provides the condition of solvability but also constructs the suboptimal h filter this formulation furthermore allows one to solve the epsilon optimal h filtering problem via convex optimization techniques where the epsilon optimality implies that theh norm of the resulting closed loop transfer function is greater than or equal to the infimum say gamma inf of the h norms of all possible closed loop transfer functions but is less than or equal to epsilon gamma for an extremely small positive number epsilon which will depend on the inf accuracy of the algorithms and the precision of a computer

scalarization in vector optimization in this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem this will be done for weakly minimal and minimal solutions respectively finally the results will be applied to a certain class of approximation problems

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

a state space approach to analysis of almost periodic nonlinear systems with sector nonlinearities the nonlinear system considered in this paper consists of two components a linear system and a time varying nonlinear element in the feedback connection and is almost periodic it is shown using a state space approach or lyapunov approach that if the well known circle criterion is satisfied then there exists an almost periodic solution which is uniformly asymptotically stable in the large furthermore it is also shown that the spectra of the almost periodic solution can be characterized by those of the input and the time varying nonlinearity

dynamical behaviors analysis of memristor based fractional order complex valued neural networks with time delay abstract the robust stability for memristor based fractional order complex valued neural networks fcvnns with time delay is investigated here in complex plane by using the lyapunov method and under the sense of filippov solutions the existence of unique equilibrium and globally asymptotic stability for such neural networks nns have been obtained when the nonlinear complex valued activation functions could be split into two real and imaginary parts moreover locally asymptotic stability for such neural nns have been proposed when the nonlinear complex activation functions are bounded lastly three numerical examples are given to confirm the efficiency of theorems

fault detection and isolation for a class of uncertain state feedback fuzzy control systems this paper investigates the fault detection and isolation fdi problem for a class of nonlinear state feedback control systems with parameter uncertainties first the considered nonlinear systems are described by multiple t s fuzzy models with uncertain grades of membership and local nonlinear parts in normal case and faulty cases then a switching technique is introduced to address the uncertain grades of membership external disturbances local nonlinear parts faults and the coupling of them in a multiple model scheme a bank of fdi observers are constructed each of which is based on the t s model that describes the system in the presence of a particular fault such that one of them can track the current system state and the corresponding observer estimate error can converge exponentially to zero finally two examples are given to illustrate the effectiveness and advantages of the new results

fault detection for t s fuzzy systems with partly unmeasurable premise variables abstract this paper studies the fault detection problem for t s fuzzy systems with partly unmeasurable premise variables by using measurable premise variables and estimations of unmeasurable premise variables of fuzzy models as the premise variables of observers a novel fuzzy fault detection observer scheme is constructed and the corresponding design condition is proposed via a set theoretic description different from the conventional fault detection observer schemes where all premise variables of the observer are the estimations of the premise variables in the fuzzy systems the proposed method can take full advantage of the partly measurable premise variables for achieving a better fault detection performance a numerical example is given to illustrate the effectiveness of the proposed method

convergent fault estimation for linear systems with faults and disturbances the problem of convergent fault estimation for a class of linear systems with faults and disturbances is addressed for the first time in this technical note a differential equation based convergence theorem of mean sequence of estimates is proposed which provides an iterative mean estimation technique that has not been fully reported yet in the literature based on the technique a convergent fault estimation strategy for the linear system in consideration is designed and the convergence of mean sequence of fault estimates is proved theoretically an iterative algorithm is given subsequently to compute the fault estimates numerical simulation results demonstrate the effectiveness and merits of the proposed method

brief h control and filtering of discrete time stochastic systems with multiplicative noise linear discrete time systems with stochastic uncertainties in their state space matrices are considered the problems of finite horizon filtering and output feedback control are solved taking into account possible cross correlations between the uncertain parameters in both problems a cost function is defined which is the expected value of the relevant standard h performance index with respect to the uncertain parameters a solution to the filtering problem is obtained first by applying the adjoint system and deriving a bounded real lemma for this system this solution guarantees a prescribed estimation level of accuracy while minimizing an upper bound on the covariance of the estimation error the solution of the filtering problem is also extended to the infinite horizon case the results of the filtering problem are used to solve the corresponding output feedback problem a filtering example is given where a comparison is made with the results obtained using bounded uncertainty design techniques

fault detection for linear discrete time systems with output quantisation abstractthis paper is concerned with the problem of fault detection for a class of linear discrete time quantised feedback systems and system outputs are respectively quantised by a uniform quantiser and a non uniform quantiser a novel unified method is proposed to deal with the two different types of quantisation errors i e the quantisation errors are considered as unknown inputs of the residual generator then an optimal residual generator is constructed to guarantee a suitable trade off between the sensitivity to faults and the robustness against disturbances as well as quantisation errors in order to detect the occurrence of faults the generated residual signal is evaluated and then two different thresholds based on the stochastic properties of quantisation errors are designed for these two quantisers in addition the false alarm rate is introduced to evaluate the fault detection performance finally two examples are given to illustrate the feasibility of the proposed approach

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

robust h spl infin filter design for uncertain linear systems with multiple time varying state delays the problem of robust h spl infin filtering for continuous time uncertain linear systems with multiple time varying delays in the state variables is investigated the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain the aim is to design a stable linear filter assuring asymptotic stability and a prescribed h spl infin performance level for the filtering error system irrespective of the uncertainties and the time delays sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities which can be efficiently solved by means of powerful convex programming tools with global convergence assured an example illustrates the proposed methodology

a decoupled approach to filter design for stochastic systems abstractthis paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems this result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept two kinds of observers are treated the full order and reduced order cases

second order global optimality conditions for convex composite optimization in recent years second order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established in this paper second order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition this result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification in particular second order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained 1998 the mathematical programming society inc published by elsevier science b v

adaptive fuzzy decentralized control for a class of strong interconnected nonlinear systems with unmodeled dynamics the state feedback decentralized stabilization problem is considered for interconnected nonlinear systems in the presence of unmodeled dynamics the functional relationship in affine form between the strong interconnected functions and error signals is established which makes backstepping based fuzzy control successfully generalized to strong interconnected nonlinear systems by combining adaptive control with both backstepping design and the approximation property of fuzzy systems an adaptive decentralized control algorithm is developed it is demonstrated by both theoretical analysis and simulation study that the proposed control strategy ensures semiglobally uniformly ultimately bounded of all signals within the closed loop systems

robust h filters for markovian jump linear systems under sampled measurements abstract in this paper a new class of markovian jump linear system model with polytopic parameter uncertainty continuous disturbance and discrete disturbance is introduced the transition rate matrix of the markov process and the parameters of the system are either exactly known or unknown but belong to a given polytope the general criteria for the stochastic stability of this model and the method for designing a robust stable linear time invariant h filter under sampled measurements are derived in terms of certain linear matrix inequalities lmis finally a numerical example is given to show that the method is effective and feasible

a max plus based algorithm for a hamilton jacobi bellman equation of nonlinear filtering the hamilton jacobi bellman hjb equation associated with the robust hinfty filter as well as the mortensen filter is considered these filters employ a model where the disturbances have finite power the hjb equation for the filter information state is a first order equation with a term that is quadratic in the gradient yet the solution operator is linear in the max plus algebra this property is exploited by the development of a numerical algorithm where the effect of the solution operator on a set of basis functions is computed off line the precomputed solutions are stored as vectors of coefficients of the basis functions these coefficients are then used directly in the real time computations

the optimal projection equations for reduced order state estimation first order necessary conditions for optimal steady state reduced order state estimation for a linear time invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form in contrast to the lone matrix riccati equation arising in the full order kalman filter case the optimal steady state reduced order estimator is characterized by three matrix equations one modified riccati equation and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains this coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by full order estimator design or full order estimator design followed by estimator reduction techniques the results given here complement recently obtained results which characterize the optimal reduced order model by means of a pair of coupled modified lyapunov equations 7 and the optimal fixed order dynamic compensator by means of a coupled system of two modified riceati equations and two modified lyapunov equations 6

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

h filtering for networked systems with partly known distribution transmission delays this paper studies the h filtering problem for a class of discrete time networked systems with partly known distribution transmission delays it is assumed that the random sensor filter delay satisfies markovian characteristics but the transition probabilities of the delay transferring from one value to others are partly known a novel measurement model is proposed to reflect the random delay of the transmission modes and the resulting filtering error system is modeled as a markovian jump system mjs with multiple modes and state delay sufficient conditions are derived for the filtering error system to be stochastically stable and ensure a prescribed h disturbance attenuation level bound by using mode dependent lyapunov functional approach based on the derived conditions a design procedure for the h filter is also presented a numerical example is provided to show the design process of the filter and the effectiveness of the proposed method

robust h exponential filtering for uncertain stochastic time delay systems with markovian switching and nonlinearities in this paper we deal with the robust h exponential filtering problem for a class of uncertain stochastic time delay systems with markovian switching and nonlinear disturbances the system under consideration involves parameter uncertainties ito type stochastic disturbances markovian jump parameters unknown nonlinear disturbances as well as time varying delays which vary in a range and dependent on the mode of the operation the aim of this problem is to design a markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean square stable and a prescribed h disturbance attenuation level is guaranteed novel delay range dependent sufficient conditions are proposed to guarantee the existence of the desired robust exponential filter which are derived in terms of linear matrix inequalities lmis then the explicit expression of the desired filter parameters is characterized an illustrative numerical example is provided to demonstrate the effectiveness of the proposed method

game theory approach to optimal linear state estimation and its relation to the minimum h sub infinity norm estimation a possible game theory approach to optimal state estimation is presented it is found that in a certain differential game the minimizer s policy is identical to the one obtained by optimal estimation in the minimum h sub infinity norm sense this interpretation of h sub infinity optimal state estimation provides better insight into the mechanism of h sub infinity optimal filtering especially in the case where the exogenous signals are not energy bounded

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

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

robust scheduling filter design for a class of nonlinear stochastic poisson signal systems nonlinear dynamic systems may suffer from both continuous wiener noise and discontinuous poisson noise this paper studies a robust filter design for a class of nonlinear stochastic poisson signal systems with external disturbances currently there are no good filtering design methods to treat the discontinuous poisson noise filter problem based on the ito levy formula a robust h infty filter design is proposed for nonlinear stochastic poisson signal systems by solving a hamilton jacobi inequality hji for the robust filter design of a nonlinear stochastic poisson signal system however such an hji is difficult to solve hence this study employs the polytopic linear model plm scheduling scheme to approximate this hji by a set of linear matrix inequalities lmis so that the h infty robust filter design problem for a nonlinear stochastic poisson signal system can be simplified the optimal h infty robust scheduling filter design problem for the nonlinear stochastic poisson signal system is also discussed since the plm interpolation method transforms the hji constrained optimization problem into an lmi constrained optimization problem which can be efficiently solved using the lmi toolbox in matlab an optimal filtering level gamma ast the minimum value of the filtering error to noise ratio in a mean square sense can be achieved finally a simulation example of a robust trajectory estimation problem in an anti tactical ballistic missile radar system with discontinuous random maneuvering jets is given to illustrate the design procedure and to confirm the estimation performance of the proposed h infty robust scheduling filter

generalized quasiconvex mappings and vector optimization quasiconvexity for mappings is generalized in such a way that this notion gives the sufficiency of necessary optimality conditions such as multiplier rules one can show that it is the weakest type of generalized convexity notions in the sense that this generalized quasiconvexity holds if certain multiplier rules are sufficient for optimality it also yields the equivalence of local and global minima the theory is applied to a mufti objective programming problem and a vector approximation problem

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

fault detection and isolation for affine fuzzy systems with sensor faults this paper investigates the fault detection and isolation fdi problem for a class of nonlinear systems with sensor outage faults the considered nonlinear systems are described as affine fuzzy models and the system outputs are chosen as the premise variables of fuzzy models different from the existing results the influence of sensor faults on premise variables is considered as a result the well known parallel distributed compensation scheme cannot be used for fdi filters design by using the structural information encoded in the fuzzy rules the affine fuzzy system is represented by multiple operating regime based models in fault free case and faulty cases in the multiple model scheme a bank of piecewise fdi filters are constructed each of them is based on the affine fuzzy model that describes the system in the presence of a specified fault the fault dependent residual signals generated from the filters are used for detecting and isolating the specified fault the fdi filter design conditions are obtained in the formulation of linear matrix inequalities finally a numerical example is given to illustrate the effectiveness and merits of the proposed method

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

delay dependent l2 l filter design for stochastic time delay systems abstract this paper is concerned with the problem of l 2 l filter design for a class of stochastic time delay systems a delay dependent sufficient condition is presented which guarantees the existence of a linear filter ensuring that the filtering error system is stochastically asymptotically stable and its l 2 l performance satisfies a prescribed level a desired filter can be constructed by solving certain linear matrix inequalities a numerical example is given to demonstrate the effectiveness of the proposed method

convex composite multi objective nonsmooth programming this paper examines nonsmooth constrained multi objective optimization problems where the objective function and the constraints are compositions of convex functions and locally lipschitz and g teaux differentiable functions lagrangian necessary conditions and new sufficient optimality conditions for efficient and properly efficient solutions are presented multi objective duality results are given for convex composite problems which are not necessarily convex programming problems applications of the results to new and some special classes of nonlinear programming problems are discussed a scalarization result and a characterization of the set of all properly efficient solutions for convex composite problems are also discussed under appropriate conditions

a transformation approach to stochastic model reduction a new and direct approach to stochastic model reduction is developed the order reduction algorithm is obtained by establishing an equivalence between canonical correlation analysis and solutions to algebraic riccati equations also the concept of balanced stochastic realization bsr plays a fundamental role asymptotic stability of the reduced order realization is established and spectral domain interpretations for the bsr are given

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

moment stability of nonlinear discrete stochastic systems with time delays based on h representation technique in this paper mean square stability of nonlinear discrete stochastic systems with time delays is investigated we obtain the second order moment equations of discrete stochastic systems by virtue of the h representation technique by the comparison principle and the established moment equations some moment stability theorems for nonlinear discrete stochastic systems with time delays are established a numerical example is presented to illustrate the efficiency of our results at the end of the paper

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

fault detection for t s fuzzy systems with past output measurements abstract this paper is concerned with the fault detection fd filter design problem for the discrete time nonlinear systems with past output measurements and sensor saturation the considered discrete time nonlinear systems are described by t s fuzzy models a decomposition method is used to deal with the characteristics of sensor saturation a new fd filter with past output measurements is firstly proposed by using the lyapunov functional method subsequently the design conditions are given in terms of convex problems constrained by linear matrix inequalities lmi moreover it is shown that the fd filter with past output measurements can achieve better fd performances than the existing ones with current output measurements finally some simulation results are given to illustrate the advantages of the proposed design method

fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties in this paper the problem of robust dynamic output feedback control for a class of discrete time nonlinear systems with parametric uncertainties is studied the parametric uncertainties are assumed to be of a linear fractional form first the takagi sugeno t s fuzzy model is employed to represent the nonlinear system then novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities lmis the proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods

robust h sub spl infin filtering of stationary continuous time linear systems with stochastic uncertainties the problem of applying h sub spl infin filters on stationary continuous time linear systems with stochastic uncertainties in the state space signal model is addressed these uncertainties are modeled via white noise processes the relevant cost function is the expected value of the standard h sub spl infin performance index with respect to the uncertain parameters the solution is obtained via a stochastic bounded real lemma that results in a modified riccati inequality this inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters the method proposed is also applied to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h sub 2 h sub spl infin filtering for the above system is also treated the theory developed is demonstrated by a practical example

robust filtering design of piecewise discrete time linear systems this work presents two filter design methods for piecewise discrete time linear systems based on a piecewise lyapunov function it is shown that the resulting filtering error system is globally stable with guaranteed h sub spl infin or generalized h sub 2 performance and the filter gains can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software two simulation examples are also given to illustrate the performance of the proposed approaches

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation

brief nonlinear h filtering of sampled data systems this paper considers the problem of h filtering for nonlinear sampled data systems sufficient conditions are obtained for the existence of filters that guarantee the l 2 gain from an exogenous input to an estimation error is less than or equal to a prescribed value these conditions are expressed in terms of both continuous and discrete hamilton jacobi equations