exact closed form solution for the vibration modes of the euler bernoulli beam with multiple open cracks abstract in this study exact closed form expressions for the vibration modes of the euler bernoulli beam in the presence of multiple concentrated cracks are presented the proposed expressions are provided explicitly as functions of four integration constants only to be determined by the standard boundary conditions the enforcement of the boundary conditions leads to explicit expressions of the natural frequency equations besides the evaluation of the natural frequencies neither computational work nor recurrence expressions for the vibration modes are required the cracks that are not subjected to the closing phenomenon are modelled as a sequence of dirac s delta generalised functions in the flexural stiffness the eigen mode governing equation is formulated over the entire domain of the beam without enforcement of any continuity conditions which are already accounted for in the adopted flexural stiffness model the vibration modes of beams with different numbers of cracks under different boundary conditions have been analysed by means of the proposed closed form expressions in order to show their efficiency

stabilization of highly nonlinear hybrid systems by feedback control based on discrete time state observations given an unstable hybrid stochastic differential equation sde can we design a feedback control based on the discrete time observations of the state at times 0 tau 2 tau ldots so that the controlled hybrid sde becomes asymptotically stable it has been proved that this is possible if the drift and diffusion coefficients of the given hybrid sde satisfy the linear growth condition however many hybrid sdes in the real world do not satisfy this condition namely they are highly nonlinear and there is no answer to the question yet if the given sde is highly nonlinear the aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid sdes under some reasonable conditions on the drift and diffusion coefficients we show how to design the feedback control function and give an explicit bound on tau the time duration between two consecutive state observations whence the new theory established in this paper is implementable

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

holder classes with boundary conditions as interpolation spaces on etudie la caracterisation de certains espaces d interpolation reels entre le domaine d un operateur differentiel elliptique avec des conditions aux limites generales et l espace de banach de fonctions continues dans lequel le domaine est plonge

smooth solutions to a class of free boundary parabolic problems we establish existence uniqueness and regularity results for solutions to a class of free boundary parabolic problems including the free boundary heat equation which arises in the so called focusing problem in the mathematical theory of combustion such solutions are proved to be smooth with respect to time for positive t if the data are smooth

a dqem for transverse vibration analysis of multiple cracked non uniform timoshenko beams with general boundary conditions in this paper a differential quadrature element method dqem for free transverse vibration analysis of multiple cracked non uniform timoshenko beams with general boundary conditions is proposed governing equations the compatibility conditions at the damaged cross sections and implementation of the external boundary conditions are derived and formulated by the differential quadrature analogue the accuracy convergence and versatility of the proposed method are confirmed by the exact solution of the uniform beam which has been presented by other authors and 2d finite element method fem numerical results for non uniform beam after the validation of the presented method the effect of quantity depth and location of the cracks on the frequency values of vibrations are investigated the achieved results show that the existence of the crack leads to a decrease in the frequencies of the vibrations through decrease in the stiffness of the beam meanwhile the compatibility conditions at the damaged section is considered as a discontinuity in slope and vertical displacement where the effect of the discontinuity in the slope is more considerable as many authors have neglected the discontinuity in the vertical displacement as it will be shown consideration of the discontinuity in the vertical displacement causes more decrease in the frequencies

a general approach to stability in free boundary problems abstract every solution of a linear elliptic equation on a bounded domain may be considered as an equilibrium of a free boundary problem the free boundary problem consists of the corresponding parabolic equation on a variable unknown domain with free boundary conditions prescribing both dirichlet and neumann data we establish a rigorous stability analysis of such equilibria including the construction of stable and unstable manifolds for this purpose we transform the free boundary problem to a fully nonlinear and nonlocal parabolic problem on a fixed domain with fully nonlinear lateral boundary conditions and we develop the general theory for such problems as an illustration we give two examples the second being the focussing flame problem in combustion theory

an asynchronous operation approach to event triggered control for fuzzy markovian jump systems with general switching policies this paper investigates the problem of event triggered control for a class of fuzzy markov jump systems with general switching policies a novel event triggered scheme is proposed to improve the transmission efficiency at each sampling instance each transition rate allows to be unknown known or only its uncertain domains value is known with the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller sufficient conditions for the resulting fuzzy markovian jump systems are established in terms of coupled linear matrix inequalities finally an example is given to illustrate the validity of the developed technique

mode independent cal h _ infty filters for markovian jump linear systems this note addresses the problem of hinfin filtering for continuous time linear systems with markovian jumping parameters the main contribution of the note is to provide a method for designing an asymptotically stable linear time invariant hinfin filter for systems where the jumping parameter is not accessible the cases where the transition rate matrix of the markov process is either exactly known or unknown but belongs to a given polytope are treated the robust hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a lyapunov function that depends on the uncertain parameters is developed the proposed filter designs are given in terms of linear matrix inequalities

identification of crack location in vibrating simply supported beams abstract the dynamics of a cracked simply supported uniform beam is treated for either bending or axial vibrations the crack is simulated by an equivalent spring connecting the two segments of the beam analysis of this approximate model results in algebraic equations which relate the natural frequencies to beam and crack characteristics these expressions are then applied to studying the inverse problem identification of crack location from frequency measurements it is found that the only information required for accurate crack identification is the variation of the first two natural frequencies due to the crack with no other information needed concerning the beam geometry or material and the crack depth or shape the proposed method is confirmed by comparing it with results of numerical finite element calculations

h_ infty filtering for discrete time switched systems with known sojourn probabilities this technical note deals with the design of mode dependent h infty filters for a class of discrete time switched systems with nonlinearities in this class of systems when the system mode changes the filter designed for the specific subsystem also switches accordingly the main contribution is on the use of the information of the sojourn probability the probability of the switched system staying in each subsystem to build new kind of switched system model when this additional information is available sojourn probabilities are easier to obtain than the transition probabilities commonly used in markovian jump systems applying the lyapunov functional method the bounded real lemma brl for the resulting filtering error system is obtained in theorem 1 the filter parameters are designed in theorem 2 by solving a set of linear matrix inequalities finally two illustrative examples are given to demonstrate the effectiveness and potential of the proposed approach

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

vibration analysis of multiple cracked non uniform beams this paper presents the energy based method for the vibration identification of non uniform euler bernoulli beams having multiple open cracks the method includes significant modifications for the energy based method presented by yang et al crack identification in vibrating beams using the energy method journal of sound and vibration 244 2 2001 339 357 the distribution of the energy consumed is determined by taking into account not only the strain change at the cracked beam surface as in general but also the considerable effect of the stress field caused by the angular displacement of the beam due to bending the rayleigh ritz approximation method is used in the analysis the method is adapted to the cases of multiple cracks with an approach based on the definition of strain disturbance variation along the beam examples are presented on cantilever beams having different truncation factors when the results are compared with a commercial finite element program and with the results of zheng and fan natural frequencies of a non uniform beam with multiple cracks via modified fourier series journal of sound and vibration 242 4 2001 701 717 good agreements are obtained the effects of truncation factors and positions of cracks on the natural frequency ratios are presented in graphics

a novel method for crack detection in beam like structures by measurements of natural frequencies abstract a novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies first an explicit expression of the natural frequencies through crack parameters is derived as a modification of the rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity this expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation the obtained nonlinear expression for natural frequencies in combination with the so called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies the developed theory has been illustrated and validated by both numerical and experimental results

structural damage detection based on the reconstructed phase space for reinforced concrete slab experimental study in this paper a parameter based on geometry changes of the reconstructed multidimensional phase space of the measured vibration signals for structural damage identification is proposed the choice of the proper delay time steps and embedding dimensions for phase space reconstruction of linear systems is discussed using the determined delay time and embedding dimensions an index changes of phase space topology cpst with multiple embedding dimensions is calculated and then used to identify the structural damage to demonstrate the reliability of the proposed method vibration test data corresponding to different damage states of a continuous reinforced concrete slab is used to calculate the cpst value for damage identification the results indicate that except the measurement points at structural supports the cpst values at all the measurement points on the structure increase with structural damage level irrespective of the damage location indicating that using a single or a minimum number of measurement points and their cpst value can effectively identify damage existence in the structure the traditional modal based indices are also calculated using the same vibration data for comparison it is found that the proposed method with cpst is the most sensitive to structural damage than any modal based index the results demonstrate that the proposed method with cpst value is very effective in identifying damage existence in the structure although it cannot quantify the damage it can be a good candidate for continuous structural health monitoring because it needs only a few sensors to detect damage existence in the entire structure

a free boundary problem stemmed from combustion theory part ii stability instability and bifurcation results we deal with a free boundary problem depending on a real parameter in a infinite strip in r2 providing stability instability and bifurcation

almost sure stabilization of uncertain continuous time markov jump linear systems this work deals with the robust almost sure as stabilization problem for continuous time markov jump linear systems mjls norm bounded uncertainties affecting the system state and input matrices are considered a deterministically testable sufficient condition for robust as stability is provided which relies on a bound on the 2 norm of the system transition matrix such a condition can be profitably employed also to design a robust feedback stabilization strategy such feedback design is based on a formulation of the sufficient condition for robust as stability in terms of an equivalent lmi problem

stability in a two dimensional free boundary combustion model we prove rigorously the stability of the planar travelling wave solution to a free boundary system in r2 arising as a model in combustion theory for appropriate values of the reduced lewis number after changements of coordinates and unknowns the problem is reduced to the stability of the null solution of a fixed boundary parabolic system the difficulties consist in the fact that the final system is fully nonlinear and the spectrum of the linearized system contains the halffine 0 they are overcome setting the problem in a suitably weighted holder space

model reduction of markovian jump systems with uncertain probabilities this paper studies the problem of model reduction for nonhomogeneous markovian jump systems the transition probability matrix of the nonhomogeneous markovian chain has the characteristic of a polytopic structure an asynchronous reduced order model is considered and the asynchronization is modeled by a hidden markov model with a partially unknown conditional probability matrix under this framework a new sufficient condition is proposed to ensure that the augmented system is stochastically mean square stable with a specified level of h infty performance finally a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained

a simplified method for natural frequency analysis of a multiple cracked beam a new method for natural frequency analysis of beam with an arbitrary number of cracks is developed on the bases of the transfer matrix method and rotational spring model of crack the resulted frequency equation of a multiple cracked beam is general with respect to the boundary conditions including the more realistic elastic end supports and can be constructed analytically by using symbolic codes the procedure proposed is advanced by elimination of numerical computation of the high order determinant so that the computer time for calculating natural frequencies in consequence is significantly reduced numerical computation has been carried out to investigate the effect of each crack the number of cracks and boundary conditions on the natural frequencies of a beam

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

vibration of beams with arbitrary discontinuities and boundary conditions abstract a general solution of the vibration of an euler bernoulli beam with arbitrary type of discontinuity at arbitrary number of locations is presented in this paper to account for the discontinuity term induced by various additional elements on the beam heaviside s function is used to express the modal displacement of the whole beam by a single function this general modal displacement function is then solved by using laplace transformation this general solution consists of four types of basic modal shapes induced by four corresponding types of discontinuity terms at the discontinuity points various discontinuity terms are obtained and expressed by the boundary values of the modal displacement in a recursive way consequently the modal displacement can be determined by examining only the conditions on the boundary in such a way the present solution reduces the vibration of beams with arbitrary discontinuities to the same order of the case without discontinuity point to demonstrate the efficiency and applicability of the present method three application examples are presented calculation example shows that the lead zirconate titanate pzt actuator should be placed as close to the fixed end as possible to achieve the best excitation effect on a cantilever beam a new method to calculate the driving point anti resonance frequency is also proposed numerical results suggest that the variation of driving point anti resonance frequency can be used to determine the location and size of crack in beams due to the generic nature of the solution and the problem the present method can be utilized in smart structures modeling and structural health monitoring of beam type structures

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

the exact explicit dynamic stiffness matrix of multi cracked euler bernoulli beam and applications to damaged frame structures abstract in this paper the closed form expression of the exact dynamic stiffness matrix of an euler bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived the procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi cracked beam derived by the same authors in a previous paper the knowledge of the exact explicit dynamic stiffness matrix of the multi cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes consistent with the distributed parameter model through the application of the well known wittrick williams algorithm some numerical applications relative to the evaluation of frequencies and the corresponding mode shapes of multi cracked framed structure are reported furthermore the closed form solution has been validated by comparing with some exact results available in the literature for a simple single cracked frame finally further new results for a multi cracked frame have been compared with those obtained by a finite element simulation

on eigenvalue sets and convergence rate of ito stochastic systems with markovian switching this technical note is concerned with stability analysis and stabilization of ito stochastic systems with markovian switching a couple of eigenvalue sets for some positive operator associated with the stochastic system under study are defined to characterize its stability in the mean square sense properties for these eigenvalue sets are established based on which we show that the spectral abscissa of these eigenvalues sets are the same and thus these eigenvalue sets are equivalent in the sense of characterizing the stability of the system also it is shown that the guaranteed convergence rate of the markovian jump ito stochastic systems can be determined by some eigenvalue set finally a linear matrix inequality based approach is proposed to design controllers such that the closed loop system has guaranteed convergence rate some numerical examples are carried out to illustrate the effectiveness of the proposed approach the research in this technical note opens several perspectives for future work stated as some open problems

robust cal h _ infty filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation the finite horizon case this paper addresses the robust h filtering problem for a class of discrete time varying markovian jump systems with randomly occurring nonlinearities and sensor saturation two kinds of transition probability matrices for the markovian process are considered namely the one with polytopic uncertainties and the one with partially unknown entries the nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the bernoulli distributions the main purpose of this paper is to design a robust filter over a given finite horizon such that the h disturbance attenuation level is guaranteed for the time varying markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation sufficient conditions are established for the existence of the desired filter satisfying the h performance constraint in terms of a set of recursive linear matrix inequalities simulation results demonstrate the effectiveness of the developed filter design scheme

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

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

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

computational analysis of multi stepped beams and beams with linearly varying heights implementing closed form finite element formulation for multi cracked beam elements abstract the model where the cracks are represented by means of internal hinges endowed with rotational springs has been shown to enable simple and effective representation of transversely cracked slender euler bernoulli beams subjected to small deflections it namely provides reliable results when compared to detailed 2d and 3d models even if the basic linear moment rotation constitutive law is adopted this paper extends the utilisation of this model as it presents the derivation of a closed form stiffness matrix and a load vector for slender multi stepped beams and beams with linearly varying heights the principle of virtual work allows for the simple inclusion of an arbitrary number of transverse cracks the derived at matrix and vector define an exact finite element for the utilised simplified computational model the presented element can be implemented for analysing multi cracked beams by using just one finite element per structural beam member the presented expressions for a stepped beam are not exclusively limited to this kind of height variation as by proper discretisation an arbitrary variation of a cross section s height can be adequately modelled the accurate displacement functions presented for both types of considered beams complete the derivations all the presented expressions can be easily utilised for achieving computationally efficient and truthful analyses

robust h control for a class of uncertain mechanical systems in this article the problem of h control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass damping and stiffness matrices two approaches norm bounded and linear fractional transformation lft uncertainty formulations are considered by using a new lyapunov krasovskii functional approach combined with the advanced techniques for achieving delay dependence improved robust h state feedback controller design methods are developed the existence condition for admissible controllers is formulated in the form of linear matrix inequalities lmis and the controller design is cast into a convex optimisation problem subject to lmi constraints if the optimisation problem is solvable a desired controller can be readily constructed the result for the norm bounded uncertainty case improves the existing ones in terms of design conservatism and that for the lft uncertainty case represents the first attempt in this direction an ill

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

h control for discrete time markov jump systems with uncertain transition probabilities in this technical note the h control problem for a class of discrete time markov jump systems mjss with uncertain transition probabilities tps is investigated the uncertain information of transition probabilities is quantized by gaussian transition probability density function pdf in light of the proposed descriptions the mjss with gaussian pdf of tps cover the systems with precisely known and partially known tps as two special cases sufficient conditions for the existence of h controller of the underlying systems are derived in term of linear matrix inequalities a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

a free boundary problem stemmed from combustion theory part i existence uniqueness and regularity results abstract we deal with a free boundary problem depending on a real parameter in a infinite strip in r 2 which admits a planar travelling wave solution for every r we prove existence uniqueness and regularity results for the solutions near the travelling wave

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

slow state variables feedback stabilization for semi markov jump systems with singular perturbations the slow state variables feedback stabilization problem for semi markov jump discrete time systems with slow sampling singular perturbations is discussed in this work a new fairly comprehensive system model semi markov jump system with singular perturbations which is more general than markov jump model is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems based on a slow state variables feedback control scheme a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated with the help of the discrete time semi markov kernel approach some sojourn time dependent and less conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed finally an illustrative example is given to show the superiority and usefulness of the proposed method

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

a separation principle for the continuous time lq problem with markovian jump parameters in this paper we devise a separation principle for the finite horizon quadratic optimal control problem of continuous time markovian jump linear systems driven by a wiener process and with partial observations we assume that the output variable and the jump parameters are available to the controller it is desired to design a dynamic markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time as in the case with no jumps we show that an optimal controller can be obtained from two coupled riccati differential equations one associated to the optimal control problem when the state variable is available and the other one associated to the optimal filtering problem this is a separation principle for the finite horizon quadratic optimal control problem for continuous time markovian jump linear systems for the case in which the matrices are all time invariant we analyze the asymptotic behavior of the solution of the derived interconnected riccati differential equations to the solution of the associated set of coupled algebraic riccati equations as well as the mean square stabilizing property of this limiting solution when there is only one mode of operation our results coincide with the traditional ones for the lqg control of continuous time linear systems

instabilities in a combustion model with two free interfaces abstract we study in a strip of r 2 a combustion model of flame propagation with stepwise temperature kinetics and zero order reaction characterized by two free interfaces respectively the ignition and the trailing fronts the latter interface presents an additional difficulty because the non degeneracy condition is not met we turn the system to a fully nonlinear problem which is thoroughly investigated when the width l of the strip is sufficiently large we prove the existence of a critical value le c of the lewis number le such that the one dimensional planar solution is unstable for 0 le le c some numerical simulations confirm the analysis

stability analysis and stabilization for nonlinear continuous time descriptor semi markov jump systems this paper investigates the stochastic stability and the state feedback control design for a class of nonlinear continuous time descriptor semi markov jump systems whose transition rates are time varying which are more general than the descriptor markov jump systems first by deriving the infinitesimal generator for stochastic lyapunov functional of descriptor semi markov jump systems a stochastic stability condition is established which guarantees this kind of systems are regular impulse free have a unique solution and are stochastically stable in order to design the state feedback controller a linear matrix inequality lmi stability condition is developed based on the lower and upper bounds of the time varying transition probability and singular value decomposition approach furthermore the state feedback controller design is developed in terms of lmi approach last numerical examples are given to demonstrate the effectiveness of the obtained methods

instabilities in a two dimensional combustion model with free boundary we prove instability of the planar travelling wave solution in a two dimensional free boundary problem modelling the propagation of near equidiffusional premixed flames in the whole plane we reduce the problem to a fixed boundary fully nonlinear parabolic system the spectrum of the linearized operator contains an interval 0 c c 0 so we cannot construct backward solutions we use an argument about stability of dynamical systems in banach spaces in order to prove pointwise instability of the moving front

stabilisation of mode dependent singular markovian jump systems with generally uncertain transition rates this paper is devoted to investigating the stability and stabilisation problems for continuous time mode dependent singular markovian jump systems smjss with generally uncertain transition rates gutrs first we establish a sufficient condition in terms of a set of coupled linear matrix inequalities lmis to ensure the systems to be regular impulse free and stochastically stable then we design a mode dependent state feedback controller to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method