robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

adaptive approximation for multiple sensor fault detection and isolation of nonlinear uncertain systems this paper presents an adaptive approximation based design methodology and analytical results for distributed detection and isolation of multiple sensor faults in a class of nonlinear uncertain systems during the initial stage of the nonlinear system operation adaptive approximation is used for online learning of the modeling uncertainty then local sensor fault detection and isolation sfdi modules are designed using a dedicated nonlinear observer scheme the multiple sensor fault isolation process is enhanced by deriving a combinatorial decision logic that integrates information from local sfdi modules the performance of the proposed diagnostic scheme is analyzed in terms of conditions for ensuring fault detectability and isolability a simulation example of a single link robotic arm is used to illustrate the application of the adaptive approximation based sfdi methodology and its effectiveness in detecting and isolating multiple sensor faults

treatment of material discontinuities in finite element computations we consider finite element analysis of problems with discontinuous material coefficients for applications in which the material interface crosses an element we develop special elements with an embedded flux constraint at the interface this new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by steven 1 supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined some local superconvergence behaviour is observed

continuously deforming finite elements a general class of time dependent co ordinate transformations is introduced in a variational formulation for evolution problems the variational problem is posed with respect to both solution and transformation field variables an approximate analysis using finite elements is developed from the continuous variational form modified forms of the variational functional are considered to ensure the deforming mesh is not top irregular ode system integrators are utilized to integrate the resulting semidiscrete systems in part i we consider the formulation for problems in one spatial dimension and time including in particular convection dominated flows described by the convection diffusion burgers and buckley leverett equations in part ii the extension of the method to two dimensions and supporting numerical experiments are presented

reliable finite time sliding mode control for singular time delay system with sensor faults and randomly occurring nonlinearities abstract this paper focuses on the finite time sliding mode control problem for singular time delay system with sensor failures and uncertain nonlinearities based on the proposed sliding mode control law sufficient criteria are provided to guarantee the closed loop system is singular sliding mode finite time boundedness in both reaching phase and sliding motion phase the prescribed sliding mode control law can drive the state trajectories onto the specified sliding surface in a short time interval furthermore the singular h finite time boundedness conditions for error system have been established with sensor faults over the whole interval through the linear matrix inequalities technique gain matrices for controller and estimator can be obtained finally numerical examples have been given to demonstrate the potentials of the proposed method

delay dependent robust stability criteria for two classes of uncertain singular time delay systems in this note the delay dependent robust stability criteria for two classes of singular time delay systems with norm bounded uncertainties are investigated first without using model transformation and bounding technique for cross terms an improved delay dependent stability criterion for the nominal singular time delay system is established in terms of strict linear matrix inequalities lmis then based on this criterion the delay dependent robust stability criteria for two classes of uncertain singular time delay systems are proposed which ensure that the systems are regular impulse free and asymptotically stable for all admissible uncertainties numerical examples are proposed to illustrate the less conservatism of the obtained results

numerical approximation of a two dimensional parabolic time dependent problem containing a delta function the convergence of a difference scheme for a two dimensional initial boundary value problem for the heat equation with concentrated capacity and time dependent coefficients of the space derivatives is considered an estimate of the rate of convergence in a special discrete w 2 2 1 sobolev norm compatible with the smoothness of the coefficients and the solution is proved

analysis of material interface discontinuities and superconvergent fluxes in finite difference theory abstract an analysis of material interface discontinuities is developed and applied in finite difference theory to determine mathematically rigorous averaging techniques for material properties this result is compared with other averaging techniques particularly harmonic averaging which is often applied in practice we also develop a class of formulas of high accuracy for post processing the difference formula to compute derivatives fluxes stresses and conduct supporting numerical studies

convergence of finite difference method for the parabolic problem with concentrated capacity and variable operator we investigate the convergence of difference schemes for the one dimensional heat equation with variable time dependent operator and the coefficient at the time derivative heat capacity containing dirac delta distribution an abstract operator method is developed for analyzing this equation estimate for the rate of the convergence in special discrete energetic sobolev norm compatible with the smoothness of the solution is obtained

internally discontinuous finite elements for moving interface problems all physical process change with time and although physicists and engineers often freeze them to simplify their model studies this is not always possible add to this the existence of several subregions within the modelling domain with different physical properties the size and number of which change with time and one has produced what might appear to be an intractable problem previous studies have shown that adaptive grids are an inconvenient way of modelling such moving interface problems and suggested that the use of a fixed grid with special discontinuous elements affords an efficient solution technique this work presents and develops the characteristic matrices for two such elements namely a quadratic triangle with an internal interface modelled by two straight lines and a quadratic isoparametric element both these elements are tested against an analytical solution to a simple poisson equation such tests reveal the performance of the proposed elements to be satisfactory except for the definition of gradients near the interface

finite time control of discrete time linear systems in this note we consider the finite time stabilization of discrete time linear systems subject to disturbances generated by an exosystem finite time stability can be used in all those applications where large values of the state should not be attained for instance in the presence of saturations the main result provided in the note is a sufficient condition for finite time stabilization via state feedback this result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite time stability all the conditions are then reduced to feasibility problems involving linear matrix inequalities lmis some numerical examples are presented to illustrate the proposed methodology

sliding mode control for singular stochastic markovian jump systems with uncertainties this paper considers sliding mode control design for singular stochastic markovian jump systems with uncertainties a suitable integral sliding function is proposed and the resulting sliding mode dynamics is an uncertain singular stochastic markovian jump system a set of new sufficient conditions is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics but also determines all the parameter matrices in the integral sliding function then a sliding mode control law is synthesized such that reachability of the specified sliding surface can be ensured finally three examples are given to demonstrate the effectiveness of the results

reliable finite time h filtering for discrete time delay systems with markovian jump and randomly occurring nonlinearities this paper is concerned with the problem of reliable finite time h filtering for discrete time varying delay systems with markovian jump and randomly occurring nonlinearities rons rons are introduced to model a class of sector like nonlinearities that occur in a probabilistic way according to a two dimensional discrete random variables joint distribution the failures of sensors are quantified by a variable varying in a given interval the time varying delay is unknown with given lower and upper bounds firstly the filtering errr dynamic system is constructed based on an h filter sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite time boundedness and stochastic finite time h filtering in both normal and fault cases the gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter respectively finally numerical examples are given to demonstrate the effectiveness of the proposed design approach

technical communique finite time control of linear systems subject to parametric uncertainties and disturbances in this paper we consider finite time control problems for linear systems subject to time varying parametric uncertainties and to exogenous constant disturbances the main result provided is a sufficient condition for robust finite time stabilization via state feedback it can be applied to problems with both non zero initial conditions and unknown constant disturbances this condition is then reduced to a feasibility problem involving linear matrix inequalities lmis a detailed example is presented to illustrate the proposed methodology

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

approximate boundary flux calculations abstract a technique for determining derivatives fluxes or stresses from finite element solutions is developed the approach is a generalization to higher dimensions of a procedure known to give highly accurate results in one dimension numerical experiments demonstrate that certain difficulties are associated with corners in the higher dimensional extensions and two variants of the method are examined we consider both triangular and quadrilateral elements and observe some interesting differences in the numerical rates of convergence finally this post processing scheme is tested for nonlinear problems

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

derivative calculation from finite element solutions abstract a technique is considered whereby very accurate derivatives of a finite element solution can be calculated efficiently it is demonstrated here that most of the necessary quantities for this subsidiary computation are available as computed by products in the preceding finite element solution procedure the calculation is shown in this note to be a particular form of a procedure for which superconvergent theoretical error estimates have been proven elsewhere numerical experiments confirm the superior accuracy in the computed derivative stress or flux

finite time h control for a class of discrete time switched singular time delay systems subject to actuator saturation this paper concerns with the finite time h control problem for a class of discrete time switched singular time delay with actuator saturation not only linear matrix inequality conditions for the systems but also average dwell time of switching signal is given to guarantee regular causal and finite time boundedness for the discrete time switched singular time delay system moreover sufficient conditions are presented to ensure the h disturbance attenuation level and the design method of h controller is developed by solving linear matrix inequalities lmi optimization problem without any decompositions of system matrices and equivalent transformation furthermore the function in the proof procedure belongs to multiple lyapunov like functions whose advantage lies in their flexibility finally numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature

robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation in this paper the problem of robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation is studied first sufficient conditions that guarantee the systems singular stochastic finite time boundedness are derived via constructing a delay dependent lyapunov krasonskii functional and linear matrix inequalities lmi approaches then the results are extended to singular stochastic finite time h boundedness furthermore with these conditions and convex optimization arithmetic the design method of h controller and conditions that ensure the h disturbance attenuation level are obtained finally some numerical examples are presented to illustrate the validity and efficiency of the proposed methods

robust sliding mode control for markovian jump singular systems with randomly changing structure abstract this paper discusses the robust optimization by a sliding mode control smc approach for uncertain singular markovian jump smj time varying delay system with nonlinear perturbation which uncertainties occur randomly firstly a different integral type sliding mode surface sms and a different lyapunov krasovskii function are introduced secondly by using linear matrix inequalities sufficient conditions are proposed to ensure the mean square exponentially admissible msea with an h performance level of the unforced uncertain smj time varying delay system in the specified sms next a composed smc law with the parameter uncertainties occurring randomly can ensure the reachability of the predefined sms finally three numerical examples are given to test the feasibility of the theory

on the convergence of finite difference schemes for the heat equation with concentrated capacity we investigate the convergence of difference schemes for the one dimensional heat equation when the coefficient at the time derivative heat capacity is c left x right 1 k delta left x xi right k const 0 represents the magnitude of the heat capacity concentrated at the point x xi an abstract operator method is developed for analyzing this equation estimates for the rate of convergence in special discrete energetic sobolev s norms compatible with the smoothness of the solution are obtained

convergence of a finite difference method for solving 2d parabolic interface problems the convergence of a difference scheme for solving two dimensional parabolic interface problems with variable coefficients is investigated an estimate of the rate of convergence in a special discrete w 2 2 1 sobolev norm compatible with the smoothness of the coefficients and solution is obtained