adaptive pole positioning in mimo linear systems by periodic multirate input controllers abstract in this paper the certainty equivalence principle is used to combine the identification method with a control structure derived from the pole placement problem which rely on periodic multirate input controllers the proposed adaptive pole placers contain a sampling mechanism with different sampling period to each system input and rely on a periodically varying controller which suitably modulates the sampled outputs and reference signals of the plant under control such a control strategy allows us to arbitrarily assign the poles of the sampled closed loop system in desired locations and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system and the knowledge of a set of structural indices namely the locally minimum controllability indices of the continuous time plant an indirect adaptive control scheme is derived which estimates the unknown plant parameters and consequently the controller parameters on line from sequential data of the input and outputs of the plant which are recursively updated within the time limit imposed by a fundamental sampling period t0 using the proposed algorithm the controller determination is based on the transformation of the discrete analogous of the system under control to a phase variable canonical form prior to the application of the control design procedure the solution of the problem can then be obtained by a quite simple utilization of the concept of state similarity transformation known indirect adaptive pole placement schemes usually resort to the computation of dynamic controllers through the solution of a polynomial diophantine equation thus introducing high order exogenous dynamics in the control loop moreover in many cases the solution of the diophantine equation for a desired set of closed loop eigenvalues might yield an unstable controller and the overall adaptive pole placement scheme is unstable with unstable compensators because their outputs are unbounded the proposed control strategy avoids these problems since here gain controllers are essentially needed to be designed moreover persistency of excitation and therefore parameter convergence of the continuous time plant is provided without making any assumption either the richness of the reference signals or on the existence of specific convex sets in which the estimated parameters belong or finally on the coprimeness of the polynomials describing the arma model as in known adaptive pole placement schemes

brief robust h filtering for uncertain impulsive stochastic systems under sampled measurements this paper is concerned with the problem of robust h filtering for uncertain impulsive stochastic systems under sampled measurements the parameter uncertainties are assumed to be time varying norm bounded the aim is to design a stochastically stable filter using the locally sampled measurements which ensures both the robust stochastic stability and a prescribed level of h performance for the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given an example is provided to demonstrate the effectiveness of the proposed approach

kernel density estimation with spherical data summary we study two natural classes of kernel density estimators for use with spherical data members of both classes have already been used in practice the classes have an element in common but for the most part they are disjoint however all members of the first class are asymptotically equivalent to one another and to a single element of the second class in this sense the second class contains the first it includes some estimators which out perform all those in the first class if loss is measured in either squared error or kullback leibler senses explicit formulae are given for bias variance and loss and large sample properties of these quantities are described numerical illustrations are presented

a multirate digital controller for model matching abstract this paper presents a multirate digital controller which comprises a stable linear time invariant system with a multirate sampling scheme this controller is capable of arbitrary zero assignment pole assignment and model matching and it is applicable to plants with unstable zeros the stable controller also provides improved system intersample performance a controller design procedure is derived an example is given to illustrate the design and the system performance

nonsmooth lyapunov pairs for infinite dimensional first order differential inclusions the main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous lyapunov pairs or functions associated to first order differential inclusions in hilbert spaces these inclusions are governed by a lipschitzian perturbation of a maximally monotone operator the dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative we also propose a unifying review of many other criteria given in the literature our approach is based on advanced tools of variational analysis and generalized differentiation

stochastic stability and robust control for sampled data systems with markovian jump parameters in this paper the problems of stochastic stability and robust control for a class of uncertain sampled data systems are studied the systems consist of random jumping parameters described by finite state semi markov process sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented the conditions for the existence of a sampled data feedback control and a multirate sampled data optimal control for the continuous time uncertain markovian jump systems are also obtained the design procedure for robust multirate sampled data control is formulated as linear matrix inequalities lmis which can be solved efficiently by available software toolboxes finally a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques

optimal disturbance rejection control for nonlinear impulsive dynamical systems in this paper we develop an optimality based framework for addressing the problem of nonlinear nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances specifically we transform a given nonlinear nonquadratic hybrid performance criterion to account for system disturbances as a consequence the disturbance rejection problem is translatedinto an optimal hybridcontrol problem furthermore the resulting optimal hybrid control law is shown to render the closed loop nonlinear input output map dissipative with respect to general supply rates in addition the lyapunov function guaranteeing closed loop stability is shown to be a solution to a stead y state hybridhamilton jacobi isaacs equation andthus guaranteeing optimality 2005 elsevier ltd all rights reserved

systems of controlled functional differential equations and adaptive tracking an adaptive servomechanism is developed in the context of the problem of approximate or practical tracking with prescribed asymptotic accuracy by the system output of any admissible reference signal absolutely continuous and bounded with essentially bounded derivative for every member of a class of controlled dynamical systems modelled by functional differential equations

brief paper lyapunov function design for finite time convergence analysis twisting controller for second order sliding mode realization a generalization of the zubov method of a lyapunov function design is presented it is based on the characteristic method application and is related to resolving the first order partial differential equation of a special type a successful resolution of this equation guaranties a finite time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right hand side the suggested method is illustrated by its application to the so called twisting controller stability analysis the constructed lyapunov function as well as its level line sections is graphically illustrated

gain margin improvement using generalized sampled data hold function based multirate output compensator abstract for a siso strictly proper nonminimum phase continuous time linear time invariant lti plant it was shown in yan w b d o anderson and r r bitmead 1993 ieee trans automat contr that the closed loop gain margin obtained via a generalized sampled data hold function gshf based dynamic compensator is significantly improved over that achieved via a conventional periodic controller used in francis b a and t t georgiou 1988 ieee trans automat contr ac 33 820 832 nevertheless the compensator so designed is not necessarily strictly proper it is well known that it is practically difficult and sometimes impossible to implement a nonstrictly proper compensator due to the requirement of zero computation time further as has been shown in vidyasagar m 1985 systems and control letters 5 413 418 stabilization by a nonstrictly proper controller is never robust against singular perturbations in this paper we propose a new type of gshf based compensator which employs multirate sampling of the plant output using the proposed compensator not only the same level of gain margin as in yan w b d o anderson and r r bitmead 1993 ieee trans automat contr can be achieved but also more importantly the compensator is strictly proper

a semiparametric approach to density estimation abstract one method of fitting a parametric density function f x is first to estimate by maximum likelihood say and then to estimate f x by on the other hand when the parametric model does not hold the true density f x may be estimated nonparametrically as in the case of a kernel estimate the key idea proposed is to fit a combination of the parametric and nonparametric estimates namely where 0 1 is unknown the parameter is estimated from the data and its estimate is then used in as the proposed density estimate the main point is that we expect to be close to unity when the parametric model prevails and close to zero when it does not hold we show that under certain conditions converges to the parametric density when the parametric model holds and approaches the true f x when the parametric model does not hold the procedure was applied to a number of actual data sets in each case the maximum likelihood estimate was readily obtained and the semiparametric density es

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

an estimation algorithm for multirate sampled digital control systems abstract this paper presents an optimization based algorithm for state estimation of multirate digital control systems the algorithm features a predictor estimator structure and it is derived by employing a time invariant modelling approach to multirate systems special care is taken to ensure the causality of the derived estimation algorithm and to reduce the dimensionality inherent in multirate system modelling while maintaining a reasonably simple implementation the proposed algorithm is developed to ensure convergence in state estimation between base sampling instants as well as between model rate sampling instants

solutions to hybrid inclusions via set and graphical convergence with stability theory applications motivated by questions in stability theory for hybrid dynamical systems we establish some fundamental properties of the set of solutions to such systems using the notion of a hybrid time domain and general results on set and graphical convergence we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and upper semicontinuous with respect to initial conditions and system perturbations the general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets these results parallel what is already known for differential inclusions and difference inclusions for example the basin of attraction for a compact attractor is relatively open the attractivity is uniform from compact subsets of the basin of attraction and asymptotic stability is robust with respect to small perturbations

semistability finite time stability differential inclusions and discontinuous dynamical systems having a continuum of equilibria this paper focuses on semistability and finite time semistability for discontinuous dynamical systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we extend the theory of semistability to discontinuous autonomous dynamical systems in particular lyapunov based tests for semistability and finite time semistability for autonomous differential inclusions are established

methods of density estimation on the grassmann manifold abstract the grassmann manifold gk m k consists of k dimensional hyperplanes in r m and is equivalent to the manifold pk m k of all m m orthogonal projection matrices idempotent of rank k this paper develops a method of semiparametric density estimation on the manifold pk m k designed to nonparametrically correct a parametric model by its linear function to obtain better density estimators than the ordinary kernel density estimator we suggest two procedures to estimate the correction factors comparing with the ordinary kernel density estimator for small smoothing parameter matrix and or for large sample size n the suggested semiparametric density estimator is seen to have approximately the same variance to the order of approximation used but a smaller bias a one to one transformation of pk m k into r k m k is of use in the asymptotic investigation the general discussion is applied and examined for special kernel function discrepancy measures for matrices on pk m k and starting parametric model

inductive limits of semiprojective c algebras abstract we prove closure properties for the class of c algebras that are inductive limits of semiprojective c algebras most importantly we show that this class is closed under shape domination and so in particular under shape and homotopy equivalence it follows that the considered class is quite large it contains for instance the stable suspension of any nuclear c algebra satisfying the uct and with torsion free k 0 group in particular the stabilized c algebra of continuous functions on the pointed sphere is isomorphic to an inductive limit of semiprojectives

two delay robust digital control and its applications avoiding the problem on unstable limiting zeros in the design of linear control systems the existence of unstable zeros makes it difficult to construct many control systems when the usual digital control scheme is used unstable zeros appear in the discrete time model due to the existence of limiting zeros even though the continuous time plant is minimal phase to avoid this unstable zero problem two new digital control schemes called two delay output control and two delay input control are proposed these control systems are proved to have no finite zeros asymptotic inverse systems pole assignable unknown input observers and output feedback controllers having the ltr loop transfer recovery property are developed using the two delay output control zero assignable control systems and model matching control systems are developed using the two delay input control

the dixmier property and tracial states for c algebras a t was partially supported by an nserc postdoctoral fellowship and through the epsrc grant ep n00874x 1 acknowledgements we are grateful to luis santiago for helpful discussions at an early stage of this investigation we would also like to thank the referee for providing helpful comments which have led to a number of improvements

invariance principles for hybrid systems with connections to detectability and asymptotic stability this paper shows several versions of the lasalle s invariance principle for general hybrid systems the broad framework allows for nonuniqueness of solutions zeno behaviors and does not insist on continuous dependence of solutions on initial conditions instead only a mild structural property involving graphical convergence of solutions is posed the general invariance results are then specified to hybrid systems given by set valued data further results involving invariance as well as observability detectability and asymptotic stability are given

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

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 on the algebraic characterization of invariant sets of switched linear systems in this paper a suitable lasalle principle for continuous time linear switched systems is used to characterize invariant sets and their associated switching laws an algorithm to determine algebraically these invariants is proposed the main novelty of our approach is that we require no dwell time conditions on the switching laws by not focusing on restricted control classes we are able to describe the asymptotic properties of the considered switched systems observability analysis of a flying capacitor converter is proposed as an illustration

stability analysis of discontinuous quantum control systems with dipole and polarizability coupling closed quantum systems under the influence of a laser field whose interaction is modeled by a schrodinger equation with a coupling control operator containing both a linear dipole and a quadratic polarizability term are analyzed discontinuous feedbacks obtained by a lyapunov trajectory tracking procedure have recently been proposed to control these types of system the purpose of this paper is to study the asymptotic stability by considering the solutions in the filippov sense the analysis is developed by applying a variant of the lasalle invariance principle for differential inclusions numerical simulations are included to illustrate the efficiency of the discontinuous control

almost sure exponential stabilization by discrete time stochastic feedback control given an unstable linear scalar differential equation dot x t alpha x t alpha 0 we will show that the discrete time stochastic feedback control sigma x t tau tau db t can stabilize it that is we will show that the stochastically controlled system dx t alpha x t dt sigma x t tau tau db t is almost surely exponentially stable when sigma 2 2 alpha and tau 0 is sufficiently small where b t is a brownian motion and t tau is the integer part of t tau we will also discuss the nonlinear stabilization problem by a discrete time stochastic feedback control the reason why we consider the discrete time stochastic feedback control is because that the state of the given system is in fact observed only at discrete times say 0 tau 2 tau ldots for example where tau 0 is the duration between two consecutive observations accordingly the stochastic feedback control should be designed based on these discrete time observations namely the stochastic feedback control should be of the form sigma x t tau tau db t from the point of control cost it is cheaper if one only needs to observe the state less frequently it is therefore useful to give a bound on tau from below as larger as better

non autonomous systems asymptotic behaviour and weak invariance principles abstract results pertaining to asymptotic behaviour of solutions of non autonomous ordinary differential equations with locally integrably bounded right hand sides are presented ramifications for weakly asymptotically autonomous systems and adaptively controlled systems are highlighted

a function space approach to sampled data control systems and tracking problems this paper presents a new framework for hybrid sampled data control systems instead of considering the state only at sampling instants this paper introduces a function piece during the sampling period as the state and gives an infinite dimensional model with such a state space this gives the advantage that sampled data systems with built in intersample behavior can be regarded as linear time invariant discrete time systems as a result the approach makes it possible to introduce such time invariant concepts as transfer functions poles and zeros to the sampled data systems even with the presence of the intersample behavior in particular tracking problems can be studied in this setting in a simple and unified way and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions this leads to the internal model principle for sampled data systems

density estimation on the spaces of symmetric and rectangular matrices abstract this paper develops the theory of density estimation on the space s m of all m m symmetric matrices and on the space r m p of all m p rectangular matrices we consider the two methods kernel density estimation and density estimation by orthogonal series and illustrate them with examples for the normal kernel density functions and for the hermite orthonormal bases with symmetric and rectangular matrix arguments on s m and r m p respectively the problem of estimating unknown joint density functions of multiple random matrices is also discussed

a note on generalized hold functions abstract in this note we study the generalized hold functions for use of digital control of continuous time systems first we define and solve the problem of simultaneous stabilization and minimization it is shown that every plant with a strictly proper transfer function is simultaneously stabilizable and minimizable provided that the sampling interval is small enough we also consider robust designs of generalized hold functions a condition is given for the stability of a system using generalized hold functions in the presence of uncertainty

nonpathological lyapunov functions and discontinuous caratheodory systems differential equations with discontinuous right hand side and solutions intended in caratheodory sense are considered for these equations sufficient conditions which guarantee both lyapunov stability and asymptotic stability in terms of nonsmooth lyapunov functions are given an invariance principle is also proven

periodically varying compensation of time invariant systems linear time invariant discrete time scalar systems under periodically varying output feedback and the associated problems of stabilization and arbitrary eigenvalue assignment are investigated the general form of the characteristic polynomial of the closed loop periodically varying system is obtained and some detailed results are provided for the second order case interesting research questions are pointed out

a recurrence principle for stochastic difference inclusions the invariance principle is extended to a recurrence principle and is developed for stochastic difference inclusions for these systems random solutions are not unique under appropriate lyapunov like conditions it is established for every random solution that almost every complete sample path converges to the largest weakly totally recurrent set contained in a level set of the lyapunov like function such a set is not larger and is sometimes smaller than the largest weakly invariant set contained in the level set the principle is useful for establishing robust uniform asymptotic stability in probability or robust uniform strong recurrence under weak lyapunov conditions for stochastic discrete time control systems that employ discontinuous feedback laws examples demonstrate the achieved results

global asymptotic stability of a pid control system with coulomb friction for a point mass subject to coulomb friction in feedback with a pid controller we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions we study the set of all equilibria and we establish its global asymptotic stability using a discontinuous lyapunov like function and a suitable lasalle s invariance principle the well posedness of the proposed model allows to establish useful robustness results including an iss property from a suitable input in a perturbed context simulation results are also given to illustrate our statements

output stabilization via pole placement of discrete time linear periodic systems the output stabilization problem for discrete time linear periodic systems is solved both the state feedback control law and the state predictor are based on a suitable time invariant state sampled reformulation associated with a periodic system preliminary concepts of periodic system theory are briefly recalled in particular the structural properties of a linear discrete time periodic system are properly related to those of a time invariant system associated with it by resorting to such a time invariant reformulation the output stabilization problem via pole placement is solved the stabilizing controller is constituted by a control law and an asymptotic state predictor both of which are shown to be periodic

a razumikhin type lemma for functional differential equations with application to adaptive control a lemma of razumikhin type pertaining to boundedness of solutions of functional differential equations is presented this lemma is subsequently invoked in the analysis of adaptive strategies that guarantee approximate tracking with prescribed asymptotic error bound of reference signals of sobolev class w 1 for two classes of uncertain systems modelled by controlled nonlinear functional differential equations

an integral invariance principle for differential inclusions with applications in adaptive control the byrnes martin integral invariance principle for ordinary differential equations is extended to differential inclusions on bbb r n the extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes

nonparametric density estimation with a parametric start the traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes the present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities for example the normal while not losing much in precision when the true density is far from the parametric class the idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor this works well in cases where the correction factor function is less rough than the original density itself extensive comparisons with the kernel estimator are carried out including exact analysis for the class of all normal mixtures the new method with a normal start wins quite often even in many cases where the true density is far from normal procedures for choosing the smoothing parameter of the estimator are also discussed the new estimator should be particularly useful in higher dimensions where the usual nonparametric methods have problems the idea is also spelled out for nonparametric regression

stability of the limiting zeros of sampled data systems with zero and first order holds this paper is concerned with the zeros of sampled data systems resulting from continuous time systems preceded by a hold and followed by a sampler the holds we shall consider are a zero order hold and a first order hold for sufficiently small or large sampling periods such zeros are called limiting zeros for sufficiently small sampling periods they are known to consist of two different types of zeros the zeros of the first type correspond to the zeros of the original continuous time system while those of the second type have no continuous time counterparts we first show basic properties of the zeros of sample data systems for sufficiently small sampling periods next we clarify in more detail the correspondence between the former type zeros of the sampled data systems and the zeros of the original continuous time system including the stability property of these zeros we also study stability properties of the latter type zeros in addition we study limiting zeros for sufficiently large sampli

transformations in density estimation abstract for the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations in this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data the density estimate of the original data is the back transform by change of variables of the global window width estimate of the transformed data s density we explore choosing the transformation from suitable parametric families data based selection rules for the choice of transformations and the window width are discussed application to real and simulated data demonstrates the usefulness of our proposals

using fuzzy logic to design separation function in flocking algorithms flocking algorithms essentially consist of three components alignment cohesion and separation to track a desired trajectory the flock center should move along the desired trajectory and thus the fourth component navigation is necessary the alignment cohesion and navigation components are well implemented through consensus protocols and tracking controls while the separation component is designed through heuristic based approaches this paper proposes a fuzzy logic solution to the separation component the ts rules and gaussian membership functions are used in fuzzy logic for fixed network flocking a standard stability proof by using lasalle s invariance principle is provided for dynamic network flocking a filipov solution definition is given for nonsmooth dynamics then a lasalle s invariance principle for nonsmooth dynamics is used to prove the stability a group of mobile robots with double integrator dynamics is simulated for the flocking algorithms in a 2 d environment

multi 2 rate control from a 2 periodic perspective generalized 2 rate control this technical note finds that a conventional 2 rate controller which receives feedback at t but provides control at 2t intervals has a 2 periodic core and augments this core to have a generalized 2 rate control that has complete loop zero and pole placement capability an algorithm for controller parameter evaluation for pole zero placement using only linear algebraic steps has been developed the controller also ensures zero steady state and improved transient ripples its superiority in respect of gain margin compensation is illustrated for a third order plant with an unstable pole and a non minimum phase zero

lasalle yoshizawa corollaries for nonsmooth systems in this technical note two generalized corollaries to the lasalle yoshizawa theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right hand sides lyapunov based analysis methods that achieve asymptotic convergence when the candidate lyapunov derivative is upper bounded by a negative semi definite function in the presence of differential inclusions are presented a design example illustrates the utility of the corollaries

brief paper a unified dissipativity approach for stability analysis of piecewise smooth systems the main objective of this paper is to present a unified dissipativity approach for stability analysis of piecewise smooth pws systems with continuous and discontinuous vector fields the filippov definition is considered for the solution of these systems using the concept of generalized gradients for nonsmooth functions sufficient conditions for the stability of a pws system are formulated based on lyapunov theory the importance of the proposed approach is that it does not need any a priori information about attractive sliding modes on switching surfaces which is in general difficult to obtain a section on application of the main results to piecewise affine pwa systems followed by a section with extensive examples clearly show the usefulness of the proposed unified methodology in particular we present an example with a stable sliding mode where the proposed method works and previously suggested methods fail

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

locally parametric nonparametric density estimation this paper develops a nonparametric density estimator with parametric overtones suppose f x is some family of densities indexed by a vector of parameters we define a local kernel smoothed likelihood function which for each x can be used to estimate the best local parametric approximant to the true density this leads to a new density estimator of the form f x o x thus inserting the best local parameter estimate for each new value of x when the bandwidth used is large this amounts to ordinary full likelihood parametric density estimation while for moderate and small bandwidths the method is essentially nonparametric using only local properties of data and the model alternative ways more general than via the local likelihood are also described the methods can be seen as ways of nonparametrically smoothing the parameter within a parametric class properties of this new semiparametric estimator are investigated our preferred version has approximately the same variance as the ordinary kernel method but potentially a smaller bias the new method is seen to perform better than the traditional kernel method in a broad nonparametric vicinity of the parametric model employed while at the same time being capable of not losing much in precision to full likelihood methods when the model is correct other versions of the method are approximately equivalent to using particular higher order kernels in a semiparametric framework the methodology we develop can be seen as the density estimation parallel to local likelihood and local weighted least squares theory in nonparametric regression

block form control of linear time invariant discrete time systems defined over commutative rings abstract a new approach based on a block input block output state model is developed for the study of linear time invariant discrete time systems whose coefficients belong to a commutative ring with 1 it is well known that such systems arise in the study of various classes of complex linear systems including systems depending on parameters and multidimentional systems by time compressing the block input state representation new results are obtained on the construction of a memoryless block form state feedback control law that yields a type of assignability and or deadbeat control these results are then dualized to yield results on a new type of state observer based on a block of output measurements the observer and state feedback controller are then combined to yield new results on input output regulation and set point tracking for systems defined over an arbitrary commutative ring in the last part of the paper the block input form is utilized to study the stabilization of systems defined over a normed algebra

meagre functions and asymptotic behaviour of dynamical systems a measurable function x j r x x a metric space is said to be c meagre if c x is non empty and for every closed set k x with k c x 1 k has 5nite lebesgue measure this concept of meagreness is shown to provide a unifying framework which facilitates a variety of characterizations extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems by way of motivation consider the initial value problem f x x 0 rn with f rn rn locally lipschitz and denote its unique solution by x t t de5ned on its maximal interval of existence i 0 let g rn r be continuous assume that x is a bounded solution of the initial value problem in which case i 0 then g x is uniformly continuous if in addition g x l1 then we may conclude by an elementary observation frequently referred to as barb alat s lemma 5 see also 18 section 21 lemma 1 that g x t 0 as t 0 since by boundedness x t approaches as t its non empty compact invariant limit set b we also conclude that b g 1 0 it follows that x t tends as t to the largest invariant subset of g 1 0 this is a short proof of theorem 1 2 of 6 the proof in 6 is based on arguments involving properties of the dow generated by the dieerential

on weak invariance principles for nonlinear switched systems in this technical note we develop two weak invariance principles for nonlinear switched systems we first present a union weak invariance principle for switched systems which includes as a special case the integral invariance principle it is shown that the switched solution approaches the largest weakly invariant set of the combined zero loci of the output functions then we extend the union weak invariance principle to an intersection weak invariance principle which greatly reduces the convergence region unlike the existing results in which the constructions of lyapunov functions are inevitable our principles do not require the existence of lyapunov functions numerical examples are presented to demonstrate the feasibility of our principles as well as applications to multi agent consensus problems

generalized lyapunov and invariant set theorems for nonlinear dynamical systems in this paper we develop generalized lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the lyapunov function and the system dynamics are removed in particular local and global stability theorems are given using lower semicontinuous lyapunov functions furthermore generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized lyapunov level surfaces the proposed results provide transparent generalizations to standard lyapunov and invariant set theorems

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

a generalization of krasovskii lasalle theorem for nonlinear time varying systems converse results and applications this paper presents a practically applicable characterization of uniform global asymptotic stability uas and ugas for general nonlinear time varying systems under certain output dependent conditions in the spirit of the krasovskii lasalle theorem the celebrated krasovskii lasalle theorem is extended from two directions one is using the weak zero state detectability property associated with reduced limiting systems of the system in question to generalize the condition that the maximal invariance set contained in the zero locus of the time derivative of the lyapunov function is the zero set another one is using an almost bounded output energy condition to relax the assumption that the time derivative of the lyapunov function is negative semi definite then the uas and ugas properties of the origin can be guaranteed by employing these two improved conditions related to certain output function for uniformly lyapunov stable systems the proposed conditions turn out to be also necessary under some mild assumptions and thus give a new characterization of ugas and uas through an equivalence relation the proposed detectability condition can also be verified in terms of usual pe condition to validate the proposed results the obtained stability criteria are applied to a class of time varying passive systems and to revisit a tracking control problem of nonholonomic chained systems for the latter under certain persistency of excitation conditions the k exponential stability is achieved based on our approach

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

hybrid output feedback stabilization for lti systems with single output this note presents a hybrid control scheme for a class of continuous time lti systems that cannot be stabilized by a single static output feedback sof controller the main idea here is to design multiple sof gains and proper logic rules that orchestrate switching among these gains so as to achieve the global stability one challenge however is that the switching logic should be in the output feedback form as well this may seriously restrict the possible choices of switching surfaces especially when the output is just a scalar to overcome this difficulty a multirate sampling control scheme is proposed under this framework a hybrid output feedback stabilizing controller is designed and sufficient controller synthesis conditions are proposed as linear matrix inequalities based on multiple lyapunov function theorems the note concludes with a discussion on possible extensions and future research topics

multirate robust digital control for fuzzy systems with periodic lyapunov function sampled data control which is capable of stabilizing general nonlinear systems is of great current interest in this paper the takagi sugeno ts fuzzy model is used to represent the nonlinear plant the paper is primarily concerned with designing digital controllers for the ts fuzzy continuous time model to stabilize the closed loop system in the problem formulation we only assume that the sampled values at a sampling rate of 1 t sub s are available for control within the sampling intervals the fuzzy controller uses the sampled data at the sampling instants to fire a fuzzy rule and generate a digital control action series this digital control action is then fed into the nonlinear system through a zero order holder in this paper two kinds of digital controllers are designed multirate and single rate digital controllers within a sampling interval the single rate controller is static while the multirate controller is periodically time varying i e the control action is switched at a small switching period t clearly for the single rate case this switching period t is equal to the sampling period t sub s this paper presents a design procedure for the multirate fuzzy controller with the single rate control as a special case the results are formulated as linear matrix inequalities numerical example shows the effectiveness of the proposed design procedures

recurrence and lasalle invariance principle abstract in this paper we consider three different notions of recurrence chain recurrence strong chain recurrence and generalized recurrence where the generalized recurrence is introduced by auslander 1964 and the strong chain recurrence is derived from the idea of a strong chain defined by easton 1978 we prove that for a quasi gradient flow in a compact metric space these three recurrences are equivalent finally we establish an invariance principle i e the limit set of a precompact orbit is contained in the generalized recurrent component of zero derivative set of a lyapunov function

a dual rate digital compensator for zero assignment abstract this paper considers design of a simple dual rate digital compensator drdc for assignment of system zeros the drdc comprises a linear time invariant system with a dual rate sampling scheme it is shown that zeros of a discrete system can be arbitrarilassigned by drdc corresponding to the block sampling period and that drdc is applicable to non minimum phase plants a design procedure and an example are given

residually finite dimensional operator algebras abstract we study non selfadjoint operator algebras that can be entirely understood via their finite dimensional representations in contrast with the elementary matricial description of finite dimensional c algebras in the non selfadjoint setting we show that an additional level of flexibility must be allowed motivated by this peculiarity we consider a natural non selfadjoint notion of residual finite dimensionality we identify sufficient conditions for the tensor algebra of a c correspondence to enjoy this property to clarify the connection with the usual self adjoint notion we investigate the residual finite dimensionality of the minimal and maximal c covers associated to an operator algebra

a projective c algebra related to k theory the c algebra qc is the smallest of the c algebras qa introduced by cuntz j cuntz a new look at kk theory k theory 1 1 1987 31 51 in the context of kk theory an important property of qc is the natural isomorphism k0 a lim qc mn a our main result concerns the exponential boundary map from k0 of a quotient b to k1 of an ideal i we show if a k0 element is realized in hom qc b then its boundary is realized as a unitary in i the picture we obtain of the exponential map is based on a projective c algebra p that is universal for a set relations slightly weaker than the relations that define qc a new shorter proof of the semiprojectivity of qc is described smoothing questions related the relations for qc are addressed

invariance like results for nonautonomous switched systems this paper generalizes the lasalle yoshizawa theorem to switched nonsmooth systems the filippov and krasovskii regularizations of a switched system are shown to be contained within the convex hull of the filippov and krasovskii regularizations of the subsystems respectively a common candidate lyapunov function that has a negative semidefinite generalized time derivative along the trajectories of the subsystems is shown to be sufficient to establish lasalle yoshizawa like results for the switched system of independent interest are the results on approximate continuity and filippov regularization of set valued maps reduction of differential inclusions using lipschitz continuous regular functions and comparative remarks on different generalizations of the time derivative along the trajectories of a nonsmooth system

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

extensions of weak invariance principle for nonlinear switched systems with time invariant and time varying subsystems abstract this paper addresses the stability problem for nonlinear switched systems with both time invariant and time varying subsystems given that lyapunov like functions are difficult to construct for nonlinear switched systems generalized invariance principles are established based on observer functions for nonlinear switched systems where the subsystems share lyapunov like functions the generalized invariance principles can be specialized to lyapunov based invariance principles where accurate convergent region can be obtained in addition to the above efforts the definitions of p limit system and limit system set are presented under which the proposed invariance principles are extended to nonlinear switched systems with time varying subsystems illustrative examples show the effectiveness of the theoretical results

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

brief paper a state space gpc with extensions to multirate control a state space formulation for generalized predictive control gpc is presented unlike other state space formulations we derive both the state feedback controller and state estimator gains using a least squares framework the present formulation provides a set of consistent design choices for both the controller and the state estimator design it also encapsulates both single rate and multirate controllers in the same algorithm it is argued that such a design approach can be advantageous especially when the control algorithm is required to tolerate sensor failure the generality of the design method is illustrated by synthesizing two well known multirate control algorithms a link with the generalized sampled data hold function is also established

strong stabilization with infinite multivariable gain margin through linear periodic control the problem of the strong stabilization with infinite gain margin with the additional requirement of a prescribed rate of convergence of the free responses is addressed for linear time invariant discrete time multivariable plants in the case when unknown different scalar gains act either on the inputs or on the outputs necessary and sufficient conditions for the solvability of the problem by means of a stable linear periodic discrete time output feedback dynamic controller are derived algorithmic procedures are given for designing the proposed periodic controllers