stabilization bound of singularly perturbed systems subject to actuator saturation this paper considers the stabilization bound problem for singularly perturbed systems spss subject to actuator saturation a state feedback stabilization controller design method is proposed and a basin of attraction depending on the singular perturbation parameter is constructed which facilitates the formulation of the convex optimization problem for maximizing the basin of attraction of spss finally examples are given to show the advantages and effectiveness of the obtained results

sampling and interpolation in large bergman and fock spaces we obtain sampling and interpolation theorems in weighted spaces of analytic functions for radial weights of arbitrary more rapid than polynomial growth we give an application to invariant subspaces of arbitrary index in large weighted bergman spaces

stability and stabilization of two time scale switched systems in discrete time in this technical note stability and stabilization of two time scale switched linear systems in the singular perturbation form are addressed in discrete time we show that under an arbitrary switching rule stability of the slow and fast switched subsystems is not sufficient to assess stability of the original two time scale switched system even if the singular perturbation parameter tends to zero therefore we propose lmi based conditions that guarantee the asymptotic stability of the two time scale switched system using switched quadratic lyapunov functions these conditions express the fact that the coupling between fast and slow subsystems has to be taken into account in addition to stability properties of the two subsystems when the switching rule is arbitrary the presented conditions are extended to state feedback control design a numerical example illustrates the features of the proposed approach

robustness of dynamic output feedback control for singular perturbation systems abstract the problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated the solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so called auxiliary system of the slow subsystem some conditions are proposed to ensure the robustness of the actual closed loop system the exact upper bound of the parasitic parameter for the controlled system is also determined finally an actual model which failed in dynamic output feedback control in 4 is reexamined successfully here

singularly perturbed difference equations in optimal control problems a linear regular problem involving singularly perturbed difference equations is considered the basic features of singularly perturbed systems order reduction separation of time scales boundary layers etc are highlighted application to the numerical treatment of control problems involving stiff differential equations is discussed

aggregation of the policy iteration method for nearly completely decomposable markov chains a steady state optimal control problem is considered for nearly completely decomposable markov chains in order to apply the policy iteration method of r a howard dynamic programming and markov processes cambridge ma mit press 1960 a high dimensional ill conditioned system of algebraic equations must be solved in the value determination step although algorithms exist for aggregation of the steady state probability distribution problem they only provide methods for computing the cost not the dual variables using a singular perturbation approach an aggregation method for the value determination equation is developed the aggregation method is developed in three steps first a class of similarity transformations that transform the system into a singularly perturbed form is developed second an aggregation method to compute the steady state probability distribution is derived third this aggregation method is applied to the value determination step of howard s method 1960

some sufficient conditions for the division property of invariant subspaces in weighted bergman spaces the authors consider weighted bergman spaces of holomorphic l sp p integrable functions with respect to certain borel measures on a bounded plane region a closed subspace scr m of such a space is said to be invariant if z scr m subset scr m in the case of the standard bergman space of the unit disk with p 2 the authors proved in a recent joint paper with c sundberg acta math 177 1996 no 2 275 310 mr1440934 98a 46034 that every invariant subspace scr m is generated by a wandering subspace scr m ominus z scr m for the shift operator thus obtaining an analogue of the celebrated theorem of beurling an invariant space is said to have the division property if the quotient space scr m z lambda scr m is one dimensional for any lambda in the domain under certain additional hypotheses this is equivalent to the codimension one property studied earlier by s richter h hedenmalm k seip and others the main results of this paper are various sufficient conditions for an invariant subspace to have the division property in terms of the local boundary behavior of the functions in the subspace a function f analytic in the unit disc is said to be locally nevanlinna near a point lambda on the unit circle if the subharmonic function log f has a harmonic majorant in the carleson type set obtained by intersecting the unit disk with some disc centered at lambda the authors show that an invariant subspace scr m of the standard bergman space a sp p sb alpha with radial weights 1 z sp 2 sp alpha p ge 1 alpha 1 possesses the division property if some nonzero function f in the subspace is locally nevanlinna at a boundary point they observe that given an invariant subspace scr m which does not have the division property it will always contain two functions such that the space they generate does not have it either it is therefore a question of interest to determine under what conditions the space generated by two functions will possess this property the authors prove the following theorem let 1 le p infty 1 r 1 s 1 p and let f and g be two nonzero functions in a sp p such that f is locally r integrable and g is locally s integrable both in a neighborhood of a boundary point of the disc then the closed linear span of the cyclic invariant subspaces generated by f and by g has the division property an example is also given based on the earlier results of hedenmalm and seip which shows that the theorem is in a way sharp for p 2 the main results also have some interesting corollaries listed in the paper less

random weighted shifts abstract in this paper we initiate the study of a fundamental yet untapped random model of non selfadjoint bounded linear operators acting on a separable complex hilbert space we replace the weights w n 1 in the classical unilateral shift t defined as t e n w n e n 1 where e n n 1 form an orthonormal basis of a complex hilbert space by a sequence of i i d random variables x n n 1 that is w n x n this paper answers basic questions concerning such a model we propose that this model can be studied in comparison with the classical hardy bergman dirichlet spaces in function theoretic operator theory we calculate the spectra and determine their fine structures section 3 we classify the samples up to four equivalence relationships section 4 we introduce a family of random hardy spaces and determine the growth rate of the coefficients of analytic functions in these spaces section 5 we compare them with three types of classical operators section 6 this is achieved in the form of generalized von neumann inequalities the invariant subspaces are shown to admit arbitrarily large indices and their semi invariant subspaces model arbitrary contractions almost surely we discuss a beurling type theorem section 7 we determine various non selfadjoint algebras generated by t section 8 their dynamical properties are clarified section 9 their iterated aluthge transforms are shown to converge section 10 in summary they provide a new random model from the viewpoint of probability theory and they provide a new class of analytic functional hilbert spaces from the viewpoint of operator theory the technical novelty in this paper is that the methodology used draws from three largely separate sources probability theory functional hilbert spaces and the approximation theory of bounded operators

the locally stabilized finite volume method for incompressible flow a locally stabilized finite volume method for the two dimensional incompressible flow governed by stationary stokes and navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem the optimal l 2 error estimate of u h p h determined by stokes equations is also deduced some numerical examples are provided to check the efficiency of this method

the accuracy of cell vertex finite volume methods on quadrilateral meshes for linear first order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method on structured meshes consisting of distorted quadrilaterals the global error is shown to be of second order in various mesh dependent norms provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the guadrilateral on tensor product nonuniform meshes the cell vertex scheme coincides with the familiar box scheme in this case second order accuracy is shown without any additional assumption on the regularity of the mesh which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions observed in practice 17 refs

multirate and composite control of two time scale discrete time systems the design of stabilizing feedback control of singularly perturbed diserete time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control composite control strategies are developed for the case of single rate measurements all variables are measured at the same rate as well as for the case of multirate measurements slow variables are measured at a rate slower than that of fast variables

maximal minimal and primary invariant subspaces abstract let x be a complex infinite dimensional banach space an operator l on x is called of subcritical class if n 1 n 3 2 log l n t is an operator on x whose iterates have norms of polynomial growth we prove that if t has a range of finite codimension and a left inverse of subcritical class then every maximal invariant subspace of t has codimension one and if t has a finite dimensional kernel and a right inverse of subcritical class then every minimal invariant subspace of t is one dimensional using these results we obtain new information on the invariant subspace lattices of shifts and backward shifts on a wide class of banach spaces of analytic functions on the unit disc we also introduce the notion of primary invariant subspaces and determine their structure for a large class of shifts

on domain decomposition algorithms for covolume methods for elliptic problems in this paper some new two level additive schwarz domain decomposition methods are constructed and used as preconditioners for gmres for the nonsymmetric systems arising from the covolume methods for elliptic problems without any restriction on the coarse mesh size the convergence of the preconditioned gmres is obtained for both circumcentric and barycentric covolume methods with inexact solvers for subproblems the rates of convergence are shown to be independent of the number of subregions and these methods are optimal for generous overlap

the finite volume element method for diffusion equations on general triangulations this paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in mathcal r 2 using a special type of control volume the theory applies to diffusion equations of the form begin gathered nabla a nabla u f quad text in omega hfill u 0 quad text on partial omega hfill end gathered under fairly general conditions the theory establishes o h estimates of the error in a discrete mathcal h 1 seminorm under an additional assumption concerning local uniformity of the triangulation the estimate is improved to o h 2

the finite volume method based on stabilized finite element for the stationary navier stokes problem a finite volume method based on stabilized finite element for the two dimensional stationary navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem we obtain the well posedness of the fvm based on stabilized finite element for the stationary navier stokes equations moreover for quadrilateral and triangular partition the optimal h 1 error estimate of the finite volume solution u h and l 2 error estimate for p h are introduced finally we provide a numerical example to confirm the efficiency of the fvm

the method of variably scaled radial kernels for solving two dimensional magnetohydrodynamic mhd equations using two discretizations the crank nicolson scheme and the method of lines mol abstract mhd equations have many applications in physics and engineering the model is coupled equations in velocity and magnetic field and has a parameter namely hartmann the value of hartmann number plays an important role in the equations when this parameter increases using different meshless methods makes the oscillations in velocity near the boundary layers in the region of the problem in the present paper a numerical meshless method based on radial basis functions rbfs is provided to solve mhd equations for approximating the spatial variable a new approach which is introduced by bozzini et al 2015 is applied the method will be used here is based on the interpolation with variably scaled kernels the methodology of the new technique is defining the scale function c on the domain r d then the interpolation problem from the data locations x j r d transforms to the new interpolation problem in the data locations x j c x j r d 1 bozzini et al 2015 the radial kernels used in the current work are multiquadrics mq inverse quadric iq and wendland s function of course the latter one is based on compactly supported functions to discretize the time variable two techniques are applied one of them is the crank nicolson scheme and another one is based on mol the numerical simulations have been carried out on the square and elliptical ducts and the obtained numerical results show the ability of the new method for solving this problem also in appendix we provide a computational algorithm for implementing the new technique in matlab software

a stabilized multi level method for non singular finite volume solutions of the stationary 3d navier stokes equations this paper proposes and analyzes a stabilized multi level finite volume method fvm for solving the stationary 3d navier stokes equations by using the lowest equal order finite element pair without relying on any solution uniqueness condition this multi level stabilized fvm consists of solving the nonlinear problem on the coarsest mesh and then performing one newton correction step on each subsequent mesh thus only solving a large linear system an optimal convergence rate for the finite volume approximations of nonsingular solutions is first obtained with the same order as that for the usual finite element solution by using a relationship between the stabilized fvm and a stabilized finite element method then the multi level finite volume approximate solution is shown to have a convergence rate of the same order as that of the stabilized finite volume solution of the stationary navier stokes equations on a fine mesh with an appropriate choice of the mesh size h j h j 1 2 j 1 ldots j finally numerical results presented validate our theoretical findings

multirate digital control design of an optimal regulator via singular perturbation theory abstract in this paper a multirate digital control design of an optimal regulator is investigated via singular perturbation theory it is shown that the singularity perturbed continuous time regulator leads under slow and fast sampling rates to two different discrete time versions they are decomposed into slow and fast subsystems and then these solutions are combined in a proper way within the framework of such a decomposition coordination principle a multirate control design is developed naturally furthermore the problem of the asymptotic stability of a multirate controlled system is investigated and the relationship between the original continuous time version and the multirate controlled version is discussed

singular perturbation modelling of continuous and discrete physical systems the major shortcoming of the singular perturbation theory preventing its application to practical problems is that the system described by state equations is seldom given in the singularly perturbed form this paper presents a systematic procedure which converts the state equations of a large scale time invariant system to singularly perturbed form assuming that such a classification is possible this is accomplished by appropriate scaling and grouping of the state variables into slow and fast groups while retaining as many physical state variables as possible in the new state description an improved slow fast grouping of the states can result by allowing linear combination of certain available physical variables as new state variables several examples are given to illustrate the method

block lyapunov sum with applications to integral controllability and maximal stability of singularly perturbed systems a new block structured lyapunov sum for partitioned matrices is defined and basic properties are established it has similar properties to a lyapunov matrix but preserves the block structure and has similar properties to the block kronecker sum but with about half the dimension it is used to solve a maximal stability problem of integral controllability and is also used to solve for the maximal stability range of singularly perturbed systems in both cases closed formulae are obtained with lower dimensions than existing formulae

brief paper h control for fast sampling discrete time singularly perturbed systems this paper is concerned with the h control problem via state feedback for fast sampling discrete time singularly perturbed systems a new h controller design method is given in terms of solutions to linear matrix inequalities lmis which eliminates the regularity restrictions attached to the riccati based solution a method for evaluating the upper bound of singular perturbation parameter e with meeting a prescribed h performance bound requirement is also given furthermore the results are extended to robust controller design for fast sampling discrete time singularly perturbed systems with polytopic uncertainties numerical examples are given to illustrate the validity of the proposed methods

singular perturbation modelling of large scale systems with multi time scale property the problem is investigated of singular perturbation modelling which plays an important role in cases of the application of the singular perturbation method to the design and analysis of large scale systems in both continuous and discrete time versions modelling concepts based on structural properties are studied and computer oriented algorithms are developed the results of two time scale systems are extended to multi time scale cases furthermore in order to verify the validity of these studies some numerical examples are given

variational multiscale a posteriori error estimation for multi dimensional transport problems this paper presents an explicit a posteriori error estimator for the multi dimensional transport equation based on an approximation to the variational multiscale theory the technique is adequate for methods with a local error distribution such as stabilized methods yielding efficiencies close to one for both the hyperbolic and diffusive limit regarding the hyperbolic limit previous work is extended to multi dimensions adequate norms are proposed for the computation of the error and proper error intrinsic time scales are calculated for the bilinear quadrilateral and the linear triangle furthermore the model considers the element interface error along the element edges enabling the error prediction in the diffusive limit the success of the method can be explained by the fact that in stabilized methods the element local problem captures most of the error and the proposed error intrinsic time scales are an approximation to the solution of the dual problem the proposed technology which can be implemented straightforwardly in existing codes is extremely economical because it is a simple explicit postprocessing

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

optimal biquadratic finite volume element methods on quadrilateral meshes in this paper an optimal biquadratic finite volume element scheme is established and analyzed for elliptic equations on quadrilateral meshes it is proved that the new scheme has optimal o h 2 convergence rate in h 1 norm and o h 3 convergence rate in l 2 norm with the assumption that each element is an h 2 parallelogram

the mortar finite volume method with the crouzeix raviart element for elliptic problems abstract we construct and analyse a mortar finite volume method for the discretization for selfadjoint elliptic boundary value problems in r 2 this method is based on the mortar crouzeix raviart non conforming finite element spaces we prove the optimal order h 1 norm and l 2 norm error estimates between the exact solution and the mortar finite volume approximation of the elliptic problems

new stability performance results for singularly perturbed systems the guardian map theory of generalized stability of parametrized linear time invariant systems is used to prove new results on stability performance of linear time invariant singularly perturbed systems with an exogenous parameter i e systems that contain in addition to a singular parameter another uncertain parameter the results give necessary and sufficient conditions for generalized stability for all sufficiently small values of and all values of in a given interval 1 2 in addition explicit expressions for the largest upper bound on for guaranteed stability and performance are given and the cases leading to finite or infinite are clearly delineated thus the results represent a significant addition to the classical klimushev krasovskii theorem while at the same time providing closed form expressions for the maximum parameter range for stability and performance

an efficient algorithm for finding the d stability bound of discrete singularly perturbed systems with multiple time delays in this paper we present an original work on the d stabilization problem of discrete singularly perturbed systems with multiple time delays a new robust d stability criterion in terms of stability radius is first derived to guarantee that all poles of the discrete multiple time delay systems remain inside the specific disk d alpha r uncertainties then by using the technique of time scale separation we derive the corresponding slow and fast subsystems of a discrete multiple time delay singularly perturbed system the state feedback controls for the d stabilization of the slow and the fast subsystems are separately designed and a composite state feedback control for the original system is subsequently synthesized from these state feedback controls thereafter we derive a frequency domain epsilon dependent dstability criterion for the original discrete multiple time delay singularly perturbed system under the composite state feedback control if any one of the conditions of this criterion is fulfilled

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

a finite volume method based on the crouzeix raviart element for elliptic pde s in two dimensions we introduce and analyse a finite volume method for the discretization of elliptic boundary value problems in mathbb r 2 the method is based on nonuniform triangulations with piecewise linear nonconforming spaces we prove optimal order error estimates in the l 2 norm and a mesh dependent h 1 norm

large bergman spaces invertibility cyclicity and subspaces of arbitrary index in a wide class of weighted bergman spaces we construct invertible non cyclic elements these are then used to produce z invariant subspaces of index higher than one in addition these elements generate non trivial bilaterally invariant subspaces in anti symmetrically weighted hilbert spaces of sequences

a real schur form method for modeling singularly perturbed systems a method is presented for modeling a two time scale system in the singularly perturbed form the method uses an ordered real schur decomposition which can be efficiently computed using standard subroutines from eispack three results are given first it is shown that any two time scale system can be modeled in the singularly perturbed form by a transformation into an ordered real schur form followed by balancing second under some conditions on the ordered real schur decomposition a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables third necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables

the observer based controller design of discrete time singularly perturbed systems a class of linear shift invariant discrete time singularly perturbed systems with inaccessible states is considered a design technique is formulated by which the stabilizing controller can be formed through the controllers of the slow and fast subsystems sufficient conditions for stability of the closed loop system under this composite controller are given

characterization and computation for the bound e in linear time variantsingularly perturbed systems abstract this paper gives a complete solution to the bound problem in a linear time invariant singularly perturbed system a criterion is presented to determine the existence of the bound

a discontinuous finite volume method for a coupled fracture model abstract in this paper we present a discontinuous finite volume method for a hybrid dimensional coupled fracture model on triangular meshes in matrix and fracture the pressure is approximated by the discontinuous and continuous piecewise linear elements and in order to retain local conservation property the velocity is sought in the discontinuous lowest order raviart thomas element space and piecewise linear element space the proposed numerical scheme is only associated with the pressure so we avoid solving an indefinite saddle point problem in addition the discontinuous method eliminates the continuity of approximate functions across the interelement boundary so it has the advantage of high localizability and easy handling of complicated geometries optimal order error estimates for the pressure and velocity are proved and numerical experiments are carried out to confirm our theoretical analysis

a q1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh abstract in this paper we study a q 1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh it is known that the coercivity is the basement for some other theoretical results stability h 1 and l 2 error estimates etc and the existing results were mainly obtained on h 1 parallelogram meshes with scalar diffusion coefficients for the cases of full diffusion tensors and arbitrary convex quadrilateral meshes we obtain a necessary and sufficient condition for the positive definiteness of the cell matrix related to the cell bilinear form based on this result a sufficient condition is suggested to guarantee the coercivity of the scheme more interesting is that this sufficient condition covers the traditional h 1 parallelogram mesh assumption and has an explicit expression by which one can easily judge on any diffusion tensor and any mesh with arbitrary mesh size h 0 moreover an h 1 error estimate is obtained without the h 1 parallelogram assumption and some numerical results are also provided to validate the theoretical results

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

parallel reduced order controllers for stochastic linear singularly perturbed discrete systems an approach to the decomposition and approximation of linear quadratic gaussian control problems for singularly perturbed discrete systems at steady state is presented the global kalman filter is decomposed into separate reduced order local filters through the use of a decoupling transformation a near optimal control law is derived by approximating coefficients of the optimal control law the proposed method allows parallel processing of information and reduces offline and online computational requirements a real world example demonstrates the efficiency of the proposed method

stability bounds of singularly perturbed discrete systems the authors propose a systematic approach to determine the exact stability bound of singularly perturbed discrete time systems by combining three conditions of the critical stability criterion with a bialternate product for discrete time systems the stability problems of two types of singularly perturbed discrete time systems can be solved via the derived scheme several examples are given to illustrate the proposed results

a new characterization on stability bounds for singularity perturbed systems abstract in this short paper we characterize the upper bound e for the parasitic parameter e in a singularly perturbed systems which ensures stability of such a system if 0 at the same time a method is established to testify the system stability without the slow fast decomposition required in the existing literature it will be shown that this upper bound is just the minimum positive eigenvalue of a matrix pair which is explicitly constructed from the system matrix this reveals a direct relationship between the stability bound and the system matrix and may be useful in the study of robust control problems for such systems

discrete time observers for singularly perturbed continuous time systems the use of discrete time observers for nonlinear singularly perturbed continuous time systems is explored the observer design approach is based on inversion of state to measurement maps the two time scale nature of the system is exploited by constructing separate reduced order observers for the approximate slow and fast subsystems using multirate measurements and computation the reduced order observers are compared to a full order observer designed for the same system the comparison shows that although the reduced order observers exhibit some approximation error they also result in reduced computational requirements if the inversion is performed on line reduced memory requirements if the inversion is implemented by look up table and reduced stiffness the trade off between accuracy and implementation requirements always favors the reduced order approach for systems with significant separation of time scales numerical examples are provided including a case study of an observer based control system for permanent magnet synchronous motors

complementary results on the stability bounds of singularly perturbed systems in this note we will provide a new systematic approach to characterize and compute the stability bound of a singularly perturbed linear system the approach is based on the feedback system representation of an additional matrix perturbation problem the idea is to change the stability bound problem to the stability problem of an underlying feedback system this approach allows multiple choices in formulating the underlying feedback system and thus has the potential of characterizing and computing the stability bound in a number of different ways by formulating two kinds of different feedback systems some existing and new results on the stability bounds are derived based on the feedback system approach the new results complement the existing frequency domain based stability criteria and make the frequency domain technique more applicable and useful to the stability bound problem an example is provided to show the new stability criterion is effective and useful in determining the stability bound

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

robust stability of singularly perturbed discrete delay systems this paper presents new sufficient conditions for the robust stability of singularly perturbed discrete systems subjected to multiple delayed perturbations for a given spl epsi spl isin 0 spl epsi sub 0 where spl epsi sub 0

optimal control of a particular class of singularly perturbed nonlinear discrete time systems this note studies a class of discrete time nonlinear systems which depend on a small parameter using the singular perturbation theory in a systematic way we give a trajectory approximation result based on the decomposition of the model into reduced and boundary layer models this decomposition is used to analyze optimal control via maximum principle of such systems as a result significant order reduction of optimal control problems is achieved

a new parameter estimate in singular perturbations abstract a new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system general time invariant systems with a single small parameter are considered the paper employs a riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics an application of the brouwer fixed point theorem to the riccati equation and of liapunov s direct method to the fast and slow subsystems results in the desired upper bound computation of the estimate requires only the solution of two liapunov matrix equations

stabilization bound of discrete two time scale systems abstract in this paper the exact bound problem in various types of discrete two time scale tts system is considered a set of stability criteria based on the frequency domain representation is derived two interesting examples are used to demonstrate the proposed scheme

nontangential limits in pt µ spaces and the index of invariant subgroups let mu be a finite positive measure on the closed disk d over bar in the complex plane let 1 t infinity and let p t mu denote the closure of the analytic polynomials in l t mu we suppose that d is the set of analytic bounded point evaluations for p t mu and that p t mu contains no nontrivial characteristic functions it is then known that the restriction of mu to partial derivative d must be of the form h vertical bar dz vertical bar we prove that every function f is an element of p t mu has nontangential limits at h vertical bar dz vertical bar almost every point of partial derivative d and the resulting boundary function agrees with f as an element of l t h vertical bar dz vertical bar our proof combines methods from james e thomson s proof of the existence of bounded point evaluations for p t mu whenever p t mu not equal l t mu with xavier tolsa s remarkable recent results on analytic capacity these methods allow us to refine thomson s results somewhat in fact for a general compactly supported measure nu in the complex plane we are able to describe locations of bounded point evaluations for p t nu in terms of the cauchy transform of an annihilating measure as a consequence of our result we answer in the affirmative a conjecture of conway and yang we show that for 1 t infinity dim m zm 1 for every nonzero invariant subspace m of p t mu if and only if h not equal 0 we also investigate the boundary behaviour of the functions in p t mu near the points z is an element of partial derivative d where h z 0 in particular for 1 t infinity we show that there are interpolating sequences for p t mu that accumulate nontangentially almost everywhere on z h z 0 less

a two time scale neurodynamic approach to constrained minimax optimization this paper presents a two time scale neurodynamic approach to constrained minimax optimization using two coupled neural networks one of the recurrent neural networks is used for minimizing the objective function and another is used for maximization it is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization the effectiveness and characteristics of the proposed approach are illustrated using several examples furthermore the proposed approach is applied for h infty model predictive control

output feedback sliding mode control for sampled data systems we address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type by taking into account the disturbance compensation a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances in the framework of singular perturbation analysis it is shown that the closed loop system exhibits good robustness against exogenous disturbances

linear graph transformations on spaces of analytic functions let h be a hilbert space of analytic functions with multiplier algebra m h and let m f t 1 f t n 1 f f is an element of d be an invariant graph subspace for m h n here n 2 d subset of h is a vector subspace t i d h are linear transformations that commute with each multiplication operator m phi is an element of m h and m is closed in h n in this paper we investigate the existence of non trivial common invariant subspaces of operator algebras of the type a m a is an element of b h ad subset of d at i f t i af for all f is an element of d in particular for the bergman space l 0 2 we exhibit examples of invariant graph subspaces of fiber dimension 2 such that a m does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for m c 2015 elsevier inc all rights reserved less

stability bounds of singularity perturbed systems a necessary and sufficient condition is developed for computing the upper bound in sub 0 of the parasitic parameter in in a singularly perturbed system which ensures stability of such a system if 0

a characteristic operator function for the class of n hypercontractions we consider a class of bounded linear operators on hilbert space called n hypercontractions which relates naturally to adjoint shift operators on certain vector valued standard weighted bergman spaces on the unit disc in the context of n hypercontractions in the class c0 we introduce a counterpart to the so called characteristic operator function for a contraction operator this generalized characteristic operator function wn t is an operator valued analytic function in the unit disc whose values are operators between two hilbert spaces of defect type using an operator valued function of the form wn t we parametrize the wandering subspace for a general shift invariant subspace of the corresponding vector valued standard weighted bergman space the operator valued analytic function wn t is shown to act as a contractive multiplier from the hardy space into the associated standard weighted bergman space

on the stability bounds of singularly perturbed systems the stability bound problem of linear time invariant singularly perturbed systems is considered a set of new stability conditions based on the frequency domain representation is derived the stability criteria can be easily verified by computing certain singular values within finite frequency intervals illustrative examples show that the proposed criteria actually induce a less conservative epsilon bound than the existing criteria and for certain cases an infinite epsilon bound may be obtained

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

variational multiscale a posteriori error estimation for systems the euler and navier stokes equations this paper extends explicit a posteriori error estimators based on the variational multiscale theory to systems of equations in particular the emphasis is placed on flow problems the euler and navier stokes equations three error estimators are proposed the standard the naive and the upper bound numerical results show that with a very economical algorithm the attained global and local efficiencies for the naive approach are reasonably close to unity whereas the standard and upper bound approaches give respectively approximate lower and higher error estimates

singularly perturbed boundary value problems in discrete systems various types of singularly perturbed boundary value problems arising in discrete systems are formulated for the general type it is seen that the degenerate problem is of reduced order and hence shows its inability to accommodate all the given boundary conditions those left over boundary conditions are readmitted through appropriate corrections for the initial and final boundary layers a perturbation method is developed to obtain an approximate solution composed of an outer series initial boundary layer correction series and final boundary layer correction series an important feature of the method is that the corrections for the original boundary value problem are solved as an initial value problem and a final value problem facilitating a considerable reduction in computation an example is given to demonstrate the method

finite volume schemes for hamilton jacobi equations we introduce two classes of monotone finite volume schemes for hamilton jacobi equations the corresponding approximating functions are piecewise linear defined on a mesh consisting of triangles the schemes are shown to converge to the viscosity solution of the hamilton jacobi equation

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

on the accuracy of the finite volume element method based on piecewise linear polynomials we present a general error estimation framework for a finite volume element fve method based on linear polynomials for solving second order elliptic boundary value problems this framework treats the fve method as a perturbation of the galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of fve methods in particular the error estimates and counterexamples in this paper will confirm that the fve method cannot have the standard o h2 convergence rate in the l2 norm when the source term has the minimum regularity only being in l2 even if the exact solution is in h2

robust stability of singularly perturbed systems the robust stability problem of linear time invariant singularly perturbed systems is discussed where the system matrix may have a parameter perturbation bounded by the h norm a sufficient condition for the upper bound of e is given such that the stability of the actual system or the full order model can be inferred from the analysis of the reduced order system or the slow model in separate time scales

uniform convergence of finite volume element method with crouzeix raviart element for non self adjoint and indefinite elliptic problems in this paper we consider the finite volume element method based on the crouzeix raviart element and prove the existence uniqueness and uniform convergence of the finite volume element approximations for the non self adjoint and indefinite elliptic problems under minimal elliptic regularity assumption

exponential stabilization of singularly perturbed switched systems subject to actuator saturation this paper considers the problem of exponential stabilization for a class of singularly perturbed switched systems subject to actuator saturation a time dependent switching law is designed to obtain the exponential stabilization conditions of the switched systems with unstabilizable subsystems based on the multiple lyapunov functions method depending on singular perturbation parameters a domain of attraction is constructed furthermore in order to maximize an estimate of the domain of attraction convex optimization problems are formulated finally a numerical example is presented in order to illustrate the effectiveness of the established results

bloch functions and asymptotic tail variance let p denote the bergman projection on the unit disk dd p z d w 1 zw 2da w z d where dada is normalized area measure we prove that if z 1 z 1 on dd then the integral i a r 02 exp ar4 p rei 2log 11 r2 d 2 0 r 1 has the bound i a r c a 10 1 a 3 2i a r c a 10 1 a 3 2 for 0 1a 1 no such uniform bound is possible we interpret the theorem in terms the asymptotic tail variance of such a bergman projection p p by the way the asymptotic tail variance induces a seminorm on the bloch space this improves upon earlier work of makarov which covers the range 0 a 264 0 1542 we then apply the theorem to obtain an estimate of the universal integral means spectrum for conformal mappings with a k quasiconformal extension for 0 k 10 k 1 the estimate reads for t ct c and 0 k 10 k 1 b k t 14k2 t 2 1 7k 2 for t 2k 1 7k 2 k t 1 1 7k 2 for t 2k 1 7k 2 which should be compared with the conjecture by prause and smirnov to the effect that for real t with t 2 k t 2 k we should have b k t 14k2t2

block bialternate sum and associated stability formulae abstract a new block bialternate sum of a partitioned square matrix with itself is defined and some basic properties established it has similar properties to the bialternate sum but it preserves the block structure of the summand it is used in place of the block kronecker sum and the block lyapunov sum to solve maximal stability problems of stable systems under low gain integral control and of singularly perturbed systems it is also used to find the critical gains for a first order controller with a scalar plant from which all stabilizing first order controllers can be constructed in each stability problem the internal dimensions of the resulting closed formulae are lower than those currently available

additive average schwarz method for a crouzeix raviart finite volume element discretization of elliptic problems with heterogeneous coefficients in this paper we introduce an additive schwarz method for a crouzeix raviart finite volume element discretization of a second order elliptic problem with discontinuous coefficients where the discontinuities are both inside the subdomains and across and along the subdomain boundaries we show that depending on the distribution of the coefficient in the model problem the parameters describing the generalized minimal residual method gmres convergence rate of the proposed method depend linearly on the mesh parameters inlineequation not available see fulltext also under certain restrictions on the distribution of the coefficient the convergence of the gmres method is independent of jumps in the coefficient

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

on the construction and analysis of high order locally conservative finite volume type methods for one dimensional elliptic problems locally conservative finite volume type methods based on continuous piecewise polynomial functions of degree r ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension the new methods extend and generalize the classical finite volume method based on piecewise linear functions we derive a priori error estimates in the l2 h1 and l infty norm and discuss superconvergence effects for the error and its derivative explicit residual based a posteriori error bounds in the l2 and energy norm are also derived we compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates

robust stability of two time scale systems with nonlinear uncertainties this note is concerned with the robust stability problem of uncertain two time scale systems where the only information available for system uncertainties is their norm upper bounds the stability bound spl epsiv sup is derived via a state transformation and the constructive use of a lyapunov function finally examples are given to illustrate the applications of the proposed results

mortar upwind finite volume element method for convection diffusion problems abstract in this paper we consider the mortar upwind finite volume element method with local linear conforming finite element space for the convection diffusion problems and show that the mortar upwind finite volume element approximations derived are convergent with optimal order in the h 1 norm

sliding mode control for singularly perturbed systems this paper addresses the design of sliding mode controllers for singularly perturbed systems the full order system is separated into slow and fast subsystems and a sliding mode controller is designed for each subsystem a composite of these controls is then implemented on the full order system it is shown that if specific reaching conditions are satisfied for the reduced order models and an additional condition is met then the reaching conditions are also satisfied for the full order model furthermore sufficient conditions are derived which guarantee that the approximation error between the controlled reduced order response and the controlled full order model response is small a numerical example is given which successfully demonstrates the techniques developed in this paper

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

decomposition of two time scale linear systems via the relevant eigenspace this paper presents a very reliable and computationally simple algorithm to transform a two time scale system in the singularly perturbed form by permutation followed by scaling assuming that certain conditions are satisfied the algorithm is based on computing orthonormal bases which span the left and the right invariant subspaces associated with the slow eigenvalues the algorithm does not require the system to be diagonalizable moreover the algorithm works even if the original system is badly scaled examples are given to illustrate the proposed algorithm

brief paper design of observer based controllers for a class of discrete systems design of observers and observer based controllers for linear discrete control systems with fast and slow modes are considered in this paper the time separation is expressed in terms of an inequality relating norms of system submatrices it is shown that reconstruction of fast and slow states can be accomplished by a full order observer the gains of which are computed using a two stage procedure then provided that the fast subsystem is asymptotically stable it is shown that a low order observer based controller can be designed with independent gain matrices to stabilize the original discrete system the theoretical analysis is illustrated by a ninth order boiler system model

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods