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

closed loop stabilization of planar bilinear switched systems in this paper we address the closed loop switched stabilization problem for planar bilinear systems under the assumption that the control is one dimensional and takes only the values 0 and 1 we construct a class of state static memoryless stabilizing feedback laws which preserve the properties of open loop switching signals in order to prove the stability of the implemented system we use lyapunov techniques for differential equations with discontinuous righthand side finally we point out some possible extensions of our result and compare it with related results previously proven by other authors

brief paper robustness of exponential stability of a class of stochastic functional differential equations with infinite delay we regard the stochastic functional differential equation with infinite delay dx t f x t dt g x t dw t as the result of the effects of stochastic perturbation to the deterministic functional differential equation email protected t f x t where x t x t q c 0 r n is defined by x t q x email protected email protected 0 we assume that the deterministic system with infinite delay is exponentially stable in this paper we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable

robustness properties of an algorithm for the stabilisation of switched systems with unbounded perturbations abstractin this paper it is shown that an algorithm for the stabilisation of switched systems introduced by the authors is robust with respect to perturbations which are unbounded in the supremum norm but bounded in a power like sense the obtained stability results comprise among others both the exponential input to state stability and the exponential integral input to state stability properties of the closed loop system and give a better description of the behaviour of the closed loop system

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

on superregular matrices and mdp convolutional codes superregular matrices are a type of lower triangular toeplitz matrix that arises in the context of constructing convolutional codes having a maximum distance profile these matrices are characterized by the property that the only submatrices having a zero determinant are those whose determinants are trivially zero due to the lower triangular structure in this paper we discuss how superregular matrices may be used to construct codes having a maximum distance profile we also present an upper bound on the minimum size a finite field must have in order that a superregular matrix of a given size can exist over that field this in turn gives an upper bound on the smallest field size over which an mdp n k convolutional code can exist

asynchronously switched control of discrete impulsive switched systems with time delays this paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching the so called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous by using the average dwell time adt approach sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed loop system is exponentially stable the desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed method

exponential stabilization of a constrained bilinear system for a bilinear system that is open loop neutrally stable a quadratic state feedback control has been proposed to ensure global asymptotical stability of the closed loop system in this paper a new nonlinear control is proposed so that the closed loop system is not only asymptotically stable but also exponentially stable the new control results in a much faster state convergence rate than the quadratic control furthermore it can be applied to systems with tight saturation limits on the control input

on reachability and stabilization of switched linear systems reachability and stabilization issues for switched linear control systems are addressed a necessary and a sufficient condition are presented for reachability under mild assumptions we prove that the switched linear control systems are stabilizable in addition we show that an element driven switching stabilization strategy can be explicitly constructed

on controllability of switched linear systems in this paper the controllability of a switched linear system which is a collection of linear time invariant systems along with some maps for switching among them is addressed first a controllable state set is defined as a basic tool to discuss the controllability condition next it is proved that the controllability of a multi input system is equivalent to that of a single input system finally a sufficient and necessary condition for controllability of third order systems is presented according to the proof of this criterion we state a conjecture on the controllability condition of n dimensional systems a numeric example is given to illustrate the result

resilient stabilization of switched linear control systems against adversarial switching this paper studies the problem of stabilizing discrete time switched linear control systems slcss using continuous input by a user against adversarial switching by an adversary it is assumed that at each time the adversary knows the user s decision on the continuous input but not vice versa a quantitative metric of stabilizability is proposed systems at the margin of stabilizability are further classified and studied via the notions of defectiveness and reducibility analytical bounds on the stabilizability metric are derived using semi norms with tight bounds provided by extremal norms numerical algorithms are also developed for computing this metric an application example in networked control systems is presented

the improved lasalle type theorems for stochastic functional differential equations abstract the main aim of this paper is to improve some results obtained by mao x mao the lasalle type theorems for stochastic functional differential equations nonlinear stud 7 2000 307 328 our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above for example we need only the local lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions to guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation sfde under the weaker conditions imposed in this paper we establish a generalised existence and uniqueness theorem which covers a wider class of nonlinear sfdes as demonstrated by the examples discussed in this paper moreover from our improved results follow some new criteria on the stochastic asymptotic stability for sfdes

the bando calabi futaki character and its lifting to a group character the bando calabi futaki character of a compact kahler manifold is an obstruction to the existence of kahler metrics with constant scalar curvature which is a generalization of the futaki character of a fano manifold in this paper we shall establish an interpretation of the bando calabi futaki character as a secondary characteristic class by using this interpretation we shall also prove that the bando calabi futaki character can be lifted to a group character

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching this paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system a design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures and the dwell time approach is utilized for the stability analysis then the approach is extended to take into account stochastic switched system with lipschitz nonlinearities and structured uncertainties finally a numerical example is employed to verify the proposed method

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

observer design of discrete time impulsive switched nonlinear systems with time varying delays this paper investigates the problem of observer design for discrete time impulsive switched nonlinear systems with time varying delays firstly based on the average dwell time approach and the lyapunov krasovskii functional technique a delay dependent exponential stability criterion for the discrete time impulsive switched nonlinear systems with time varying delays is derived in terms of a set of linear matrix inequalities lmis then sufficient conditions for the existence of an observer that guarantees the exponential stability of the corresponding error system are proposed finally two numerical examples are given to illustrate the effectiveness of the proposed method

on the h0 h stabilization of switched nonlinear systems via state dependent switching rule abstract this paper considers switching stabilization of some general nonlinear systems assuming certain properties of a convex linear combination of the nonlinear vector fields two ways of generating stabilizing switching signals are proposed i e the minimal rule and the generalized rule both based on a partition of the time state space the main theorems show that the resulting switched system is globally uniformly asymptotically stable and globally uniformly exponentially stable respectively it is shown that the stabilizing switching signals do not exhibit chattering i e two consecutive switching times are separated by a positive amount of time in addition under the generalized rule the switching signal does not exhibit zeno behavior accumulation of switching times in a finite time stability analysis is performed in terms of two measures so that the results can unify many different stability criteria such as lyapunov stability partial stability orbital stability and stability of an invariant set applications of the main results are shown by several examples and numerical simulations are performed to both illustrate and verify the stability analysis

an integral type multiple lyapunov functions approach for switched nonlinear systems an integral type multiple lyapunov functions mlfs approach for switched nonlinear systems is set up for the first time which gives a more general condition for analyzing the behavior of switched nonlinear systems since the branicky s nonincreasing condition is no longer assumed and the generalized mlfs condition is a special case of the condition provided meanwhile based on the integral type mlfs approach global stabilization for a class of switched nonlinear systems in p normal form is achieved by constructing state feedback controllers of subsystems and a proper switching law where the solvability of the problem under study for individual subsystems is not assumed two examples are also provided to demonstrate the effectiveness of the proposed design method

k energy on polarized compactifications of lie groups abstract in this paper we study mabuchi s k energy on a compactification m of a reductive lie group g which is a complexification of its maximal compact subgroup k we give a criterion for the properness of k energy on the space of k k invariant kahler potentials in particular it turns to give an alternative proof of delcroix s theorem for the existence of kahler einstein metrics in case of fano manifolds m we also study the existence of minimizers of k energy for general kahler classes of m

global stabilisation of switched nonlinear systems in p normal form with mixed odd and even powers this article investigates the problem of global stabilisation for a class of switched nonlinear systems in p normal form whose subsystems are not assumed to be asymptotically stabilisable unlike the existing results on systems in p normal form where the power order is only positive odd integer we allow positive even integer of the power order using the convex combination method and the adding a power integrator technique we construct a switching law and design state feedback controllers of individual subsystems explicitly by a recursive design algorithm to guarantee asymptotic stability of the closed loop system the designed method is also extended to the global stabilisation problem of switched nonlinear systems in p normal form with zero dynamics as an application of the proposed design method a continuously stirred tank reactor is studied

robust stabilizing control laws for a class of second order switched systems abstract for a class of second order switched systems consisting of two linear time invariant lti subsystems we show that the so called conic switching law proposed previously by the present authors is robust not only in the sense that the control law is flexible to be explained further but also in the sense that the lyapunov stability resp lagrange stability properties of the switched system are preserved in the presence of certain kinds of vanishing perturbations resp nonvanishing perturbations the analysis is possible since the conic switching laws always possess certain kinds of quasi periodic switching operations we also propose for a class of nonlinear second order switched systems with time invariant subsystems a switching control law which locally exponentially stabilizes the entire nonlinear switched system provided that the conic switching law exponentially stabilizes the linearized switched systems consisting of the linearization of each nonlinear subsystem this switched control law is robust in the sense mentioned above

stability condition for sampled data based control of linear continuous switched systems abstract most practical systems are continuous in nature but with discrete sampled feedback when digital control is utilized this paper investigates the stabilization problem of switched linear continuous time systems with sampled data based control for both known and unknown arbitrary switching processes on the basis of lyapunov stability theory a sufficient global exponential stability condition related to dwell time and sampling period is established for the latter case on line one step adaptive estimation algorithm is derived and integrated with sampled feedback for control design validation and verification of the established result are conducted through cruise control of train systems

a constructive approach to reachability realization of discrete time switched linear systems this paper studies the reachability of discrete time switched linear systems a new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly detailed comparison between the obtained result and that reported in the open literature is also made which verifies the advantage of the proposed approach

a class of one dimensional mds convolutional codes a class of one dimensional convolutional codes will be presented they are all mds codes i e have the largest distance among all one dimensional codes of the same length n and overall constraint length furthermore their extended row distances are computed and they increase with slope at least n in certain cases of the algebraic parameters we will also derive parity check matrices of vandermonde type for these codes finally cyclicity in the convolutional sense of 8 will be discussed for our class of codes it will turn out that they are cyclic if and only if the field element used in the generator matrix has order n this can be regarded as a generalization of the block code case

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

asymptotic stabilization of the bilinear time invariant system via piecewise constant feedback abstract sufficient conditions for the asymptotic stabilization in a preassigned domain of the nonhomogeneous bilinear system bls via piecewise constant feedback are given based on those for an auxillary bls with additional control in the drift term application to the swing equation is also discussed

stability and input to state stability for stochastic systems and applications this paper is concerned with establishing some stability and input to state stability iss properties in terms of two different measures h0 and h for nonlinear systems of stochastic differential equations of ito type to analyze these properties classical lyapunov s method and a comparison principle are used to justify the proposed theoretical results applications to state estimating systems of luenberger type and feedforward or cascade systems enhanced with numerical examples and simulations are presented

robust reliable stabilization of uncertain switched neutral systems with delayed switching this paper investigates the problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system and the parameter uncertainties are assumed to be norm bounded a state feedback controller is proposed to guarantee exponential stability and reliability for switched neutral systems and the dwell time approach is utilized for the stability analysis and controller design a numerical example is given to illustrate the effectiveness of the proposed method

hilbert series and obstructions to asymptotic semistability abstract given a polarized manifold there are obstructions for asymptotic chow semistability described as integral invariants which can be regarded as characters of the lie algebra of holomorphic vector fields in this paper we show that on toric fano manifolds the linear span of those lie algebra characters coincides with the derivatives of the laurent series of the hilbert series

exponential stabilization of discrete time switched linear systems this article studies the exponential stabilization problem for discrete time switched linear systems based on a control lyapunov function approach it is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control lyapunov function such a converse control lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic lyapunov functions for convenience or heuristic reasons in addition it is also proved that if a switched linear system is exponentially stabilizable then it must be stabilizable by a stationary suboptimal policy of a related switched linear quadratic regulator lqr problem motivated by some recent results of the switched lqr problem an efficient algorithm is proposed which is guaranteed to yield a control lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable

robustness of stability of nonlinear systems with stochastic delay perturbations abstract suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential functional equation in this paper a sufficient condition is given so that the perturbed system remains exponentially stable in the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable

stabilization of switched linear systems with time delay in detection of switching signal a feedback stabilization problem for switched linear systems with time delay in detection of switching signal is formulated first online state feedback controller design method for asymptotic stability and exponential stability is given then offline state feedback controller design method for asymptotic stability and exponential stability is given as well

robust stability of uncertain stochastic differential delay equations in this paper we first discuss the robust stability of uncertain linear stochastic differential delay equations we then extend the theory to cope with the robust stability of uncertain semi linear stochastic differential delay equations we shall also give several examples to illustrate our theory

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

on the stabilizability of discrete time switched linear systems novel conditions and comparisons in this paper we deal with the stabilizability property for discrete time switched linear systems a recent necessary and sufficient characterization of stabilizability based on set theory is considered as the reference for comparing the computation oriented sufficient conditions the classical bmi conditions based on lyapunov metzler inequalities are considered and extended novel lmi conditions for stabilizability derived from the geometric ones are presented that permit to combine generality with computational affordability for the different conditions the geometrical interpretations are provided and the induced stabilizing switching laws are given the relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity

finite time stabilization for a class of switched time delay systems under asynchronous switching switched control systems can be used to describe many practical processes with switching phenomena such as power electronics mechanical systems etc in this paper the problem of finite time stabilization under asynchronous switching is dealt with for a class of switched time delay systems with nonlinear disturbances firstly the nonlinear uncertainties are transformed into the linear time varying forms via the differential mean value theorem under some assumptions secondly by applying the average dwell time method and convexity principle a finite time stability condition for the unforced switched time delay system is established finally an asynchronous switching state feedback controller is designed which renders the considered system finite time stable a numerical example is provided to show the effectiveness of the developed results

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

the bando calabi futaki character as an obstruction to semistability the purpose of this note is to correct some errors in b and c of main theorem in mn and to make an additional observation in particular we shall give a first nonvanishing example of the obstruction obstrasymp m l introduced in m2

stabilisability of nonlinear systems by means of time dependent switching rules given a family of linear systems which admit an asymptotically stable convex combination the existence of stabilising time dependent switching rules can be proved by using the baker campbell hausd

robust h control of discrete switched system with time delay this paper deals with the stabilization and robust h infinity control of discrete switched system with time delay the switching is time driven and the design is based on the average dwell time method the controller parameters and the permissible switching sequence subject to the given average dwell time can be obtained by solving a set of linear matrix inequalities lmis two examples are given to demonstrate the proposed methods

stabilization of switched linear systems with quantized output and switching delays this paper addresses the problem of designing time varying quantizers for the stabilization of switched linear systems with quantized output and switching delays the detection delays of switches are assumed to be time varying but bounded and the dwell time of the switching signal is assumed to be larger than the maximum delay given a switching controller we analyze reachable sets of the closed loop state by using a common lyapunov function and then construct a quantizer that guarantees asymptotic stability a sufficient condition for the existence of such a quantizer is characterized by the maximum switching delay and the dwell time

stabilization of second order lti switched systems this paper studies and solves the problem of asymptotic stabilization of switched systems consisting of unstable secondorder linear time invariant lti subsystems necessary and sufficient conditi

stochastic stabilisation of functional differential equations in this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential equation given an unstable functional differential equation dx t dt f t xt we stochastically perturb it into a stochastic functional differential equation dx t f t xt dt x t db t where is a matrix and b t a brownian motion while xt x t 0 under the condition that f satisfies the local lipschitz condition and obeys the one side linear bound we show that if the time lag is sufficiently small there are many matrices for which the stochastic functional differential equation is almost surely exponentially stable while the corresponding functional differential equation dx t dt f t xt may be unstable

stochastic stabilization of differential systems with general decay rate some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general decay rate are first proved then these results are interpreted as suitable stabilization ones for deterministic and stochastic systems also they permit us to construct appropriate linear stabilizers in some particular situations

central kahler metrics the determinant of the ricci endomorphism of a kahler metric is called its central curvature a notion well defined even in the riemannian context this work investigates two types of kahler metrics in which this curvature potential gives rise to a potential for a gradient holornorphic vector field these metric types generalize the kahler einstein notion as well as that of bando and mabuchi 1986 whenever possible the central curvature is treated in analogy with the scalar curvature and the metrics are compared with the extremal kahler metrics of calabi an analog of the futaki invariant is employed both invariants belonging to a family described in the language of holomorphic equivariant cohomology it is shown that one of the metric types realizes the minimum of an l 2 functional defined on the space of kahler metrics in a given kahler class for metrics of constant central curvature results are obtained regarding existence uniqueness and a partial classification in complex dimension two consequently on a manifold of fano type such metrics and kahler einstein metrics can only exist concurrently an existence result for the case of non constant central curvature is slated and proved in a sequel to this work

stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching the stability of a class of hybrid stochastic retarded systems hsrss with an asynchronous switching controller is investigated in this model the controller design relies on the observed jumping parameters which are however delayed and thus can not be measured in real time precisely this delayed time interval referred to as the asynchronous switching interval is markovian and dependent on the actual switching signal the sufficient conditions under which the system is either stochastically asymptotic stable or input to state stable are obtained by applying the extended razumikhin type theorem to the asynchronous switching interval these results are less conservative as it is only required that the designed lyapunov function is non decreasing it is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying markov process which is a conclusion similar to that in asynchronous deterministic switched systems the effectiveness and correctness of the obtained results are finally verified by a numerical example

constructions of mds convolutional codes maximum distance separable mds convolutional codes are characterized through the property that the free distance attains the generalized singleton bound the existence of mds convolutional codes was established by two of the authors by using methods from algebraic geometry this correspondence provides an elementary construction of mds convolutional codes for each rate k n and each degree spl delta the construction is based on a well known connection between quasi cyclic codes and convolutional codes

asymptotic controllability by means of eventually periodic switching rules in this paper we introduce the notion of eventually periodic switching signal we prove that if a family of linear vector fields satisfies a mild finite time controllability condition and for each initial state there exists a time dependent switching signal which asymptotically drives the system to the origin possibly allowing different signals for different initial states then the same goal can be achieved by means of an eventually periodic switching signal this enables us to considerably reduce the dependence of the control law on the initial state in this sense the problem addressed in this paper can be reviewed as a switched system theory version of the classical problem of investigating whether or to what extent a nonlinear asymptotically controllable system admits stabilizing feedback laws

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

class kl estimates and input to state stability analysis of impulsive switched systems abstract in this paper we investigate input to state stability of impulsive switched systems the goal is to bridge two apparently different but both useful stability notions input to state stability and stability in terms of two measures in the hybrid systems setting based on two class kl function estimates and a comparison theorem for impulsive differential equations two sets of sufficient lyapunov type conditions for input to state stability in terms of two measures are obtained for impulsive switched systems these conditions exploit some nonlinear integral constraints in terms of generalized dwell time conditions to balance the continuous dynamics and impulsive dynamics so that input to state stability is achieved despite possible instability of individual continuous subsystems or destabilizing impulsive effects an illustrative example is presented together with numerical simulations to demonstrate the main results

multiplier ideal sheaves and integral invariants on toric fano manifolds we extend nadel s results on some conditions for the multiplier ideal sheaves to satisfy which are described in terms of an obstruction defined by the first author applying our extension we can determine the multiplier ideal subvarieties on toric del pezzo surfaces which do not admit kahler einstein metrics we also show that one can define multiplier ideal sheaves for kahler ricci solitons and extend the result of nadel using the holomorphic invariant defined by tian and zhu

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

on the algebraic parameters of convolutional codes with cyclic structure in this paper convolutional codes with cyclic structure will be investigated these codes can be understood as left principal ideals in a suitable skew polynomial ring it has been shown in 4 that only certain combinations of the algebraic parameters field size length dimension and forney indices can occur for such cyclic codes we will investigate whether all these combinations can indeed be realized by a suitable cyclic code and if so how to construct such a code a complete characterization and construction will be given for minimal cyclic codes it is derived from a detailed investigation of the units in the skew polynomial ring

hybrid stabilization and synchronization of nonlinear systems with unbounded delays the stabilization of nonlinear systems with bounded and unbounded time delays via hybrid control is studied we investigate and identify switching rules for which stabilization can be verified a priori when this approach is inadequate stabilizing state dependent switching rules are constructed this method is based on partitioning the state space into switching regions unwanted physical behavior such as chattering and zeno behavior is avoided sufficient conditions are established using razumikhin like theorems the theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay the findings are illustrated through numerical simulations

asymptotic stability and smooth lyapunov functions abstract we establish that differential inclusions corresponding to upper semicontinuous multifunctions are strongly asymptotically stable if and only if there exists a smooth lyapunov function since well known concepts of generalized solutions of differential equations with discontinuous right hand side can be described in terms of solutions of certain related differential inclusions involving upper semicontinuous multifunctions this result gives a lyapunov characterization of asymptotic stability of either filippov or krasovskii solutions for differential equations with discontinuous right hand side in the study of weak as opposed to strong asymptotic stability the existence of a smooth lyapunov function is rather exceptional however the methods employed in treating the strong case of asymptotic stability are applied to yield a necessary condition for the existence of a smooth lyapunov function for weakly asymptotically stable differential inclusions this is an extension to the context of lyapunov functons of brockett s celebrated covering condition from continuous feedback stabilization theory

stabilization for switched stochastic neutral systems under asynchronous switching in this paper the mean square exponential stability of switched stochastic neutral systems with time varying delay under asynchronous switching is investigated a new lyapunov function dependent on the controllers switching signal is constructed which can counteract the difficulty of controller design to stabilize the system under asynchronous switching moreover the value of the lyapunov function is allowed to increase during mismatched periods based on the average dwell time approach a sufficient condition expressed by a set of linear matrix inequalities lmis is derived to guarantee the mean square exponential stability for the closed loop system and the controllers with asynchronous switching are designed finally a numerical example illustrates the effectiveness of the results

convolutional goppa codes in this correspondence we define convolutional goppa codes over algebraic curves and construct their corresponding dual codes examples over the projective line and over elliptic curves are described obtaining in particular some maximum distance separable mds convolutional codes

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 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

some results on the stabilization of switched systems this paper deals with the stabilization of switched systems with respect to w r t compact sets we show that the switched system is stabilizable w r t a compact set by means of a family of switched signals if and only if a certain control affine system whose admissible controls take values in a polytope is asymptotically controllable to that set in addition we present a control algorithm that based on a family of open loop controls which stabilizes the aforementioned control system a model of the system and the states of the switched system generates switching signals which stabilize the switched system in a practical sense we also give results about the convergence and the robustness of the algorithm

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

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

controllability and stabilizability of switched linear systems in this paper we study the conjecture made in ieee trans automat control 47 8 2002 1401 concerning the existence of basic switching sequence for switched systems and give it an affirmative answer and a construction method this paper proves that for switched linear system there exists a switching sequence such that the controllable state set of this switching sequence is equal to the controllable state set of the system hence the controllability can be realized by using only one switching sequence then the result is extended to the systems with time delay in controls furthermore we define the stabilizability of switched linear systems and based on certain transformation of state coordinate we give a necessary and sufficient condition for the stabilizability two examples are presented to illustrate the obtained results

a study of a class of stochastic differential equations with non lipschitzian coefficients we study a class of stochastic differential equations with non lipschitz coefficients a unique strong solution is obtained and the non confluence of the solutions of stochastic differential equations is proved the dependence with respect to the initial values is investigated to obtain a continuous version of solutions the modulus of continuity of coefficients is assumed to be less than x y log open image in new window finally a large deviation principle of freidlin wentzell type is also established in the paper

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching