system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

almost output regulation of lft systems via gain scheduling control abstractoutput regulation of general uncertain systems is a meaningful yet challenging problem in spite of the rich literature in the field the problem has not yet been addressed adequately due to the lack of an effective design mechanism in this paper we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation lft with time varying parametric uncertainties and unknown external perturbations a novel semi lft gain scheduling output regulator structure is proposed such that the associated control synthesis conditions guaranteeing both output regulation and l2 disturbance attenuation performance are formulated as a set of linear matrix inequalities lmis plus parameter dependent linear matrix equations which can be solved separately a numerical example has been used to demonstrate the effectiveness of the proposed approach

the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

analysis of asymptotic preserving dg imex schemes for linear kinetic transport equations in a diffusive scaling in this paper some theoretical aspects will be addressed for the asymptotic preserving discontinuous galerkin implicit explicit dg imex schemes recently proposed in j jang f li j m qiu and t xiong high order asymptotic preserving dg imex schemes for discrete velocity kinetic equations in a diffusive scaling http arxiv org abs 1306 0227 2013 submitted for kinetic transport equations under a diffusive scaling we will focus on the methods that are based on discontinuous galerkin dg spatial discretizations with the p k polynomial space and a first order implicit explicit imex temporal discretization and apply them to two linear models the telegraph equation and the one group transport equation in slab geometry in particular we will establish uniform numerical stability with respect to knudsen number varepsilon using energy methods as well as error estimates for any given varepsilon when varepsilon rightarrow 0 a rigorous asymptotic analysis of the schemes is also obta

a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

on fluid limit for the semiconductors boltzmann equation abstract this paper is devoted to the derivation of non linear drift diffusion equations from the semiconductor boltzmann equation collisions are taken into account through the non linear pauli operator but we do not assume relation on the cross section such as the so called detailed balance principle in turn equilibrium states are implicitly defined this article follows and completes the contribution of mellet monatsh math 134 4 2002 305 329 where the electric field is given and does not depend on time here we treat the self consistent problem the electric potential satisfying the poisson equation by means of a hilbert expansion we shall formally derive the asymptotic model in the general case we shall then rigorously prove the convergence in the one dimensional case by using a modified hilbert expansion

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

the radiative transfer equations diffusion approximation under accretiveness and compactness assumptions abstract when the mean free path of photons is small the radiative transfer equations may be approximated by a nonlinear angular diffusion equation in order to find the diffusion equation one uses accretiveness assumptions but theses assumptions impose some conditions on the opacity to overcome this inconvenient we propose to study the solution of the radiative transfer equations by compactness techniques

well posedness of feedback systems insights into exact robustness analysis and approximate computations this paper establishes a framework for robust stability analysis of linear time invariant uncertain systems the uncertainty is assumed to belong to an arbitrary subset of complex matrices the concept used here is well posedness of feedback systems leading to necessary and sufficient conditions for robust stability based on this concept some insights into exact robust stability conditions are given in particular frequency domain and state space conditions for well posedness are provided in terms of hermitian form inequalities it is shown that these inequalities can be interpreted as small gain conditions with a generalized class of scalings given by linear fractional transformations lft using the lft scaled small gain condition in the state space setting the duality is established between the h sub spl infin norm condition with frequency dependent scalings and the parameter dependent lyapunov condition connections to the existing results including the structured singular value and the integral quadratic constraints are also discussed finally we show that our well posedness conditions can be used to give a less conservative yet computable bound on the real structured singular value this result is illustrated by numerical examples

on switching h controllers for a class of linear parameter varying systems abstract we consider switching h controllers for a class of linear parameter varying lpv systems scheduled along a measurable parameter trajectory the candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable we provide sufficient conditions to guarantee the stability of the switching lpv systems in terms of the dwell time and the average dwell time our results are illustrated with an example where switching between two robust controllers is performed for an lpv system

two dimensional approximations of three dimensional eigenvalue problems in plate theory the eigenvalues and eigenfunctions corresponding to the three dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2 are shown to converge in a specific sense to the eigenvalues and eigenfunctions of the well known two dimensional biharmonic operator of plate theory as approaches zero in the process it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature it is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three dimensional solutions in terms of powers of the method presented here applies equally well to the stationary problem of linear plate theory as shown elsewhere by p destuynder

nontrivial solutions for impulsive fractional differential equations via morse theory abstract in this paper we study the existence of nontrivial solutions for an impulsive fractional differential equation with dirichlet boundary conditions by using morse theory coupled with local linking arguments we obtain some new criteria to guarantee that the impulsive fractional differential equations have at least one nontrivial solution

on a system of nonlinear boltzmann equations of semiconductor physics a system of kinetic equations of semiconductors is studied these are vlasov poisson equations with additional nonlinear boltzmann operators first h theorems for these integral operators are given and their null space is determined then the existence and uniqueness of smooth solutions is proven the proof relies on the construction of a sequence of solutions for a suitable linearized system which converges strongly

efficient lmi based quadratic stabilization of interval lpv systems with noisy parameter measures the purpose of this note is to consider the quadratic stabilization of lpv systems in the realistic case where only gaussian noisy parameter measures are available though neglected in the actual literature on lpv systems this question is particular important because in all situations of a practical interest the parameter measurements or estimates are never exact the assumed noisy nature of physical parameter readings requires a specifically developed approach consisting of mixed robust and lpv control methods in the present case an approach based on a vertex result on interval time varying itv matrices is proposed this allows the solvability conditions to be stated in terms of a set of lmi s whose number is independent of the number of time varying parameters

linear matrix inequalities in robustness analysis with multipliers abstract we show that a number of standard robustness tests can be reinterpreted as special cases of the application of the passivity theorem with the appropriate choice of multipliers we show how these tests can be performed using convex optimization over linear matrix inequalities

initial and boundary conditions for diffusive linear transport problems the initial and boundary layer analyses of an asymptotic expansion that yields a diffusive description of linear particle transport are carried out in some generality this yields initial and boundary conditions that apply to the diffusion equation previously reported in the literature effects treated include boundary curvature the variation of the transport boundary condition along the bounding surface and spatial and temporal variations of the interaction coefficients cross sections in the initial and boundary layers

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

improved upper bounds for the mixed structured singular value in this paper we take a new look at the mixed structured singular value problem a problem of finding important applications in robust stability analysis several new upper bounds are proposed using a very simple approach which we call the multiplier approach these new bounds are convex and computable by using linear matrix inequality lmi techniques we show most importantly that these upper bounds are actually lower bounds of a well known upper bound which involves the so called d scaling for complex perturbations and g scaling for real perturbations

a new asymptotic preserving scheme based on micro macro formulation for linear kinetic equations in the diffusion limit we propose a new numerical scheme for linear transport equations it is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts we also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part by using a suitable time semi implicit discretization our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes it is asymptotic preserving in the following sense when the mean free path of the particles is small our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model a uniform stability property is proved for the simple telegraph model various boundary conditions are studied our method is validated in one dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes

an asymptotic induced scheme for nonstationary transport equations in the diffusive limit an asymptotic induced scheme for nonstationary transport equations with the diffusion scaling is developed the scheme works uniformly for all ranges of mean free paths it is based on the asymptotic analysis of the diffusion limit of the transport equation a theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven moreover numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit we present a mathematical analysis of the asymptotic preserving scheme proposed in m lemou and l mieussens siam j sci comput 31 2008 pp 334 368 for linear transport equations in kinetic and diffusive regimes we prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles this property is satisfied under an explicitly given cfl condition this condition tends to a parabolic cfl condition for small mean free paths and is close to a convection cfl condition for large mean free paths our analysis is based on very simple energy estimates

diffusion approximation and computation of the critical size this paper is devoted to the mathematical definition of the extrapolation length which appears in the diffusion approximation to obtain this result we describe the spectral properties of the transport equation and we show how the diffusion approximation is related to the computation of the critical size the paper also contains some simple numerical examples and some new results for the milne problem introduction the computation of the critical size and the diffusion approximation for the transport equation have been closely related and this is due to the following facts first the computation of the critical size is much easier for the diffusion approximation than for the original transport equation second for the critical size one can consider a host media x nxq with x0 given and 17 a positive number the problem of the critical size is then reduced to the computation of the parameter zj it turns out that when the transport operator is almost conservative the critical value of the parameter 17 is large and it is exactly for this range of value that the diffusion approximation is accurate on the other hand the physical boundary condition for the diffusion approxi mation is of the form

convergent upper bounds of peak response of lti and polytopic ltv systems through lmis abstract this paper addresses the problem of determining the response peak of dynamical systems a classical problem in control systems the paper starts by considering the impulse response of linear time invariant lti systems a linear matrix inequality lmi condition for establishing upper bounds of the sought peak is proposed by embedding the trajectory onto the level set of a polynomial and by introducing a projection technique for evaluating the extension of this set this condition is sufficient for any degree of the polynomial which has to be chosen a priori and is also necessary whenever this degree is large enough hence the proposed methodology is extended to address the impulse response of polytopic linear time varying ltv systems in particular linear systems affected linearly by structured time varying uncertainty constrained into a polytope lastly generalizations to various responses and specializations to some structures are also presented as shown by several examples which include randomly generated systems and physical systems the proposed conditions may provide significantly less conservative results than the existing lmi methods

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

improved stability analysis and gain scheduled controller synthesis for parameter dependent systems we present new algorithms for robust stability analysis and gain scheduled controller synthesis for linear systems affected by time varying parametric uncertainties these new techniques can also be applied to parameter dependent nonlinear systems with real rational nonlinearities sufficient conditions for robust stability as well as conditions for the existence of a robustly stabilizing gain scheduled controller are given in terms of a finite number of linear matrix inequalities lmis explicit formulas for constructing robustly stabilizing gain scheduled controllers are given in terms of the feasible set of these lmis the improvement offered by our approach over existing methods for stability analysis and gain scheduled controller synthesis for parameter dependent linear systems are analyzed in theory numerical examples demonstrate that our approach can offer significant improvement in practice

multiple positive solutions of dirichlet boundary value problems for second order impulsive differential equations abstract this paper is devoted to study the existence of multiple positive solutions for the second order dirichlet boundary value problem with impulse effects the main results here is the generalization of liu and li l liu f y li multiple positive solution of nonlinear two point boundary value problems j math anal appl 203 1996 610 625 for ordinary differential equations existence is established via the theory of fixed point index in cones

convex synthesis of robust controllers for linear systems with polytopic time varying uncertainty the design of robust controllers for linear systems with structured time varying uncertainty is a fundamental problem in control systems this problem is still open because the available methods for robust analysis lead to nonconvex optimization whenever design variables are present this paper proposes a novel approach that overcomes this difficulty specifically continuous time linear systems with polytopic time varying uncertainty are considered the basic problem consists of designing a robust static output feedback controller ensuring robust asymptotical stability a novel approach is proposed through the introduction of robust stabilizability functions rsfs i e functions able to establish whether a controller is robustly asymptotically stabilizing in particular rsfs based on homogeneous polynomial lyapunov functions hplfs are searched for the proposed approach requires the solution of two convex optimization problems with constraints expressed as linear matrix inequalities lmis for any size of the lmis the proposed approach provides a sufficient condition for the existence of a sought controller moreover this condition is also necessary when the size of the lmis is large enough several extensions of the proposed methodology are presented which deal with the synthesis of controllers ensuring desired decay rate fixed order dynamic output controllers and controllers with the minimum norm

the milne problem for the radiative transfer equations with frequency dependence we study the following stationary frequency dependent transport equation 28xf a t f bv t o x o m o u e 1 1 tr t bv t fjdm 8 0 r x 1 1 2 f 2 w 2 0 u e j0 1 where bv is the well known planck function appearing in astrophysics we are able to describe the asymptotic behavior of f and t for x large when a t is of the special form a t tr m k t our method relies mainly on the monotonicity of the nonlinearity the proof does not use any linearization of the equation in particular no smallness assumption on the data yp in any sense is required resume nous etudions l equation de transport stationnaire avec dependance en frequence 2dxf a t f bv t o x o m o u e 1 1 tr t bv t fjdm 8 0 r x 1 1 2 8 2 w 2 o u e 0 1 lorsque a t est de la forme particuliere a t a m k t nous savons decrire le comportement asymptotique de f et t pour x grand notre methode repose principalement sur la monotonie de la non linearite la preuve n utilise aucune linearisation de l equation en particulier nous n avons besoin d aucune hypothese de petitesse d aucune sorte sur la donnee y

asymptotic analysis and coupling conditions for kinetic and hydrodynamic equations abstract this article is concerned with domain decomposition for kinetic and hydrodynamic equations coupling conditions at the interface between the equations are developed and investigated in particular for nonequilibrium situations at the interface new coupling conditions are developed by considering interface layers this leads to kinetic half space problems a fast procedure to solve these problems is given

an inexact interior point method for system analysis in this article a primal dual interior point algorithm for semidefinite programming that can be used for analysing e g polytopic linear differential inclusions is tailored in order to be more computationally efficient the key to the speedup is to allow for inexact search directions in the interior point algorithm these are obtained by aborting an iterative solver for computing the search directions prior to convergence a convergence proof for the algorithm is given two different preconditioners for the iterative solver are proposed the speedup is in many cases more than an order of magnitude moreover the proposed algorithm can be used to analyse much larger problems as compared to what is possible with off the shelf interior point solvers

existence and multiplicity of solutions for some dirichlet problems with impulsive effects abstract in this paper we consider the existence and multiplicity of solutions for some dirichlet impulsive problems and some existence and multiplicity results are obtained the solutions are sought by means of lax milgram theorem and some critical theorems

coprime factor based anti windup synthesis for parameter dependent systems abstract this paper presents a novel anti windup compensator synthesis for linear parameter varying lpv systems that have linear fractional transformation lft representations the lpv anti windup synthesis is based on a right coprime factor description of the lpv plant to be controlled it is shown that the anti windup compensator synthesis reduces to solving a robust l 2 gain state feedback control problem for the lpv lft system subject to input saturations the synthesis takes advantage of unstructured multipliers that is multipliers that do not commute with the parameter structure and exploits a detailed description of the parameter trajectory polytope the anti windup compensator is given in an explicit lpv lft form sharing with the plant the same order and same parameter structure

robust performance of linear parametrically varying systems using parametrically dependent linear feedback abstract in this paper a parameter dependent control problem for linear parametrically varying lpv systems is presented sufficient conditions are given that guarantee an lpv system is exponentially stable and achieves an induced l 2 norm performance objective from the disturbance to error signals the usefulness of parameter dependent controllers is motivated from a gain scheduling viewpoint the resulting synthesis problem is reformulated into a convex optimization problem which can be solved using efficient new algorithms

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

robust stability of time varying uncertain systems with rational dependence on the uncertainty robust stability of time varying uncertain systems is a key problem in automatic control this note considers the case of linear systems with rational dependence on an uncertain time varying vector constrained in a polytope which is typically addressed in the literature by using the linear fractional representation lfr a novel sufficient condition for robust stability is derived in terms of a linear matrix inequality lmi feasibility test by exploiting homogeneous polynomial lyapunov functions the square matrix representation and an extended version of polya s theorem which considers structured matrix polynomials it is shown that this condition is also necessary for second order systems and that this condition is less conservative than existing lmi conditions based on the lfr for any order

the nonaccretive radiative transfer equations existence of solutions and rosseland approximation we present an existence theory and an asymptotic analysis for the radiative transfer equations ue t xuee ue e2 ue ue 0 inx 1 ue x sn k ue t 0 u0 where u u t x t r x x rn 1 sn and ue t x 1 sn ue t x d we prove that even if has a singularity 0 1 has a solution ue l r x sn as e 0 we show that ue converges pointwise to a function u l r x solution of the degenerate parabolic equation u t f u 0 in x u x k u t 0 u0 this is achieved without any monotonicity assumption on and therefore one cannot use the theory of nonlinear contraction semigroups

stability analysis with quadratic lyapunov functions some necessary and sufficient multiplier conditions in this paper we present several conditions which are both necessary and sufficient for quadratic stability of an uncertain nonlinear system these conditions involve multiplier matrices which characterize the uncertain nonlinear terms in the system description it is known that some of these conditions are sufficient for quadratic stability one of the main contributions of this paper is to demonstrate that these conditions are also necessary conditions hence they are not conservative conditions for quadratic stability by presenting multiplier matrices for many common types of uncertain nonlinear terms the paper also demonstrates the usefulness of the multiplier matrix approach in the analysis and control of nonlinear time varying uncertain systems

quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays abstract this paper deals with the quadratic stability and linear state feedback and output feedback stabilization of switched delayed linear dynamic systems with in general a finite number of non commensurate constant internal point delays the results are obtained based on lyapunov s stability analysis via appropriate krasovsky lyapunov s functionals and the related stability study is performed to obtain both delay independent and delay dependent results it is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a in general non unique stabilizing switching law when the system is polytopic stable at some interior point of the polytope but with non necessarily stable parameterizations at the vertices defining the subsystems it is also proved that two subsystems individually parametrized in different polytopic type sets which are not quadratically stable might be stabilized by a in general non unique switching law provided that a convexity type condition is fulfilled at each existing pair of vertices one corresponding to each subsystem some extensions are provided for a typical class of neutral time delay systems

design method of gain scheduled controllers not depending on derivatives of parameters in general designing gain scheduled gs controllers for linear parameter varying lpv systems using parameter dependent lyapunov functions pdlfs yields controllers that depend on the derivatives of parameters this makes their implementation impractical because ideal parameter derivatives are not available in the real world in contrast to this for open loop system design such as filter design and inverse system design we propose a gs controller design method using pdlfs that gives controllers which do not depend on parameter derivatives although the proposed method uses structured pdlfs we show that it is as conservative as existing methods numerical examples of designing gs filters and gs right inverse systems for lpv systems are included to demonstrate our conclusion

stability radius of linear parameter varying systems and applications abstract in this paper we present a unifying approach to the problems of computing of stability radii of positive linear systems first we study stability radii of linear time invariant parameter varying differential systems a formula for the complex stability radius under multi perturbations is given then under hypotheses of positivity of the system matrices we prove that the complex real and positive stability radii of the system under multi perturbations or affine perturbations coincide and they are computed via simple formulae as applications we consider problems of computing of strong stability radii of linear time invariant time delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations we show that for a class of positive linear time delay differential systems the stability radii of the system under multi perturbations or affine perturbations are equal to the strong stability radii next we prove that the stability radii of a positive linear functional differential equation under multi perturbations or affine perturbations are equal to those of the associated linear time invariant parameter varying differential system in particular we get back some explicit formulas for these stability radii which are given recently in p h a ngoc strong stability radii of positive linear time delay systems internat j robust nonlinear control 15 2005 459 472 p h a ngoc n k son stability radii of positive linear functional differential equations under multi perturbations siam j control optim 43 2005 2278 2295 finally we give two examples to illustrate the obtained results

new models for the solution of intermediate regimes in transport theory and radiative transfer existence theory positivity asymptotic analysis and approximations in this paper we propose derive and establish the mathematical foundations of new models for the solution of intermediate regimes in transport theory and radiative transfer these new models consist of coupling the transport equations with their diffusion approximations our mathematical theory includes the existence theory the positivity of the solutions and the asymptotic analysis we also give the rate of the asymptotic decay in order to solve the new coupled problem we propose to use the transmission time marching algorithm introduced and studied in refs 10 13 15 we then study the convergence of the resulting algorithm these studies are based in an essential way on the methods we introduced in refs 14 15

fractional diffusion limit for collisional kinetic equations this paper is devoted to diffusion limits of linear boltzmann equations when the equilibrium distribution function is a maxwellian distribution it is well known that for an appropriate time scale the small mean free path limit gives rise to a diffusion equation in this paper we consider situations in which the equilibrium distribution function is a heavy tailed distribution with infinite variance we then show that for an appropriate time scale the small mean free path limit gives rise to a fractional diffusion equation

computation of interface reflection and regular or diffuse transmission of the planar symmetric radiative transfer equation with isotropic scattering and its diffusion limit in this paper we develop a numerical scheme for the interface problem in the planar symmetric radiative transfer equation with isotropic scattering such problems arise in the modeling of the propagation of energy density for waves in heterogeneous media with weak random fluctuation in the high frequency regime the idea following the earlier work of jin and wen for regular transmission and reflection is to build the interface condition which characterizes the reflection and transmission into the numerical flux the new contribution of this article is to deal with the diffuse transmission at the interface the positivity of the scheme is proven moreover we show via numerical examples that this new scheme is able to capture the correct regular or diffuse transmission and reflection through the interface and as the mean free path goes to zero capture the diffusion limit with the correct interface conditions

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

control of rational systems using linear fractional representations and linear matrix inequalities abstract every system of the form x f x u y g x u where f and g are rational functions of the state x and linear functions of the input u possesses a linear fractional representation lfr in this lfr the system is viewed as an lti system connected with a diagonal feedback element linear in the state we devise an algorithm for computing lfrs based on this construction we give sufficient conditions for various properties to hold for the open loop system these include checking whether a given polytope is stable finding a lower bound on the decay rate of trajectories initiating in this polytope computing an upper bound on the l2 gain etc all these conditions are obtained by analyzing the properties of a differential inclusion related to the lfr and given as convex optimization problems over linear matrix inequalities lmis we show how to use this approach for static state feedback synthesis we then generalize the results to dynamic output feedback synthesis in the case when f and g are linear in every state coordinate that is not measured extensions towards a class of nonrational and uncertain nonliner systems are discussed

robust analysis of lfr systems through homogeneous polynomial lyapunov functions in this note the use of homogeneous polynomial lyapunov functions hplfs for robust stability analysis of linear systems subject to time varying parametric uncertainty affecting rationally the state space matrix is investigated sufficient conditions based on linear matrix inequalities feasibility tests are derived for the existence of hplfs which ensure robust stability when the uncertain parameter vector is restricted to lie in a convex polytope it is shown that hplfs lead to results which are less conservative than those obtainable via quadratic lyapunov functions

some results for impulsive problems via morse theory abstract we use morse theory to study impulsive problems first we consider asymptotically piecewise linear problems with superlinear impulses and prove a new existence result for this class of problems using the saddle point theorem next we compute the critical groups at zero when the impulses are asymptotically linear near zero in particular we identify an important resonance set for this problem as an application we finally obtain a nontrivial solution for asymptotically piecewise linear problems with impulses that are asymptotically linear at zero and superlinear at infinity our results here are based on the simple observation that the underlying sobolev space naturally splits into a certain finite dimensional subspace where all the impulses take place and its orthogonal complement that is free of impulsive effects

uniformly rd piecewise almost periodic functions with applications to the analysis of impulsive δ dynamic system on time scales we introduce some new concepts of uniformly rd piecewise almost periodic functions on time scales and obtain some properties some new estimation inequalities and completely new theorems are established on time scales for impulsive dynamic systems several applications are given to illustrate our feasible results in the present work we introduce two equivalent concepts of uniformly rd piecewise almost periodic functions on time scales and their equivalence is proved based on this some basic properties of them are obtained then some new criteria of exponential dichotomy are established for homogeneous dynamic system on time scales also some completely new theorems are established on time scales for impulsive almost periodic dynamic systems such as favard s theorem and exponential dichotomy theorem as applications we provide a method to obtain an almost periodic solution for a given nonhomogeneous impulsive dynamic system furthermore we introduce an impulsive non autonomous nicholson s blowflies system model with patch structure and multiple nonlinear harvesting terms for which the existence and exponential stability of almost periodic solutions are studied which shows that our results can be applied feasibly and effectively

the convergence of numerical transfer schemes in diffusive regimes i discrete ordinate method in highly diffusive regimes the transfer equation with anisotropic boundary conditions has an asymptotic behavior as the mean free path epsilon tends to zero that is governed by a diffusion equation and boundary conditions obtained through a matched asymptotic boundary layer analysis a numerical scheme for solving this problem has an epsilon 1 contribution to the truncation error that generally gives rise to a nonuniform consistency with the transfer equation for small epsilon thus degrading its performance in diffusive regimes in this paper we show that whenever the discrete ordinate method has the correct diffusion limit both in the interior and at the boundaries its solutions converge to the solution of the transport equation uniformly in epsilon our proof of the convergence is based on an asymptotic diffusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete ordinate method

gain scheduling control of lft systems using parameter dependent lyapunov functions in this paper we propose a new control design approach for linear fractional transformation lft systems using parameter dependent lyapunov functions instead of assuming parameter dependency in lft fashion we consider general parameter dependent controllers to achieve better closed loop performance using full block multipliers new lpv synthesis conditions have been derived in terms of finite number of linear matrix inequalities lmis both continuous and discrete time cases are discussed a ship steering example has been used to demonstrate advantages and benefits of the proposed approach

efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems sufficient conditions for the robust stability of a class of uncertain systems with several different assumptions on the structure and nature of the uncertainties can be derived in a unified manner in the framework of integral quadratic constraints these sufficient conditions in turn can be used to derive lower bounds on the robust stability margin for such systems the lower bound is typically computed with a bisection scheme with each iteration requiring the solution of a linear matrix inequality feasibility problem we show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem which can be solved very efficiently using standard algorithms we illustrate this with several important commonly encountered special cases diagonal nonlinear uncertainties diagonal memoryless time invariant sector bounded popov uncertainties structured dynamic uncertainties and structured parametric uncertainties we also present a numerical example that demonstrates the computational savings that can be obtained with our approach

existence and uniqueness of weak solutions for nonlocal parabolic problems via the galerkin method abstract fractional differential equations are becoming increasingly popular as a modeling tool to describe a wide range of non classical phenomena with spatial heterogeneities throughout the applied science and engineering a recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal operators which include fractional laplacians on bounded domains in r n we develop the galerkin method to prove existence and uniqueness of weak solutions to nonlocal parabolic problems moreover we study the existence of orthonormal basis of eigenvectors associated to these nonlocal operators

robust saturation controller for linear time invariant system with structured real parameter uncertainties abstract this paper is focused on a robust saturation controller for the linear time invariant lti system involving both actuator s saturation and structured real parameter uncertainties the controller suggested in this paper can analytically prescribe the upper and lower bounds of parameter uncertainties and guarantee the closed loop robust stability of the system in the presence of actuator s saturation the suboptimal bang bang control method is extended to lti system with parameter uncertainties based on affine quadratic stability and multi convexity concept the robust optimal bang bang controller is newly derived by minimizing the time derivative of affine lyapunov function subjected to the limit of control force since this controller is a gain scheduled type it requires the exact knowledge of uncertain parameters another robust saturation controller with a fixed gain is proposed and the linear matrix inequality lmi based sufficient existence conditions for a fixed gain controller are derived the effectiveness and the availability of the proposed controller are investigated by a practical numerical example through numerical simulations it is confirmed that the proposed robust saturation controller is robustly stable with respect to parameter uncertainties over the prescribed range defined by the upper and lower bounds

haar based stability analysis of lpv systems a new gridding based algorithm for stability analysis of linear parameter varying lpv systems is presented the algorithm inherits the main features of classical gridding techniques it can handle a vast class of parametric dependencies as well as non convex parametric domains novelty of the proposed approach lies in the use of haar wavelet transform theory to guarantee constraint satisfaction over the entire parametric domain even for an arbitrarily sparse grid it represents a major improvement over traditional gridding approaches which fail to provide such a certificate without requiring a posteriori verification tests the resulting algorithms rely on semidefinite programing and are related to sufficient stability conditions whose degree of conservatism decreases as the grid density and the haar truncation level increase two numerical examples corroborate the validity of the proposed algorithms

periodic boundary value problems for a class of second order impulsive integro differential equations in banach spaces abstract this paper investigates periodic boundary value problems for a class of second order nonlinear impulsive integro differential equations of mixed type in a banach space by establishing a comparison result criteria on the existence of maximal and minimal solutions are obtained

brief lpv systems with parameter varying time delays analysis and control in this paper we address the analysis and state feedback synthesis problems for linear parameter varying lpv systems with parameter varying time delays it is assumed that the state space data and the time delays are dependent on parameters that are measurable in real time and vary in a compact set with bounded variation rates we explore the stability and the induced l 2 norm performance of these systems using parameter dependent lyapunov functionals in addition the design of parameter dependent state feedback controllers that guarantee desired l 2 gain performance is examined both analysis and synthesis conditions are formulated in terms of linear matrix inequalities lmis that can be solved via efficient interior point algorithms

generalized solutions of the radiative transfer equations in a singular case this paper is devoted to the study of the radiative transfer equations first we prove a global existence theorem which allows a blow up of the opacity v when 0 thus it extends mercier s previous result 13 this proof relies mainly on a nonlinear version of hille yosida theorem see crandall ligett 9 then we prove the uniqueness of the semigroup solving tr and some regularity results in the class of functions with bounded variation finally we prove the convergence of some splitting algorithms associated to tr

an asymptotic preserving scheme for linear kinetic equation with fractional diffusion limit we present a new asymptotic preserving scheme for the linear boltzmann equation which under appropriate scaling leads to a fractional diffusion limit our scheme rests on novel micro macro decomposition to the distribution function which splits the original kinetic equation following a reshuffled hilbert expansion as opposed to classical diffusion limit a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter our idea is while solving the macro micro part in a truncated velocity domain truncation only depends on numerical accuracy to incorporate an integrated tail over the velocity space that is beyond the truncation and its major component can be precomputed once with any accuracy such an addition is essential to drive the solution to the correct asymptotic limit numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes

generalized robust gain scheduled pid controller design for affine lpv systems with polytopic uncertainty in the paper a generalized guaranteed cost output feedback robust gain scheduled pid controller synthesis is presented for affine linear parameter varying systems under polytopic model uncertainty the controller synthesis is generalized in a sense that it covers robust robust gain scheduled and robust switched with arbitrary switching algorithm pid controller design the proposed centralized decentralized controller method is based on bellman lyapunov equation guaranteed cost and parameter dependent quadratic stability the proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities bmi which can efficiently be solved or further linearized as the main result the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters hence there is no need for applying multi convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method the viability of the novel design technique is demonstrated and evaluated through numerical examples

sufficient and necessary lmi conditions for robust stability of rationally time varying uncertain systems this technical note addresses robust stability of uncertain systems with rational dependence on unknown time varying parameters constrained in a polytope first the technical note proves that a sufficient linear matrix inequality lmi condition that we previously proposed based on homogeneous polynomial lyapunov functions hplfs and on the introduction of an extended version of polya s theorem is also necessary second the technical note proposes a new sufficient and necessary lmi condition by exploiting properties of the simplex and sum of squares sos parameter dependent polynomials lastly the technical note investigates relationships among these conditions and conditions based on the linear fractional representation lfr it is worth remarking that sufficient and necessary lmi conditions for this problem have not been proposed yet in the literature

a two surface problem of the electron flow in a semiconductor on the basis of kinetic theory a steady flow of electrons in a semiconductor between two parallel plane ohmic contacts is studied on the basis of the semiconductor boltzmann equation assuming a relaxation time collision term and the poisson equation for the electrostatic potential a systematic asymptotic analysis of the boltzmann poisson system for small knudsen numbers scaled mean free paths is carried out in the case where the debye length is of the same order as the distance between the contacts and where the applied potential is of the same order as the thermal potential a system of drift diffusion type equations and their boundary conditions is obtained up to second order in the knudsen number a numerical comparison is made between the obtained system and the original boltzmann poisson system

stability analysis and gain scheduled state feedback control for continuous time systems with bounded parameter variations the problems of robust stability analysis and state feedback control based on gain scheduling for continuous time systems with time varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article with respect to previous results in the literature two main contributions of the article are i the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones ii the conditions can be extended to cope with the problem of control design for this class of system parameter dependent linear matrix inequality lmi conditions are given for the existence of a parameter dependent lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability two convex procedures based on lmis exhibiting distinct complexities are proposed to solve the problem of robust stability an extension to deal with the computation of a stabilising parameter dependent state feedback gain for this class of time varying systems is also provided as a sequence of lmis of increasing precision examples illustrate the results including comparisons with other techniques from the literature

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

micro macro schemes for kinetic equations including boundary layers we introduce a new micro macro decomposition of collisional kinetic equations in the specific case of the diffusion limit which naturally incorporates the incoming boundary conditions the idea is to write the distribution function f in all its domain as the sum of an equilibrium adapted to the boundary which is not the usual equilibrium associated with f and a remaining kinetic part this equilibrium is defined such that its incoming velocity moments coincide with the incoming velocity moments of the distribution function a consequence of this strategy is that no artificial boundary condition is needed in the micro macro models and the exact boundary condition on f is naturally transposed to the macro part of the model this method provides an asymptotic preserving numerical scheme that generates a very good approximation of the space boundary values at the diffusive limit without any mesh refinement in the boundary layers our numerical results are in very good agreement with the exact so c

h control with parametric lyapunov functions a new control synthesis approach is proposed for linear parametrically varying lpv systems using parameter dependent quadratic lyapunov functions the synthesis problem is formulated via a set of linear matrix inequalities lmis when solved parameter dependent controllers are obtained that stabilize the lpv systems and achieve guaranteed performance in an l2 gain sense the new approach includes the case of parameter independent lyapunov functions and as a result provides additional flexibility in the control design

robust and gain scheduling control of lft systems through duality and conjugate lyapunov functions in this paper we study stability and performance properties of linear fractional transformation lft parameter dependent systems using duality theory and tools from convex analysis a pair of conjugate functions the convex hull and the maximum of a family of quadratic functions are used for analysis and synthesis of lft systems sufficient synthesis conditions for both robust state feedback and gain scheduling output feedback control problems are formulated as a set of linear matrix inequalities lmis with linear search over scalar variables finally a numerical example is used to demonstrate the advantages of the proposed approaches

the milne problem for high field kinetic equations half space problems of the linear boltzmann equation with a constant driving force are considered such problems model boundary layers between kinetic zones and fluid zones described by a high field limit of the boltzmann equation existence uniqueness and asymptotic behavior of solutions are studied for positive and negative driving forces in the positive case the force field accelerates the particles and we show that the solution of the half space problem is determined only by the inflow data in contrast for negative forces the behavior at infinity has to be prescribed in order to insure uniqueness due to the nonvanishing forces the problem does not possess any entropy the existence and uniqueness issues are dealt with by supersolution techniques while the asymptotic behavior is analyzed by semiexplicit integration of the equations along the characteristics in the case of relaxation time approximation a fast numerical method for computing the asymptotic state method is presented and tested