dissipativity based filtering for fuzzy switched systems with stochastic perturbation in this technical note the problem of the dissipativity based filtering problem is considered for a class of t s fuzzy switched systems with stochastic perturbation firstly a sufficient condition of strict dissipativity performance is given to guarantee the mean square exponential stability for the concerned t s fuzzy switched system then our attention is focused on the design of a filter to the t s fuzzy switched system with brownian motion by combining the average dwell time technique with the piecewise lyapunov function technique the desired fuzzy filters are designed that guarantee the filter error dynamic system to be mean square exponential stable with a strictly dissipative performance and the corresponding solvability condition for the fuzzy filter is also presented based on the linearization procedure approach finally an example is provided to illustrate the effectiveness of the proposed dissipativity based filter technique

stability and stabilization of switched linear time invariant systems with saddle points and switching delays this paper addresses global asymptotic stability gas and stabilization issues of switched linear time invariant lti systems with saddle points and time varying switching delays firstly two criteria of gas are proposed for such switched systems with all subsystems sharing a common unique saddle point under arbitrary periodic quasi periodic switching paths psp qsp secondly by using our stability results we design global asymptotic stabilizing controls gasc periodic quasi periodic stabilizing switching paths pssp qssp and an algorithm of gasc and pssp qssp for the switched systems finally we present a numerical example of a switching multi agent system to illustrate the effectiveness and practicality of our new results

stability analysis of switched fuzzy systems via model checking switched fuzzy systems can be used to describe the hybrid systems with fuzziness their stability issue is the most important one and has received significant attention most of the existing methods to study it are based on lyapunov functions however the existence of such functions is difficult to establish this paper presents a new method to analyze the stability a switched fuzzy system with a takagi sugeno t s fuzzy model is first transformed to a hybrid automaton ha that is linearized the reachability of this linearized one is then checked by the model checker phaver finally the stability is obtained by analyzing the reachability it is shown that a switched fuzzy system and its corresponding ha have the same behavior and that the linearization does not affect the stability analysis we demonstrate the effectiveness of our method through a case study on a differential drive two wheeled mobile robot

mathcal l _ 2 mathcal l _ infty output feedback controller design for fuzzy systems over switching parameters this paper focuses on the problem of mathcal l 2 mathcal l infty dynamic output feedback controller dofc design for nonlinear switched systems with nonlinear perturbations in the takagi sugeno fuzzy framework first the average dwell time approach is used to stabilize a nonlinear switched system exponentially under an arbitrary switching law then based on the technique of piecewise lyapunov functions a fuzzy rule dependent dofc is designed to ensure that the overall closed loop system is exponentially stable with a weighted mathcal l 2 mathcal l infty performance level left gamma alpha right the solvability condition for the desired dofc is derived using a linearization technique it is shown that the controller parameters can be obtained as solutions to a set of strict linear matrix inequalities that are numerically solvable with available standard software finally two simulation examples illustrate effectiveness of the developed technique including cognitive radio systems

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem

a new control method for state constrained nonlinear switched systems with application to chemical process this paper presents a new control method for a class of nonlinear switched systems in strict feedback form with a state constraint in the proposed approach a nonlinear mapping is first introduced to transform the problem of controlling the switched system with state constraint to a new problem of regulating the transformed system without a constraint by using the backstepping technique the designed state feedback controller ensures that the corresponding closed loop system is asymptotically stable without violation of the constraint and that all closed loop signals keep bounded furthermore we explore the use of a coordinate transformation to deal with an asymmetric state constraint as a generalised approach in the end an application example on a chemical process is shown to demonstrate the efficacy of the obtained results

adaptive tracking control for switched nonlinear systems with fuzzy actuator backlash abstract this paper concentrates on the adaptive tracking control problem for a class of switched nonlinear systems in nonstrict feedback form with uncertain actuator backlash the switching signal considered in our model is arbitrary the adaptive tracking controller design procedure is divided into three parts firstly a novel fuzzy backlash model is presented to describe the uncertain backlash then the fuzzy backlash is defuzzified and approximated by the linear combination of a linear term and a disturbance like term without constructing a backlash inverse finally an adaptive backstepping based tracking controller via common lyapunov function clf method is presented to guarantee the tracking error asymptotically converges to an adjustable region of zero the stability analysis and simulation examples are presented at the end of this paper to further verify effectiveness of our control scheme

analysis of a bilinear finite element for shallow shells i approximation of inextensional deformations we consider a bilinear reduced strain finite element formulation for a shallow shell model of reissner naghdi type the formulation is closely related to the facet models used in engineering practice we estimate the error of this scheme when approximating an inextensional displacement field we make the strong assumptions that the domain and the finite element mesh are rectangular and that the boundary conditions are periodic and the mesh uniform in one of the coordinate directions we prove then that for sufficiently smooth fields the convergence rate in the energy norm is of optimal order uniformly with respect to the shell thickness in case of elliptic shell geometry the error bound is furthermore quasioptimal whereas in parabolic and hyperbolic geometries slightly enhanced smoothness is required except for the degenerate cases where the characteristic lines are parallel with the mesh lines the error bound is shown to be sharp

stability analysis and stabilization of 2 d switched systems under arbitrary and restricted switchings in this paper the problems of stability analysis and stabilization are investigated for discrete time two dimensional 2 d switched systems which are formulated by the well known fornasini marchesini local state space model firstly by using the switched quadratic lyapunov function approach a sufficient stability condition is established for such systems under arbitrary switching signal then the extended average dwell time technique combining with the piecewise lyapunov function approach is developed and it is utilized for the stability analysis of the 2 d switched systems for the restricted switching case based on the stability analysis results sufficient conditions are presented to stabilize the 2 d switched systems finally two examples are provided to illustrate the effectiveness of the proposed new design techniques

applying the method of normal forms to second order nonlinear vibration problems vibration problems are naturally formulated with second order equations of motion when the vibration problem is nonlinear in nature using normal form analysis currently requires that the second order equations of motion be put into first order form in this paper we demonstrate that normal form analysis can be carried out on the second order equations of motion in addition for forced damped nonlinear vibration problems we show that the invariance properties of the first and second order transforms differ as a result using the second order approach leads to a simplified formulation for forced damped nonlinear vibration problems

asynchronously switched control of discrete impulsive switched systems with time delays this paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching the so called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous by using the average dwell time adt approach sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed loop system is exponentially stable the desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed method

theory of stochastic dissipative systems by introducing the escape time a new definition of the dissipativity is introduced under some assumptions that are very reasonable for most physical models based on this definition criteria on the existence and the stability of the solution are presented which can be seen as the extension of lyapunov method to the non smooth case the dissipativity is applied to cascaded nonlinear stochastic systems and interconnected systems to display the superiority of the new framework which shows that there is no need to calculate the first exit time and the escape time

discounted cost linear quadratic gaussian control for descriptor systems we consider the linear quadratic gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon based on recent results from the deterministic frame

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

local stabilization of switched affine systems this technical note considers the local stabilization problem for the class of switched affine systems the main idea is to use an alternative representation of the switched affine system as a nonlinear system with input constraints switching laws can be derived by emulating locally classical controllers it is shown that by restricting to local stabilization the classical constraint on the existence of constant stable convex combinations may be easily avoided the approach may be interpreted as a generalization where convex combinations defined as functions of the system state are being used constructive methods for deriving switching laws are proposed

robust h control for switched systems with input delays a sojourn probability dependent method in this paper a sojourn probability dependent method is proposed to investigate the robust h control for a class of switched systems with input delays the considered system has the following characteristics 1 it is a switched system consisting of a set of subsystems 2 sojourn probabilities i e the probability of switched systems staying in each subsystem are assumed to be known or partly known a prior and 3 there are input delays and parameter uncertainties in each subsystem by using the sojourn probability information a new type of switched system model is built by using the lyapunov functional method the robust mean square stability criteria are obtained for switched systems under two conditions a all sojourn probabilities of the subsystems are known b only partly sojourn probabilities are known then the robust h controller feedback gains are derived by using the cone complement linearization method an inverted pendulum system and a numerical example are given to demonstrate the effectiveness and applicability of the proposed method

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

variance constrained h control for a class of nonlinear stochastic discrete time varying systems in this paper a general event triggered framework is set up to deal with the variance constrained h control problem for a class of discrete time varying systems with randomly occurring saturations stochastic nonlinearities and state multiplicative noises based on the relative error with respect to the measurement signal an event indicator variable is introduced and the corresponding event triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not the stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well studied nonlinearities a set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations stochastic nonlinearities and state dependent noises the purpose of the addressed multiobjective control problem is to design a set of time varying output feedback controller such that over a finite horizon the closed loop system achieves both the prescribed h noise attenuation level and the state covariance constraints a recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite horizon controllers and the analytical characterization of such controllers is also given simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

normal modes for non linear vibratory systems a methodology is presented which extends to non linear systems the concept of normal modes of motion which is well developed for linear systems the method is constructive for weakly non linear systems and provides the physical nature of the normal modes along with the non linear differential equations which govern their dynamics it also provides the non linear co ordinate transformation which relates the original system co ordinates to the modal co ordinates using this transformation we demonstrate how an approximate non linear version of superposition can be employed to reconstruct the overall motion from the individual non linear modal dynamics the results presented herein for non linear systems reduce to modal analysis for the linearized system when non linearities are neglected even though the approach is entirely different from the traditional one the tools employed are from the theory of invariant manifolds for dynamical systems and were inspired by the center manifold reduction technique in this paper the basic ideas are outlined a few examples are presented and some natural extensions and applications of the method are briefly described in the conclusions

brief paper backstepping controller design for a class of stochastic nonlinear systems with markovian switching a more general class of stochastic nonlinear systems with irreducible homogenous markovian switching are considered in this paper as preliminaries the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a lyapunov function the state feedback controller is designed by regarding markovian switching as constant such that the closed loop system has a unique solution and the equilibrium is asymptotically stable in probability in the large the output feedback controller is designed based on a quadratic plus quartic form lyapunov function such that the closed loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded in probability solution in the biased case

dissipativity theory for nonlinear stochastic dynamical systems in this paper we develop stochastic dissipativity theory for nonlinear dynamical systems using basic input output and state properties specifically a stochastic version of dissipativity using both an input output as well as a state dissipation inequality in expectation for controlled markov diffusion processes is presented the results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for stochastic dissipativity of stochastic dynamical systems using two times continuously differentiable storage functions in addition feedback interconnection stability in probability results for stochastic dynamical systems are developed thereby providing a generalization of the small gain and positivity theorems to stochastic systems

shell deformation states and the finite element method a benchmark study of cylindrical shells abstract we demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation as benchmark cases we analyze in detail three simple cylindrical shell problems these problems are seemingly similar but turn out to be quite different we 1 compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models 2 for comparison compute numerically the displacements and strains corresponding to certain higher order dimension reduction models derived from the energy principle 3 demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and 4 show both theoretically and experimentally how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order

on global dissipativity of nonautonomous neural networks with multiple proportional delays this brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays by using a novel constructive approach based on some comparison techniques for differential inequalities new explicit delay independent conditions are derived using m matrix theory to ensure the existence of generalized exponential attracting sets and the global dissipativity of the system the method presented in this brief is also utilized to derive a generalized exponential estimate for a class of halanay type inequalities with proportional delays finally three numerical examples are given to illustrate the effectiveness and improvement of the obtained results

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

a convergence condition for the quadrilateral wilson element the paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test the convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation this result extends the range of applicability of wilson s element the necessity of the proposed condition is also discussed

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

passivity and passification of time delay systems in this paper the problems of passivity and passification of a class of linear time delay systems are investigated a new state transformation is developed to exhibit the delay dependence it is established that the passivity condition can be cast in a linear matrix inequality lmi format for state feedback passification it is proven that it is indifferent to use instantaneous or delayed state feedback the case of dynamic output feedback passification is also treated numerical examples are provided

sliding mode control of discrete time switched systems with repeated scalar nonlinearities this note studies the design of sliding mode control smc for discrete time hybrid stochastic switched systems with repeated scalar nonlinearities the weighed mathcal h infty gain performance is considered for the system dynamics to optimize its transient state performance first sufficient conditions are given to guarantee the corresponding system is exponentially stable while achieving a desired weighed mathcal h infty performance a new switching surface function is constructed by the average dwell time technique and the positive diagonally dominant lyapunov functional method to further reduce the conservativeness induced by the repeated scalar nonlinearity then the corresponding sliding mode dynamics are obtained and the solvability condition for the desired switching surface function is derived furthermore the synthesis of the proposed smc law is proposed to force the resulting closed loop system trajectories onto the pre specified sliding mode region with a desired level of accuracy finally the feasibility and the effectiveness of the presented new design techniques are illustrated by examples and simulations

delay dependent robust dissipativity conditions for delayed neural networks with random uncertainties this paper deals with the problem of the robust dissipativity analysis for delayed neural networks with randomly occurring uncertainties the randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated bernoulli distributed white noise sequences by using reciprocally convex approach combined with an extended wirtinger inequality some delay dependent conditions for the concerned neural networks to be stochastically strictly q s r dissipative are established finally two numerical examples are given to illustrate the reduced conservatism and effectiveness of our proposed approach

an energy method approach to the problem of elastic strip we analyze a thin elastic homogeneous strip under a smooth load and several different types of boundary conditions the strip is assumed to obey either a plane strain or a plane stress type deformation of linear theory of elasticity we characterize the 2d solution and consider dimension reduction of arbitrary order n both interior and global energy estimates for the reduction error are derived

a new superconvergence property of wilson nonconforming finite element in this paper the wilson nonconforming finite element method is considered to solve a class of two dimensional second order elliptic boundary value problems a new superconvergence property at the vertices and the midpoints of four edges of rectangular meshes is obtained

scale resolution locking and high order finite element modelling of shells abstract we demonstrate both by theory and experiment the benefits of using standard finite elements of relatively high degree in shell problems the difficulty of shell problems lies in their asymptotic diversity at zero thickness and in the multiple scale character of the deformation field when the thickness is small due to these characteristics standard finite elements of low degree often resolve the length scales of practical shell deformation very poorly unless extremely fine meshes are used however with standard finite elements of sufficiently high degree say cubic or quartic at least the quality of numerical scale resolution improves remarkably we show by simple error analysis that this effect is not problem specific but rather robust among the diversity of shell problems as numerical test cases we analyze two challenging problems in cylindrical shell geometry

time varying state feedback stabilisation of stochastic feedforward nonlinear systems with unknown growth rate abstractwe consider the time varying state feedback stabilisation problem for a class of stochastic feedforward nonlinear systems with unknown growth rate in this paper a new lasalle type theorem for stochastic time varying systems is firstly established by using the generalized weakly positive definite function as an application to deal with serious uncertainties in the unknown growth rate a time varying approach rather than an adaptive one is adopted to design the scheme of a state feedback controller for stochastic feedforward systems based on the established lasalle type theorem it is shown that all signals of the resulting closed loop system converge to zero almost surely illustrative examples are given to verify the theoretical findings

model reduction to spectral submanifolds and forced response calculation in high dimensional mechanical systems abstract we show how spectral submanifold ssm theory can be used to extract forced response curves without any numerical simulation in high degree of freedom periodically forced mechanical systems we use multivariate recurrence relations to construct the ssms achieving a major speed up relative to earlier autonomous ssm algorithms the increase in computational efficiency promises to close the current gap between studying lower dimensional academic examples and analyzing larger systems obtained from finite element modeling as we illustrate on two different discretized damped forced beam models using the exact reduction procedure via ssms for obtaining forced response curves we further demonstrate speed gains of several orders in magnitude relative to the available state of the art continuation packages while retaining accuracy

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

an analysis of finite element locking in a parameter dependent model problem we consider the bilinear finite element approximation of smooth solutions to a simple parameter dependent elliptic model problem the problem of highly anisotropic heat conduction we show that under favorable circumstances that depend on both the finite element mesh and on the type of boundary conditions the effect of parametric locking of the standard fem can be reduced by a simple variational crime in our analysis we split the error in two orthogonal components the approximation error and the consistency error and obtain different bounds for these separate components also some numerical results are shown

explicit third order model reduction formulas for general nonlinear mechanical systems abstract for general nonlinear mechanical systems we derive closed form reduced order models up to cubic order based on rigorous invariant manifold results for conservative systems the reduction is based on lyapunov subcenter manifold lsm theory whereas for damped forced systems we use spectral submanifold ssm theory to evaluate our explicit formulas for the reduced model no coordinate changes are required beyond an initial linear one the reduced order models we derive are simple and depend only on physical and modal parameters allowing us to extract fundamental characteristics such as backbone curves and forced response curves of multi degree of freedom mechanical systems to numerically verify the accuracy of the reduced models we test the reduction formulas on several mechanical systems including a higher dimensional nonlinear timoshenko beam

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

pareto optimal filter design for nonlinear stochastic fuzzy systems via multiobjective h_ bf 2 h_ bm infty optimization this paper is concerned with the multiobjective h 2 h infty filtering design problem in nonlinear signal processing which can be approximated by a takagi sugerno t s fuzzy signal system we propose a multiobjective filter design to estimate state variables from noisy measurements for nonlinear signal systems and we focus our effort on achieving optimal concurrent performance for h 2 and h infty filtering in general it is difficult to solve the multiobjective mo h 2 h infty fuzzy filter problem directly and we therefore propose an indirect approach to minimize the upper bounds and transform the mo h 2 h infty filtering problem in to a linear matrix inequality lmi constrained multiobjective problem mop in addition we propose an lmi based multiobjective evolution algorithm to efficiently find pareto optimal solutions for the mop of multiobjective fuzzy filter design for nonlinear stochastic signal processing furthermore for comparison we also suggest the mo h 2 h infty filter design problem based on the weighted sum method our proposed indirect method can be widely employed to practically address the mo filter design problem in nonlinear signal processing finally a trajectory estimation of reentry vehicle by radar is provided to illustrate the design procedure of the pareto mo optimal filter

finite time stabilization via sliding mode control this technical note investigates the sliding mode control smc design based on finite time boundedness ftb for a class of nonlinear systems a suitable smc law is constructed to drive the state trajectories onto the specified sliding surface during a specified finite possibly short time interval besides by introducing a partitioning strategy the corresponding ftb over reaching phase and sliding motion phase are guaranteed respectively and then the sufficient conditions are derived to ensure the ftb of the closed loop systems over the whole finite time interval finally a simulation example is given to show the effectiveness of the proposed design method

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

dissipativity based small gain theorems for stochastic network systems in this paper some small gain theorems are proposed for stochastic network systems which describe large scale systems with interconnections uncertainties and random disturbances by the aid of conditional dissipativity and showing times of stochastic interval small gain conditions proposed for the deterministic case are extended to the stochastic case when some design parameters are tunable in practice we invaginate a simpler method to verify small gain condition by selecting one subsystem as a monitor compared with the existing results the existence and uniqueness of solution and ultimate uniform boundedness of input are removed from requirements of input to state stability and small gain theorems

shear locking in a plane elasticity problem and the enhanced assumed strain method the enhanced assumed strain eas method is a popular tool for avoiding locking phenomena e g a remedy for shear locking in plane elasticity we consider bending dominated problems on thin bodies which can be treated as beams and prove that the degree of approximation of the eas method is at least as good as that of a beam model the hypercircle method is combined with arguments of nonconforming methods

input to state stability for discrete time nonlinear switched singular systems discrete time nonlinear switched singular systems ssss are investigated the input to state stability iss problems for discrete time nonlinear ssss are concerned the iss criteria are obtained via average dwell time approach and iterative algorithm of discrete time systems the switching rules are optimized and designed this paper investigates the input to state stability iss problems for a class of discrete time nonlinear switched singular systems ssss two novel iss criteria are proposed based on average dwell time adt approach and iterative algorithm of discrete time systems iads in particular the following two cases are considered for the underlying systems the first case is that all the sub systems are exponentially stable and the other case is that only a few sub systems are exponentially stable the corresponding iss criteria are obtained to guarantee that the closed loop systems are input to state stable via adt approach and iads we neither construct a specific lyapunov function for iss in the proof process of the stability criteria nor design a specific structure of the control inputs the design deficit of the switching controllers is optimized and the design difficulty of the switching controllers is reduced via the proposed criteria finally two numerical examples are provided to illustrate the feasibility of the results obtained

extended dissipative filtering for markovian jump interval valued fuzzy systems with uncertain transition rates abstract this paper addresses the problem of the extended dissipative filtering for a class of markovian jump interval valued fuzzy systems with uncertain transition rates first a sufficient condition of stochastic asymptotic stability and extended dissipativity is provided then by introducing some additional matrices the matrices in this sufficient condition can be decomposed into a form with only one part and its transpose containing the unknown parametric matrices of filter which is vitally important for establishing a new sufficient condition and designing an extended dissipative filter via the projection lemma attention is focused on the applications of this projection lemma twice by virtue of the feature of extended dissipative performance which differs from existing work and produces better estimated effects the new sufficient condition is of nonlinear form with respect to some matrix variables which makes the determination of extended dissipative filter difficult fortunately by transforming nonlinear matrix inequalities into a quadratic optimization problem with linear matrix inequality constraints the extended dissipative filter is developed by virtue of a cone complementarity linearization algorithm finally two numerical examples are given to show the effectiveness of our proposed approach

a benchmark study of reduced strain shell finite elements quadratic schemes we study experimentally the accuracy and reliability of some low order shell finite element schemes based on modifying the standard displacement formulation by reduced strain expressions we focus on quadrilateral elements with a quadratic displacement approximation three benchmark problems with different asymptotic behaviour in the limit of zero shell thickness is used in the experiments following the error analysis of a reduced strain scheme we study two components of the total error the approximation error and the consistency error we demonstrate that the performance of the methods is both case and mesh dependent when a bending dominated problem is solved none of the methods studied can avoid the usual worst case locking effect of the approximation error on general meshes for a membrane dominated problem the total error is typically dominated by the consistency error which often convergences slowly copyright 2000 john wiley sons ltd

upper and lower error bounds for plate bending finite elements we compare the robustness of three different low order mixed methods that have been proposed for plate bending problems the so called mitc arnold falk and arnold brezzi elements we show that for free plates the asymptotic rate of convergence in the presence of quasiuniform meshes approaches the optimal o h for mitc elements as the thickness approaches 0 but only approaches o h frac 1 2 for the latter two we accomplish this by establishing lower bounds for the error in the rotation the deterioration occurs due to a consistency error associated with the boundary layer we show how a modification of the elements at the boundary can fix the problem finally we show that the arnold brezzi element requires extra regularity for the convergence of the limiting discrete kirchhoff case and show that it fails to converge in the presence of point loads

hardening softening behaviour in non linear oscillations of structural systems using non linear normal modes the definition of a non linear normal mode nnm as an invariant manifold in phase space is used in conservative cases it is shown that normal form theory allows one to compute all nnms as well as the attendant dynamics onto the manifolds in a single operation then a single mode motion is studied the aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results using single non linear mode motion predicts the correct behaviour hence the nonlinear change of co ordinates allowing one to pass from the linear modal variables to the normal ones linked to the nnms defines a framework to properly truncate non linear vibration pdes two examples are studied a discrete system a mass connected to two springs and a continuous one a linear euler bernoulli beam resting on a non linear elastic foundation for the latter a comparison is given between the developed method and previously published results

design principles and error analysis for reduced shear plate bending finite elements in this paper we consider the problem of designing plate bending elements which are free of shear locking this phenomenon is known to afflict several elements for the reissner mindlin plate model when the thickness d of the plate is small due to the inability of the approximating subspaces to satisfy the kirchhoff constraint to avoid locking a reduction operator is often applied to the stress to modify the variational formulation and reduce the effect of this constraint we investigate the conditions required on such reduction operators to ensure that the approximability and consistency errors are of the right order a set of sufficient conditions is presented under which optimal errors can be obtained these are derived directly without transforming the problem via a hemholtz decomposition or considering it as a mixed method our analysis explicitly takes into account boundary layers and their resolution and we prove via an asymptotic analysis that convergence of the finite element approximations will occur uniformly as d rightarrow 0 even on quasiuniform meshes the analysis is carried out in the case of a free boundary where the boundary layer is known to be strong we also propose and analyze a simple post processing scheme for the shear stress our general theory is used to analyze the well known mitc elements for the reissner mindlin plate as we show the theory makes it possible to analyze both straight and curved elements we also analyze some other elements

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

exponentially incremental dissipativity for nonlinear stochastic switched systems in this paper we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state dependent switching law and multiple lyapunov functio

smc design for robust stabilization of nonlinear markovian jump singular systems in this technical note the sliding mode control smc problem is investigated for t s fuzzy model based nonlinear markovian jump singular systems subject to matched unmatched uncertainties to accommodate the model characteristics of such a hybrid system a novel integral type fuzzy sliding surface is put forward by taking the singular matrix and state dependent projection matrix into account simultaneously which is the key contribution of the note the designed surface contains two important features 1 local input matrices for different subsystems in the same system mode are allowed to be different and 2 the matched uncertainties are completely compensated and the unmatched ones are not amplified during sliding motion sufficient conditions for the stochastic admissibility of the corresponding sliding mode dynamics are presented and a fuzzy smc law is constructed to ensure the reaching condition despite uncertainties the applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system

analysis of delayed sliding mode control systems under zero order holder discretization zero order holder discretization effects in sliding mode control systems with an input delay are studied stability conditions are formulated conditions for the existence of periodic solutions are derived and the existence of periodic steady states is investigated the influence of the discretization step and the delay on the period and the amplitude of steady state oscillations is discussed structure of basins of attraction of periodic orbits with different switching patterns is studied simulation results are presented to illustrate various behaviors

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

reduced order model approximation of fuzzy switched systems with pre specified performance the reduced order model approximation problem for discrete time hybrid switched nonlinear systems is addressed via takagi sugeno t s fuzzy modelling in this paper for a high dimension hybrid switched nonlinear system our aim is on how to construct a reduced dimension hybrid switched model approximating its original high order model well with a pre specified system performance level firstly the mean square exponential stability analysis is provided in which it guarantees the given weighted h system performance level for the augmented error dynamic system by the average dwell time analysis approach and the hybrid switched lyapunov stability theory the solution of corresponding model reduction problem with pre specified performance is given by using the projection lemma the algorithm of the reduced order hybrid switched model parameters is designed by the cone complementary linearization technique finally the advantage and effectiveness of the proposed reduced order model approximation approach are shown by the simulation result

the first locking free plane elastic finite element historia mathematica abstract we consider a two parameter family of conforming bilinear quadrilateral finite element formulations for plane elastic problems with homogeneous isotropic material the approach taken earlier by belytschko et al is based on numerical strain reductions and stabilization and may be viewed as an extension reformulation of the classical turner rectangle of 1956 we present the full theory of this approach in the energy norm framework the analysis is based on splitting the error in two orthogonal components the approximation error and the equilibrium or consistency error the theory covers the full parametric dependence of the plane elastic problem emphasizing in particular the case of beam like bodies with arbitrarily small aspect ratios the theory shows that depending on the mesh the stabilized reduced strain formulation is capable of avoiding some or even all the parametric locking effects characteristic to 2d elastic problems we analyze first these locking effects in the context of standard bilinear fem

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

passivity based non fragile control for markovian jump systems with aperiodic sampling in this paper the problem of non fragile passive control for markovian jump systems with aperiodic sampling is investigated the considered controller is assumed to have either additive or multiplicative norm bounded uncertainties a time dependent lyapunov functional capturing the available information of the sampling pattern is constructed to derive a sufficient condition for non fragile stochastic passivity of the resultant closed loop system based on the condition a mode independent state feedback sampled data controller is designed such that for all admissible uncertainties the closed loop system is robustly stochastically passive two illustrative examples are included to demonstrate the effectiveness and merits of the proposed techniques

analysis of a bilinear finite element for shallow shells ii consistency error we consider a bilinear reduced strain finite element of the mitc family for a shallow reissner naghdi type shell we estimate the consistency error of the element in both membrane and bending dominated states of deformation we prove that in the membrane dominated case under severe assumptions on the domain the finite element mesh and the regularity of the solution an error bound o h t 1h1 s can be obtained if the contribution of transverse shear is neglected here t is the thickness of the shell h the mesh spacing and s a smoothness parameter in the bending dominated case the uniformly optimal bound o h is achievable but requires that membrane and transverse shear strains are of order o t2 as t 0 in this case we also show that under sufficient regularity assumptions the asymptotic consistency error has the bound o h

sliding mode control of singular stochastic markov jump systems an investigation has been made into the sliding mode control smc problem for singular stochastic markov systems ssmss in this paper by using replacement of matrix variables a new mean square admissibility criterion of ssmss is proposed first based on this admissibility criterion the desired state feedback controller is designed to guarantee the closed loop system to be mean square admissible then the obtained results given in the form of strict linear matrix inequalities are applied to solve smc problem of ssmss in order to illustrate the workability and applicability of the theoretic results developed numerical examples are provided

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

nonlinear normal modes for damped geometrically nonlinear systems application to reduced order modelling of harmonically forced structures in order to build efficient reduced order models roms for geometrically nonlinear vibrations of thin structures a normal form procedure is computed for a general class of nonlinear oscillators with quadratic and cubic nonlinearities the linear perturbation brought by considering a modal viscous damping term is especially addressed in the formulation a special attention is focused on how all the linear modal damping terms are gathered together in order to define a precise decay of energy onto the invariant manifolds also defined as nonlinear normal modes nnms then this time independent formulation is used to reduce the dynamics governing the oscillations of a structure excited by an external harmonic force the validity of the proposed roms is systematically discussed and compared with other available methods in particular it is shown that large values of the modal damping of the slave modes may change the type of nonlinearity hardening softening behaviour of the directly excited master mode two examples are used to illustrate the main features of the method a two degrees of freedom dof system allows presentation of the main results through a simple example then a water filled circular cylindrical shell with external resonant forcing is considered in order to show the ability of the method to substantially reduce the dynamics of a continuous structure 2006 elsevier ltd all rights reserved

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

t s fuzzy based sliding mode controller design for discrete time nonlinear model and its applications abstract this paper investigates the takagi sugeno t s fuzzy based sliding mode control smc design of the discrete time nonlinear model by constructing a suitable fuzzy membership functions fmfs dependent lyapunov function the sufficient conditions are derived such that the resultant discrete time t s fuzzy model can achieve strictly q s r dissipative where q s and r are known matrices with compatible dimensions satisfying q 0 and r r t and is a positive constant then the desired control gain can be obtained by solving a set of linear matrix inequalities lmis besides that a fuzzy smc is designed to assure reaching condition a modified fuzzy sliding mode controller is also constructed to adapt input saturation finally simulation results are presented to demonstrate the applicability and effectiveness of the proposed approaches