stabilization by means of state space depending switching rules abstract in this paper we consider switched systems defined by a pair of linear systems x a 1 x x a 2 x such that there exists a neutrally stable linear combination of the matrices a 1 a 2 under an additional assumption we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense the result is illustrated by some simulations and examples

on a common quadratic lyapunov function for widely distant systems a sufficient condition concerning the construction of a common quadratic lyapunov function for widely distant linear systems is presented the condition is set on a mutual relation matrix whose size is just equal to the number of the coefficient matrices

delay independent minimum dwell time for exponential stability of uncertain switched delay systems in this technical note the problem of delay independent minimum dwell time for exponential stability of uncertain switched delay systems is considered piecewise time varying lyapunov functionals functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time varying delays this type of delicately constructed lyapunov functionals functions can efficiently eliminate the jump phenomena of adjacent lyapunov functionals functions at switching times without imposing any restriction on the sizes of time delays by applying this type of lyapunov functionals functions it is shown that if each subsystem is delay independently exponentially stable then under some conditions there exists a delay independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time delays two numerical examples are provided to demonstrate the efficiency of the proposed approach

construction of lyapunov krasovskii functionals for switched nonlinear systems with input delay abstract this paper studies the stability issue for switched nonlinear systems with input delay and disturbance it is assumed that for the nominal system an exponential stabilizing controller is predesigned such that the switched system is stable under a certain switching signal and a piecewise lyapunov function for the corresponding closed loop system is known however in the presence of input delay and disturbance the system may be unstable under the same switching signal for this case a new lyapunov krasovskii functional is firstly constructed based on the known lyapunov function then by employing this new functional a new switching signal satisfying the new average dwell time conditions is constructed to guarantee the input to state stability of the system under a certain delay bound the bound on the average dwell time is closely related to the bound on the input delay finally numerical examples are given to illustrate the effectiveness of the proposed theory

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

stabilization of switched linear systems in this note we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency for both cases of known and unknown switching functions feedback laws are designed to achieve exponential stability for the later case a method combining on line adaptive estimation and feedback stabilization is developed in the controller design

the local converse theorem for so 2n 1 and applications in this paper we characterize irreducible generic representations of so 2n 1 k where k is a p adic field by means of twisted local gamma factors the local converse theorem as applications we prove that two irreducible generic cuspidal automorphic representations of so 2n 1 a where a is the ring of adeles of a number field are equivalent if their local components are equivalent at almost all local places the rigidity theorem and prove the local langlands reciprocity conjecture for generic supercuspidal representations of so 2n 1 k

efficient solution of the simplified p n equations in this paper we show new solver strategies for the multigroup sp n equations for nuclear reactor analysis by forming the complete matrix over space moments and energy a robust set of solution strategies may be applied power iteration shifted power iteration rayleigh quotient iteration arnoldi s method and a generalized davidson method each using algebraic and physics based multigrid preconditioners have been compared on the c5g7 mox test problem as well as an operational pressurized water reactor model our results show that the most efficient approach is the generalized davidson method which is 30 40 times faster than traditional power iteration and 6 10 times faster than arnoldi s method

suboptimal switching control consistency analysis for switched linear systems this paper introduces the concept of consistency for continuous time switched linear systems having the switching function as a primary control signal to be designed a switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems conditions under which a min type switching strategy is strictly consistent for the classes of h2 and h performance indexes are determined this property makes clear the importance of switching systems control design in both theoretical and practical application frameworks moreover with this property it is not necessary to assume that all the subsystems are not stable in order to make a switching strategy design problem well posed the theory is illustrated by means of several academic examples

a novel multigrid method for sn discretizations of the mono energetic boltzmann transport equation in the optically thick and thin regimes with anisotropic scattering part i this paper presents a new multigrid method applied to the most common sn discretizations petrov galerkin diamond differenced corner balanced and discontinuous galerkin of the mono energetic boltzmann transport equation in the optically thick and thin regimes and with strong anisotropic scattering unlike methods that use scalar dsa diffusion preconditioners for the source iteration this multigrid method is applied directly to an integral equation for the scalar flux thus unlike the former methods that apply a multigrid strategy to the scalar dsa diffusion operator this method applies a multigrid strategy to the integral source iteration operator which is an operator for 5 independent variables in spatial three dimensions 3 d 3 in space and 2 in angle and 4 independent variables in spatial 2 d 2 in space and 2 in angle the core smoother of this multigrid method involves applications of the integral operator since the kernel of this integral operator involves the transport sweeps applyin

an lmi approach for h analysis and control of discrete time piecewise affine systems in this paper we investigate some analysis and control problems for discrete time hybrid systems in the piece wise affine form by using arguments from the dissipativity theory for non linear systems we show that h x analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system in this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input

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

switched observer based adaptive neural control of mimo switched nonlinear systems with unknown control gains in this paper the problem of adaptive neural output feedback control is addressed for a class of multi input multioutput mimo switched uncertain nonlinear systems with unknown control gains neural networks nns are used to approximate unknown nonlinear functions in order to avoid the conservativeness caused by adoption of a common observer for all subsystems an mimo nn switched observer is designed to estimate unmeasurable states a new switched observer based adaptive neural control technique for the problem studied is then provided by exploiting the classical average dwell time adt method and the backstepping method and the nussbaum gain technique it effectively handles the obstacle about the coexistence of multiple nussbaum type function terms and improves the classical adt method since the exponential decline property of lyapunov functions for individual subsystems is no longer satisfied it is shown that the technique proposed is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed loop system under a class of switching signals with adt and the tracking errors converge to a small neighborhood of the origin the effectiveness of the approach proposed is illustrated by its application to a two inverted pendulum system

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

estimation and synthesis of reachable set for switched linear systems this paper focuses on the problems of reachable set estimation and state feedback controller design for discrete time switched linear systems under bounded peak disturbances for the reachable set estimation problem a lyapunov based inequality is developed based on the multiple lyapunov strategy by choosing appropriate lyapunov functions the ellipsoidal reachable set estimation conditions of discrete time switched linear systems are obtained in order to make the estimated ellipsoids as small as possible three optimization approaches are proposed specifically the genetic algorithm is used to search for the optimal parameters satisfying the obtained reachable set estimation conditions in addition the state feedback controller design problem for discrete time switched linear systems is considered the function of the controller is to manipulate the reachable set of the closed loop system to lie within a given ellipsoid or make the reachable set small finally the effectiveness of the obtained results is verified through some numerical examples

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

smooth dynamic output feedback control for multiple time delay systems with nonlinear uncertainties the dynamic output feedback control problem is considered for a class of systems with multiple time delays and nonlinear uncertainties based on the control input matrix and output matrix we decompose the system into two subsystems the dynamic compensator is designed for the first subsystem and then the output feedback controller is constructed based on the compensator and the second subsystem by using the introduced new lyapunov krasovskii functional we show that the solution of the resultant closed loop system converges exponentially to an adjustable bounded region compared with the previous works the developed controller in this paper is memoryless and smooth which only uses the system output the control design conditions are relaxed because of the developed dynamic compensator the result is further extended to the general nonlinear case the corresponding dynamic nonlinear output feedback control method is proposed finally simulations are performed to show the potential of the proposed methods

generalized lyapunov function theorems and its applications in switched systems abstract generalized lyapunov theorems of nonlinear systems are developed wherein all regularity assumptions on traditional lyapunov function are removed in particular stability theorems of nonlinear systems are presented by replacing v along the system trajectories is non increasing with v along the system trajectories may increase its value during some proper time intervals furthermore stability theorems of discrete time and continuous time switched system with unstable subsystems are derived using the generalized lyapunov theorems two numerical examples are included to illustrate the effectiveness of the method

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

output feedback control of switched nonlinear systems using multiple lyapunov functions abstract this work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints the key feature of the proposed methodology is the integrated synthesis via multiple lyapunov functions of lower level bounded nonlinear feedback controllers together with upper level switching laws that orchestrate the transitions between the constituent modes and their respective controllers both the state and output feedback control problems are addressed under the assumption of availability of full state measurements a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding stability region for each mode a set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed loop system when complete state measurements are unavailable a family of output feedback controllers are synthesized using a combination of bounded state feedback controllers high gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain a different set of switching rules based on the evolution of the state estimates generated by the observers is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes the differences between the state and output feedback switching strategies and their implications for the switching logic are discussed and a chemical process example is used to demonstrate the proposed approach

passivity and feedback passification of switched discrete time linear systems abstract this paper focuses on the passivity analysis and feedback passification for switched discrete time linear systems using multiple storage functions under a certain switching law controllers and switching laws are designed based on complete and partial state measurements respectively conditions for strict passivity of a switched discrete time system are obtained without the requirement of strict passivity of subsystems in the case of partial state measurements dynamic output feedback controllers for subsystems are designed and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed loop switched system finally a numerical example is provided to demonstrate the feasibility of the theoretical results

stability of switched nonlinear systems with delay and disturbance we consider a class of nonlinear time varying switched control systems for which stabilizing feedbacks are available we study the effect of the presence of a delay in the input of switched nonlinear systems with an external disturbance by contrast with most of the contributions available in the literature we do not assume that all the subsystems of the switched system we consider are stable when the delay is present through a lyapunov approach we derive sufficient conditions in terms of size of the delay ensuring the global exponential stability of the switched system moreover under appropriate conditions the input to state stability of the system with respect to an external disturbance is established

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

caracterisation de la correspondance de langlands locale par les facteurs e de paires soitf un corps local non archimedien a corps residuel fini la conjecture de langlands locale prouvee par laumon rapoport et stuhler quandf est de caracteristique non nulle associe a une classe d isomorphisme de representations irreductibles du groupe de weil def une classe d isomorphisme de representations admissibles irreductibles supercuspidales d un groupe lineaire surf le groupe gl n f si est de dimensionn nous prouvons dans cet appendice qu il existe au plus une telle correspondance qui preserve les facteurs e de paires et coincide en dimension 1 avec l application donnee par la theorie du corps de classes

two level fourier analysis of a multigrid approach for discontinuous galerkin discretization in this paper we study a multigrid mg method for the solution of a linear second order elliptic equation discretized by discontinuous galerkin dg methods and we give a detailed analysis of the convergence for different block relaxation strategies we find that pointwise block partitioning gives much better results than the classical cellwise partitioning both for the baumann oden method and for the symmetric dg method with and without interior penalty ip the block relaxation methods jacobi gauss seidel and symmetric gauss seidel give excellent smoothing procedures in a classical mg setting independent of the mesh size simple mg cycles give convergence factors of 0 075 0 4 per iteration sweep for the different discretization methods studied

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

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

finite gain lp stability for hybrid dynamical systems we characterize the finite gain l p stability properties for hybrid dynamical systems by defining a suitable concept of the hybrid l p norm we introduce hybrid storage functions and provide sufficient lyapunov conditions for the l p stability of hybrid systems which cover the well known continuous time and discrete time l p stability notions as special cases we then focus on homogeneous hybrid systems and prove a result stating the equivalence among local asymptotic stability of the origin global exponential stability existence of a homogeneous lyapunov function with suitable properties for the hybrid system with no inputs and input to state stability and we show how these properties all imply l p stability finally we characterize systems with direct and reverse average dwell time properties and establish parallel results for this class of systems we also make several connections to the existing results on dissipativity properties of hybrid dynamical systems

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

robust switching adaptive control of multi input nonlinear systems during the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parameters new design tools such as adaptive feedback linearization adaptive back stepping control lyapunov functions clfs and robust control lyapunov functions rclfs nonlinear damping and switching adaptive control have been introduced most of the results developed are applicable to single input feedback linearizable systems and parametric strict feedback systems these results however cannot be applied to multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf in this paper we develop a general procedure for designing robust adaptive controllers for a large class of multi input nonlinear systems this class of nonlinear systems includes as a special case multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf the proposed approach uses tools from the theory of rclf and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable the proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances

adaptive tracking control for a class of uncertain switched nonlinear systems this paper is concerned with the problem of tracking control for a class of switched nonlinear systems in lower triangular form with unknown functions and arbitrary switchings two classes of state feedback controllers are constructed by adopting the adaptive backstepping technique and both of them are designed by using the common lyapunov function clf method the first controller is designed under multiple adaptive laws then the second one is designed based on constructing a maximum common adaptive parameter which can overcome the problem of over parameterization of the first controllers it is shown that the designed state feedback controllers can ensure that all the signals remain bounded and the tracking error converges to a small neighborhood of the origin finally simulation results are presented to show the effectiveness of the proposed approaches

a geometric approach for reachability and observability of linear switched impulsive systems abstract this paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices first some new concepts with respect to the reachability and unobservability are introduced especially span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces then the geometric characterization of the span reachable and unobservable sets is presented moreover the relations between the span reachable set unobservable set and the invariant subspaces of such systems are discussed finally corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed

on the realization of maximal simple types and epsilon factors of pairs let g be the group of rational points of a general linear group over a non archimedean local field f we show that certain representations of open compact mod centre subgroups of g the maximal simple types of bushnell and kutzko can be realized as concrete spaces in the level zero case our result is essentially due to gel fand this allows us for a supercuspidal representation pi of g to compute a distinguished matrix coefficient of pi by integrating we obtain an explicit whittaker function for pi we use this to compute the varepsilon factor of pairs for supercuspidal representations pi 1 pi 2 of g when pi 1 and the contragredient of pi 2 differ only at the tame level more precisely pi 1 and check pi 2 contain the same simple character we do this by computing both sides of the functional equation defining the epsilon factor using the definition of jacquet piatetskii shapiro shalika we also investigate the behavior of the varepsilon factor under twisting of pi 1 by tamely ramified quasi characters our results generalize the special case pi 1 check pi 2 totally wildly ramified due to bushnell and henniart

stabilization of planar switched systems this paper considers the problem of stabilization of single input planar switched systems we assume the switching law is observable a formula is presented which provides a necessary and sufficient condition for the system to be quadratically stabilizable a set of linear inequalities are given to describe the set of all quadratic lyapunov functions the solvability and the control design technique are clearly described in a straightforward computation algorithm

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

a discontinuous galerkin method for the mono energetic fokker planck equation based on a spherical interior penalty formulation we present a new discretization of the mono energetic fokker planck equation we build on previous work kophazi and lathouwers 2015 where we devised an angular discretization for the boltzmann equation allowing for both heterogeneous and anisotropic angular refinement the angular discretization is based on a discontinuous finite element method on the unit sphere here we extend the methodology to include the effect of the fokker planck scatter operator describing small angle particle scatter we describe the construction of an interior penalty method on the sphere surface results are provided for a variety of test cases ranging from purely angular to fully three dimensional the results show that the scheme can resolve highly forward peaked flux distributions with forward peaked scatter

langlands parameters for epipelagic representations of hbox gl _ n let f be a non archimedean local field an irreducible cuspidal representation of mathrm gl n f is epipelagic if its swan conductor equals 1 we give a full and explicit description of the langlands parameters of such representations in terms of elementary representation theory and local class field theory

a proof of the finite field analogue of jacquet s conjecture in this paper the proof of the finite field analogue of jacquet s conjecture on local converse theorem for cuspidal representations of general linear groups is given more precisely the set of twisted gamma factors of pi big gamma pi times tau psi mid tau in scr g t 1 le t le big n over 2 big big together with a central character omega pi determine uniquely up to isomorphism the irreducible cuspidal representation pi of rm gl n bbb f q where cal g t denotes the set of irreducible generic representations of rm gl t bbb f q and bbb f q denotes a finite field of q elements

multigrid in energy preconditioner for krylov solvers we have added a new multigrid in energy mge preconditioner to the denovo discrete ordinates radiation transport code this preconditioner takes advantage of a new multilevel parallel decomposition a multigroup krylov subspace iterative solver that is decomposed in energy as well as space angle forms the backbone of the transport solves in denovo the space angle energy decomposition facilitates scaling to hundreds of thousands of cores the multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of krylov iterations required for convergence this preconditioner is well suited for use with advanced eigenvalue solvers such as rayleigh quotient iteration and arnoldi

regional stabilization of input delayed uncertain nonlinear polynomial systems this paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time varying input delay and polytopic parameter uncertainty a linear matrix inequality approach based on the lyapunov krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states numerical examples demonstrate the potentials of the proposed stabilization approach

a space angle dgfem approach for the boltzmann radiation transport equation with local angular refinement in this paper a new method for the discretization of the radiation transport equation is presented based on a discontinuous galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization to cope with the discontinuous spatial nature of the solution a generalized riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes a new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem the resulting numerical fluxes for the various possible cases where neighboring elements have an equal higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation the choice of discontinuous trial functions not only has the advantage of easing local refinement it also facilitates the use of efficient sweep based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution the approach is illustrated by a series of numerical experiments results show high orders of convergence for the scalar flux on angular refinement the generalized riemann upwinding procedure leads to stable and consistent solutions further the sweep based solver performs well when used as a preconditioner for a krylov method

stability and robustness analysis for curve tracking control using input to state stability we study an important class of feedback controllers that arise in curve tracking problems for robotics previous experimental results suggested the robust performance of the control laws under perturbations here we use input to state stability to prove predictable tolerance and safety bounds that ensure robust performance under perturbations and time delays our proofs are based on an invariant polygon argument and a new strict lyapunov function design

output tracking control of nonlinear switched cascade systems using a variable structure control method this article is concerned with the output tracking control problem for a class of nonlinear switched cascade systems under some average dwell time based switching laws firstly stabilisation problem of this class of switched systems is considered then the result is extended to the output tracking control problem based on the variable structure control technique and the characteristic of the system the variable structure controllers and the average dwell time are designed the effectiveness of the proposed design approach is illustrated with simulation results

an angular multigrid preconditioner for the radiation transport equation with fokker planck scattering in a previous paper hennink and lathouwers 2017 we developed a finite element discretization for the boltzmann transport equation with forward peaked scatter modeled by the fokker planck approximation the discretization was based on the discontinuous galerkin method in both space and angle it was expected and found that the regular source iteration algorithm for the boltzmann equation is not effective in solving the discretized system and becomes excessively expensive for problems with many angular degrees of freedom the purpose of this paper is to develop a multigrid scheme as preconditioner for the above mentioned discretization the method exploits the nested nature of the meshes and the natural prolongation restriction between meshes by galerkin projection a set of test problems ranging from pure spherical diffusion to the complete boltzmann transport problem in 3d are presented to illustrate that the method is very effective resulting in iteration counts nearly independent of problem size even for highly non isotropically refined angular meshes

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

spatial multigrid for isotropic neutron transport a spatial multigrid algorithm for isotropic neutron transport is presented in x y geometry the linear system is obtained using discrete ordinates in angle and corner balance finite differencing in space spatial smoothing is accomplished by a four color block jacobi relaxation where the diagonal blocks correspond to 4 cell blocks on the spatial grid a bilinear interpolation operator and its transpose are used for the grid transfer operators good convergence factors were observed for homogeneous material properties heterogeneous material properties prove more difficult especially the case of a vacuum region surrounded by a thick diffusive region in this case a small amount of absorption or effective absorption in a time dependent problem restores good convergence numerical results are presented

integral input to state stability for hybrid delayed systems with unstable continuous dynamics this paper considers integral input to state stability iiss for a class of hybrid time delay systems discrete dynamics includes impulsive and switching signals and continuous dynamics is not necessarily stable based on multiple lyapunov krasovskii functionals a dwell time bound is explicitly given to guarantee iiss of the hybrid delayed system compared with existing results on related problems the obtained stability criteria can be applied to a larger class of hybrid delayed systems moreover the obtained dwell time bound is less conservative than existing ones at last an example related to networked control systems ncss is provided to illustrate the effectiveness of the proposed result

stabilisation of second order lti switched positive systems the stabilisation problem of second order switched positive systems consisting of two unstable subsystems is considered in this article by considering the vector fields and geometric characteristics a necessary and sufficient condition for the stabilisability of second order switched positive systems with two unstable subsystems is provided furthermore it is shown via this condition that neither second order switched positive systems consisting of two subsystems with unstable nodes nor second order switched positive systems consisting of one subsystem with unstable nodes and the other with a saddle point can be stabilised via any switching law

finite valued feedback laws and piecewise classical solutions abstract often in engineering literature we find control systems in which the open loop inputs are piecewise constant and take values in a finite set such open loop inputs cause the system to have fairly regular solutions on the other hand when acting in closed loop feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type in fact pathological behaviours such as the accumulation of discontinuities may appear zeno phenomenon we give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviours

multigroup diffusion preconditioners for multiplying fixed source transport problems several preconditioners based on multigroup diffusion are developed for application to multiplying fixed source transport problems using the discrete ordinates method by starting from standard one group diffusion synthetic acceleration dsa a multigroup diffusion preconditioner is constructed that shares the same fine mesh as the transport problem as a cheaper but effective alternative a two grid coarse mesh multigroup diffusion preconditioner is examined for which a variety of homogenization schemes are studied to generate the coarse mesh operator finally a transport corrected diffusion preconditioner based on application of the newton shulz algorithm is developed the results of several numerical studies indicate the coarse mesh diffusion preconditioners work very well in particular a coarse mesh transport corrected diffusion preconditioner reduced the computational time of multigroup gmres by up to a factor of 17 and outperformed best case gauss seidel results by over an order of magnitude for all problems studied

stability of time delay feedback switched linear systems we address stability of state feedback switched linear systems in which delays are present in both the feedback state and the switching signal of the switched controller for switched systems with average dwell time switching signals we provide a condition in terms of upper bounds on the delays and in terms of a lower bound on the average dwell time to guarantee asymptotic stability of the closed loop the condition also implies that in general feedback switched linear systems are robust with respect to both small state delays and small switching delays our approach combines existing multiple lyapunov function techniques with the merging switching signal technique which gives relationships between the average dwell times of two mismatched switching signals and their mismatched times a methodology for numerical solution based on linear matrix inequality is also included

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

brief paper design of switching sequences for controllability realization of switched linear systems in this paper we study the problem of designing switching sequences for controllability of switched linear systems each controllable state set of designed switching sequences coincides with the controllable subspace both aperiodic and periodic switching sequences are considered for the aperiodic case a new approach is proposed to construct switching sequences and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d d d 1 1 here d is the dimension of the controllable subspace d email protected i 1 m where a i b i are subsystems for the periodic case we show that the controllable subspace can be realized within d switching periods

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

bibo stability of linear switching systems in this paper we show that for linear switching systems of the form x sub n 1 a sub n x sub n u sub n 1 where the matrices a sub n are chosen arbitrarily from a given set of matrices bounded input bounded output stability implies uniform exponential stability

incremental h control for switched nonlinear systems abstract in this paper we investigate the incremental h control for switched nonlinear systems by using a state dependent switching law and an average dwell time approach incorporated with multiple lyapunov functions even if all subsystems are unstable a sufficient condition for the incremental h control problem to be solvable is derived based on the design state dependent switching law furthermore when all subsystems are incrementally globally asymptotically stable igas the switched nonlinear system under the average dwell time scheme is igas and possesses a weighted incremental l2 gain then we extend this result to the case where both igas subsystems and unstable subsystems coexist if the activation time ratio between igas subsystems and unstable ones is not less than a specified constant sufficient conditions for the weighted incremental h performance of the switched system are guaranteed two numerical examples are given to illustrate the validity of the proposed approach

space time streamline upwind petrov galerkin methods for the boltzmann transport equation abstract this paper presents a space time streamline upwind petrov galerkin formulation for the time dependent boltzmann transport equation conventional linear space time formulations typically take the distance across space time elements as the representative distance across which dissipation is introduced the proposed method however calculates the representative distances based on the gradient of the solution in space time therefore the method in its most general form is non linear the calculation of distances based on the solution gradient means that even if small time steps are used the method will attempt to optimise the numerical accuracy while eliminating any spurious oscillations unlike conventional non linear petrov galerkin formulations the proposed class of methods introduces dissipation only in the streamline direction in space time conventional non linear discontinuity capturing schemes add dissipation in the steepest gradient direction in order to demonstrate the accuracy and robustness in terms of suppressing spurious oscillations the method is applied to a series of one group 2 d fixed source steady state and time dependent radiation transport problems

switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems this paper investigates the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems where the solvability of the adaptive stabilization problem for subsystems is unnecessary a new switched adaptive control technique for the problem studied is set up by exploiting the generalized multiple lyapunov functions method and the parameter separation technique different update laws are designed to reduce the conservativeness caused by adoption of a common update law for all subsystems also the proposed technique permits removal of a common restriction in which the parameterization in the switched systems is restricted to a linear parameterization as an application of the proposed design technique stabilization for a class of non triangular switched systems with nonlinear parameterization is achieved by design of adaptive controllers since no subsystem of such a switched system is assumed to be adaptively stabilizable the problem under study cannot be handled by the existing methods a two inverted pendulums as a practical example is also provided to demonstrate the effectiveness of the proposed design method

decentralized adaptive fuzzy output feedback control of switched large scale nonlinear systems in this paper a decentralized adaptive fuzzy output feedback control problem is discussed for a class of switched large scale nonlinear systems without the measurements of the system states fuzzy logic systems are used to approximate the unknown nonlinear functions and a switched observer is designed to avoid the conservativeness caused by adoption of a common observer for all subsystems a common coordinate transformation of all subsystems is constructed to get rid of individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme meanwhile since the exponential decline property of lyapunov functions for individual subsystems is no longer satisfied in this paper the classical average dwell time method cannot be directly applied based on this a switched observer based decentralized adaptive fuzzy output feedback control technique is set up by exploiting the average dwell time method and backstepping it is proved that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded under a class of switching signals with average dwell time while the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed control scheme is illustrated by its applications to a two inverted pendulum system and a quadruple tank process system

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check

lyapunov krasovskii functionals for switched nonlinear input delay systems under asynchronous switching this paper investigates the input to state stability for switched nonlinear input delay systems under asynchronous switching suppose a feedback control law has been designed such that the nominal closed loop system is exponentially stable for a certain switching signal and suppose further that a corresponding lyapunov function for the nominal closed loop system is available in the presence of input delay and asynchronous switching the system may not be stable under the same switching signal for this case we explicitly construct lyapunov krasovskii functionals based on the knowledge of the known lyapunov function then by using the constructed lyapunov krasovskii functionals a new switching delay dependent switching signal satisfying the new mode dependent average dwell time conditions is provided to guarantee the input to state stability of the system with respect to the disturbance under a certain input delay bound two examples are given to illustrate the effectiveness of the proposed theory