efficient iterative techniques for soft decision decoding of reed solomon codes two new iterative soft decision decoding methods for reed solomon rs codes are proposed these methods are based on bit level belief propagation bp decoding in order to make bp decoding effective for rs codes we use an extended binary parity check matrix with a lower density and reduced number of 4 cycles compared to the original binary parity check matrix of the code in the first proposed method we take advantage of the cyclic structure of rs codes based on this property we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix for each shifted version of received symbols the distribution of reliability values will change and deterministic errors can be avoided this method results in considerable performance improvement of rs codes compared to hard decision decoding the performance is also superior to some popular soft decision decoding methods the second method is based on information correction in bp decoding it means that we determine least reliable bits and by changing their channel information the convergence of the decoder is improved compared to the first method this method needs less bp iterations less complexity but its performance is not as good

continuous selections of trajectories of hybrid systems we present results on existence of continuous selections of trajectories of hybrid systems evolving according to lipschitz nonlinear inclusions first we utilize the skorohod metric to define both a family of pseudo metrics and a metric on the set of trajectories accepted by the hybrid automaton we show that under a non zeno condition the latter metric is complete second the existence of continuous selections with respect to the family of pseudo metrics is proved under a relatively mild assumption of transversality

robust stability of hybrid limit cycles with multiple jumps in hybrid dynamical systems for a broad class of hybrid dynamical systems we establish results for robust asymptotic stability of hybrid limit cycles with multiple jumps per period hybrid systems are given in terms of differential and difference equations with set constraints hybrid limit cycles are given by compact sets defined by periodic solutions that flow and jump under mild assumptions we show that asymptotic stability of such hybrid limit cycles is not only equivalent to asymptotic stability of a fixed point of the associated poincare map but also robust to perturbations specifically robustness to generic perturbations which capture state noise and unmodeled dynamics and to inflations of the flow and jump sets are established in terms of mathcal k mathcal l bounds a two gene network with binary hysteresis is presented to illustrate the notions and results throughout the paper

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

robust trajectory tracking for a class of hybrid systems an internal model principle approach this paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events switching systems parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes to deal with the hybrid nature of the system and the possible discontinuities of its solutions at switching times a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed the innovative design of the discrete time dynamics of the compensator guarantees the robust existence of a steady state response giving zero tracking error in the controlled output and local convergence to it

on the convergence of linear switched systems this paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems we provide a collection of results that use weak dwell time dwell time strong dwell time permanent and persistent activation hypothesis the obtained results are shown to be tight by counterexample finally we apply our result to the three cell converter

relaxed persistent flow jump conditions for uniform global asymptotic stability for hybrid systems sufficient conditions are derived for the uniform global asymptotic stability of a given closed set these conditions are written in terms of a lyapunov function candidate and assume a semiglobal practical persistent flow resp persistent jump property of the solutions to the hybrid system the use of the new conditions is illustrated via the stability analysis of a physically inspired example and of an event triggered control algorithm

non binary decoder diversity for dense or locally dense parity check codes in this paper a new and promising framework called non binary decoder diversity is presented based on the observation that different non binary tanner graphs of the same binary code decoded with a non binary belief propagation decoder can have distinct convergence behaviors and fixed points the goal of this work is to propose a decoder with linear complexity in the blocklength and with performance close to maximum likelihood decoding this framework is especially interesting for binary codes which are dense or locally dense and for which the usual binary iterative decoders perform far from the optimum curves by using the diversity brought by decoding distinct tanner graphs of the same code the proposed technique has very good decoding performance for three very different test cases which are known to be complex decoding problems i near maximum likelihood decoding mld of bch codes on the bpsk awgn channel ii performance results which outperform bounded distance decoding of bch codes over a binary symmetric channel bsc and finally iii decoding performance better than the bcjr based turbo decoder for parallel duo binary turbo codes

robust stabilization of chained systems via hybrid control the problem of global robust exponential stabilization of nonholonomic chained systems is addressed and solved by means of a hybrid state feedback control law it is shown that the control law yields global exponential stability and global robustness against a class of small measurement errors actuator noises and exogenous disturbances

a common framework for complete and incomplete attitude synchronization in networks with switching topology in this paper we study attitude synchronization for elements in the unit sphere in mathbb r scriptscriptstyle scriptscriptstyle 3 and for elements in the three dimensional 3 d rotation group for a network with switching topology the agents angular velocities are assumed to be the control inputs and a switching control law for each agent is devised that guarantees synchronization provided that all elements are initially contained in a region which we identify later in the paper the control law is decentralized and it does not require a common orientation frame among all agents we refer to synchronization of unit vectors in mathbb r scriptscriptstyle 3 as incomplete synchronization and of 3 d rotation matrices as complete synchronization our main contribution lies in showing that these two problems can be analyzed under a common framework where all agents dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension

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

output to state stability for hybrid systems output to state stability oss is a dual notion of input to state stability for dynamical systems this paper presents lyapunov and asymptotic characterizations of oss for hybrid dynamical systems emphasizing that a globally detectable i e nonuniformly oss hybrid system admits a smooth oss lyapunov function

basic properties and characterizations of incremental stability prioritizing flow time for a class of hybrid systems abstract this paper introduces incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints the specific class of hybrid systems considered are those that do not have consecutive jumps nor zeno behavior the notion of incremental asymptotic stability is used to describe the behavior of the distance between every pair of solutions to the system having stable behavior incremental stability and approaching zero asymptotically incremental attractivity a version of this notion that is uniform in hybrid time with respect to initial conditions is also introduced these notions prioritize flow time and are illustrated in examples basic properties of the class of systems are considered and those implied by the new notions are revealed an equivalence characterization of the uniform notion is provided in terms of a k l function moreover sufficient and necessary conditions under which asymptotic stability implies the new incremental notions are provided we consider the case when the original hybrid system has an asymptotically stable compact set and also the case when an auxiliary hybrid system which has twice the dimension of the original system has a diagonal like set asymptotically stable

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

iterative decoding of one step majority logic deductible codes based on belief propagation previously the belief propagation bp algorithm has received a lot of attention in the coding community mostly due to its near optimum decoding for low density parity check ldpc codes and its connection to turbo decoding in this paper we investigate the performance achieved by the bp algorithm for decoding one step majority logic decodable osmld codes the bp algorithm is expressed in terms of likelihood ratios rather than probabilities as conventionally presented the proposed algorithm fits better the decoding of osmld codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding ldpc codes although it has been believed that osmld codes are far inferior to ldpc codes we show that for medium code lengths say between 200 1000 bits the bp decoding of osmld codes can significantly outperform bp decoding of their equivalent ldpc codes the reasons for this behavior are elaborated

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

efficient linear programming decoding of hdpc codes we propose several improvements for linear programming lp decoding algorithms for high density parity check hdpc codes first we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts from redundant parity checks second we propose an efficient mixed integer decoder utilizing the branch and bound method we further enhance the proposed decoders by removing inactive constraints and by adapting the parity check matrix prior to decoding according to the channel observations based on simulation results the proposed decoders achieve near ml performance with reasonable complexity

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

input output to state stability this work explores lyapunov characterizations of the input output to state stability ioss property for nonlinear systems the notion of ioss is a natural generalization of the standard zero detectability property used in the linear case the main contribution of this work is to establish a complete equivalence between the ioss property and the existence of a certain type of smooth lyapunov function as corollaries one shows the existence of norm estimators and obtains characterizations of nonlinear detectability in terms of relative stability and of finite energy estimates

differential automata and their discrete simulators on presente la notion d automate differentiel pour la formulation d une classe de problemes aux valeurs initiales sur des champs vectoriels hysteretiques

analyzing the stability of switched systems using common zeroing output systems this paper introduces the notion of common zeroing output systems czos to analyze the stability of switched systems the concept of czos allows one to verify weak zero state detectability it characterizes a common behavior of any individual subsystem when the output signal for each subsystem is approaching zero heuristically speaking it removes the effect of switching behavior and thus enables one to analyze stability properties in systems with complex switching signals with the help of czos the krasovskii lasalle theorem can be extended to switched nonlinear time varying systems with both arbitrary switching and more general restricted switching cases for switched nonlinear time invariant systems the needed detectability condition is further simplified leading to several new stability results particularly when a switched linear time invariant system is considered it is possible to generate a recursive method which combines a krasovskii lasalle result and a nested matrosov result to find a czos if it exists the power of the proposed czos is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions

a general stability criterion for time varying systems using a modified detectability condition uniform asymptotic stability for general nonlinear time varying systems is investigated from the output to state viewpoint a unified criterion is proposed using a modified detectability condition and certain integral inequalities the criterion extends the krasovskii lasalle theorem to nonperiodic time varying systems an example taken from the tracking control of mobile robots is given to illustrate that much as the invariance principle of lasalle is used in studying the stability of time invariant systems our results can be used to study the stability of nonperiodic time varying systems by checking the modified detectability condition

computing automorphism groups of error correcting codes an algorithm is described for computing the automorphism group of an error correcting code the algorithm determines the order of the automorphism group and produces a set of monomial permutations which generate the group it has been implemented on a computer and has been used successfully on a great number of codes of moderate length

fast reconstruction methods for bandlimited functions from periodic nonuniform sampling a well known generalization of shannon s sampling theorem states that a bandlimited function can be reconstructed from its periodic nonuniformly spaced samples if the effective sampling rate is at least the nyquist rate analogous to shannon s sampling theorem this generalization requires that an infinite number of samples be available which however is never the case in practice most existing reconstruction methods for periodic nonuniform sampling yield very low order often not even first order accuracy when only a finite number of samples is given in this paper we propose a fast numerically robust root exponential accurate reconstruction method the efficiency and accuracy of the algorithm is obtained by fully exploiting the sampling structure and utilizing localized fourier analysis we discuss applications in analog to digital conversion where nonuniform periodic sampling arises in various situations finally we demonstrate the performance of our algorithm by numerical examples

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

on the existence of control lyapunov functions and state feedback laws for hybrid systems for a class of hybrid systems given in terms of constrained differential and difference equations inclusions we study the existence of control lyapunov functions when compact sets are asymptotically stable as well as the stabilizability properties guaranteed when control lyapunov functions exist an existence result asserting that asymptotic stabilizability of a compact set implies the existence of a smooth control lyapunov function is established when control lyapunov functions are available conditions guaranteeing the existence of stabilizing continuous state feedback control laws are provided

enhancing iterative decoding of cyclic ldpc codes using their automorphism groups for cyclic ldpc codes we propose to use their automorphism groups to improve the iterative decoding performance the basic idea is to construct nonequivalent parity check matrices via column permutations three types of iterative decoders are devised to take advantage of the code s automorphism group in this paper we focus on cyclic ldpc codes defined by a circulant parity check matrix and consider two known subgroups of the automorphism group of a cyclic code for the large class of idempotent based cyclic ldpc codes in the literature we show that the two subgroups only provide equivalent parity check matrices and thus cannot be harnessed for iterative decoding towards exploiting the automorphism group of a code we propose a new class of cyclic ldpc codes based on pseudo cyclic mds codes with two information symbols for which nonequivalent parity check matrices are obtained simulation results show that for our constructed codes of short lengths the automorphism group can significantly enhance the iterative decoding performance

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

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

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

o n sup 2 log sub 2 n filtered backprojection reconstruction algorithm for tomography we present a new fast reconstruction algorithm for parallel beam tomography the new algorithm is an accelerated version of the standard filtered backprojection fbp reconstruction and uses a hierarchical decomposition of the backprojection operation to reduce the computational cost from o n sup 3 to o n sup 2 log sub 2 n we discuss the choice of the various parameters that affect the behavior of the algorithm and present numerical studies that demonstrate the cost versus distortion tradeoff comparisons with fourier reconstruction algorithms and a multilevel inversion algorithm by brandt et al both of which also have o n sup 2 log sub 2 n cost suggest that the proposed hierarchical scheme has a superior cost versus distortion performance it offers rms reconstruction errors comparable to the fbp with considerable speedup for an example with a 512 spl times 512 pixel image and 1024 views the speedup achieved with a particular implementation is over 40 fold with reconstructions visually indistinguishable from the fbp

characterizations of input to state stability for hybrid systems abstract we study input to state stability iss for a broad class of hybrid systems which are combinations of a differential equation on a constraint set and a difference equation on another constraint set for this class of hybrid systems we establish the equivalence of iss nonuniform iss and the existence of a smooth iss lyapunov function by additionally assuming that the right hand side of the differential equation has a convex property with respect to inputs moreover we demonstrate by examples that the equivalence may fail when such a convexity assumption is removed

asymptotic stability in hybrid systems via nested matrosov functions a theorem on nested matrosov functions is extended to time varying hybrid systems it provides sufficient conditions for uniform global asymptotic stability of a compact set an application to parameter identification with state resets is made and illustrated on an example

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

asymptotic characterizations of input output to state stability for discrete time systems abstract we establish the equivalence between global detectability and output to state stability for difference inclusions with outputs and we present equivalent asymptotic characterizations of input output to state stability for discrete time nonlinear systems these new stability characterizations for discrete time systems parallel what have been developed for continuous time systems in angeli et al uniform global asymptotic stability of differential inclusions j dynamical control systems 10 2004 391 412 and angeli et al seperation principles for input output and integral input to state stability siam j control optim 43 2004 256 276

on the stability and stabilization of quaternion equilibria of rigid bodies we study attitude control of rigid bodies on quaternion coordinates under three mathematically different perspectives depending on how the system dynamics are assumed to evolve in the first case we suppose that one equilibrium point is chosen a priori and a continuous controller is used under the assumption that the rigid body always spins in the same direction in the second case we relax the assumption that the sense of rotation is constant finally a third scenario is considered in which hybrid switching control is used to choose the direction in which to spin that is both equilibria are continuously considered with regard to less energy consumption it is showed that each of three scenarios must be treated in a different theoretical setting a comparative study in simulations is also provided

quaternion based hybrid feedback for robust global attitude synchronization we apply recent results on robust global asymptotic stabilization of the attitude of a single rigid body to the problem of globally synchronizing the attitude of a network of rigid bodies using a decentralized strategy the proposed hybrid feedback scheme relies on the communication of a binary logic variable between each pair of neighboring rigid bodies that determines the orientation of a torque component acting to reduce their relative error through a hysteretic switch of this logic variable the hybrid feedback achieves global synchronization under the assumption that the network is connected and acyclic the hysteresis eliminates chattering while preventing the unwinding phenomenon apparent in some quaternion based attitude control schemes the results are exercised in a numerical example

recovering band limited signals under noise we consider the problem of recovering a band limited signal f t from noisy data yk f k spl tau spl gt epsilon sub k where spl tau is the sampling rate starting from the truncated whittaker shannon cardinal expansion with or without sampling windows both cases yield inconsistent estimates of f t we propose estimators that are convergent to f t in the pointwise and uniform sense the basic idea is to cut down high frequencies in the data and to use suitable oversampling spl tau spl les spl pi spl omega spl omega being the bandwidth maximum frequency of f t the simplest estimator we propose is given by f spl circ sub n t spl tau spl sigma t k spl tau spl les n spl tau yksin spl omega t k spl tau spl pi t k spl tau t spl les n spl tau generalizations of f spl circ sub n including sampling windows are also examined the main aim is to examine the mean squared error mse properties of such estimators in order to determine the optimal choice of the sampling rate spl tau yielding the fastest possible rate of convergence the best rate for the mse we obtain is o in n n

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

on the representation of switched systems with inputs by perturbed control systems this paper provides representations of switched systems described by controlled differential inclusions in terms of perturbed control systems the control systems have dynamics given by differential equations and their inputs consist of the original controls together with disturbances that evolve in compact sets their sets of maximal trajectories contain as a dense subset the set of maximal trajectories of the original system several applications to control theory dealing with properties of stability with respect to inputs and of detectability are derived as a consequence of the representation theorem 2004 elsevier ltd all rights reserved

lyapunov based hybrid loops for stability and performance of continuous time control systems we construct hybrid loops that augment continuous time control systems we consider a continuous time nonlinear plant in feedback with a possibly non stabilizing given nonlinear dynamic continuous time state feedback controller the arising hybrid closed loops are guaranteed to follow the underlying continuous time closed loop dynamics when flowing and to jump in suitable regions of the closed loop state space to guarantee that a positive definite function v of the closed loop state and or a positive definite function v p of the plant only state is non increasing along the hybrid trajectories sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions for the linear case we illustrate specific choices of the functions v and v p which allow for the reduction of the overshoot of a scalar output the proposed approaches are illustrated on linear and nonlinear examples

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

efficient evaluation of oversampled functions abstract it has been known since long that an oversampled function can be represented by a generalized sinc series which converges much faster than the usual one we show that the speed of convergence is exponential and give numerical approximations to the kernel function involved in the generalized series the practical consequence is that a bandlimited function which is oversampled can be evaluated at any point with accuracy o l e l using o l operations

closed curve solutions and limit cycles in a class of second order switched nonlinear systems this paper studies the problem of finding the initial states for which the solution of a class of switched systems consisting of unstable second order nonlinear subsystems is convergent a method is described and applied to establish the regions in the plane where it is possible to define a switching law such that the solution of a class of switched nonlinear systems converges to the origin we prove that under certain conditions these regions are delimited by closed curve solutions of the switched system furthermore a sufficient condition for the closed curve solution to be a limit cycle is presented finally a numerical example is included in order to illustrate the results

near optimum universal belief propagation based decoding of low density parity check codes in this paper we propose a belief propagation bp based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified bp based algorithm the normalization factors can be obtained not only by simulation but also importantly theoretically this new bp based algorithm is much simpler to implement than bp decoding as it requires only additions of the normalized received values and is universal i e the decoding is independent of the channel characteristics some simulation results are given which show this new decoding approach can achieve an error performance very close to that of bp on the additive white gaussian noise channel especially for low density parity check ldpc codes whose check sums have large weights the principle of normalization can also be used to improve the performance of the max log map algorithm in turbo decoding and some coding gain can be achieved if the code length is long enough

smooth lyapunov functions for hybrid systems part i existence is equivalent to robustness hybrid systems are dynamical systems where the state is allowed to either evolve continuously flow on certain subsets of the state space or evolve discontinuously jump from other subsets of the state space for a broad class of such systems characterized by mild regularity conditions on the data we establish the equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth lyapunov function this result unifies and generalizes previous results for differential and difference inclusions with outer semicontinuous and locally bounded right hand sides furthermore we give a description of forward completeness of a hybrid system in terms of a smooth lyapunov like function

construction of synergistic potential functions on so 3 with application to velocity free hybrid attitude stabilization we propose a systematic and comprehensive procedure for the construction of synergistic potential functions which are instrumental in hybrid control design on text so 3 a new map via angular warping on text so 3 is introduced to generate a central family of potential functions allowing an explicit determination of the critical points and the synergistic gap some optimization results on the synergistic gap are also provided the proposed synergistic potential functions are used for the design of a global velocity free hybrid attitude stabilization scheme relying solely on inertial vector measurements

random edge local complementation with applications to iterative decoding of high density parity check codes we describe the application of edge local complementation elc to a tanner graph associated with a binary linear code c various properties of elc are described mainly the special case of isomorphic elc operations and the relationship to the automorphism group of the code aut c and the generalization of elc to weight bounding elc wb elc operations under which the number of edges remains upper bounded elc generates all systematic parity check matrices the orbit of the code so wb elc facilitates a restriction to low weight matrices of this orbit we propose using elc and wb elc as a source of diversity to improve iterative soft input soft output decoding of high density parity check hdpc codes with the sum product algorithm spa a motivation of elc enhanced spa decoding is locality that diversity is achieved by local graph action and is well suited to the local actions that constitute the spa and allows for parallel software implementation simulation data on the error rate performance of the proposed spa elc and spa wbelc iterative decoding algorithms is shown for several hdpc codes a gain is reported over spa decoding and over a recently proposed algorithm to decode hdpc codes using permutations from aut c elc enhanced decoding extends the scope of iterative decoding to codes with trivial aut c

input output to state stability for discrete time systems this paper presents lyapunov characterizations of uniform output to state stability and uniform input output to state stability ioss with respect to disturbances for discrete time dt nonlinear systems we show the equivalence of the following three properties for dt systems uniform ioss existence of a smooth lyapunov function for uniform ioss and existence of a state norm estimator this equivalence result is a dt counterpart of krichman et al 2001 input output to state stability siam journal on control and optimization 39 1874 1928 theorem 2 4 and a generalization of jiang and wang 2002 a converse lyapunov theorem for discrete time systems with disturbances systems and control letters 45 49 58 theorem 1 1 and jiand and wang 2001 input to state stability for discrete time nonlinear systems automatica 37 857 869 theorem 1 email protected 4

hybrid output feedback for attitude tracking on mathbb so 3 we present two solutions to the global exponential attitude tacking control problem using only attitude information on mathbb so 3 the first approach is based on a combined hybrid observer hybrid controller structure we derive a hybrid angular velocity observer for rigid body systems designed directly on mathbb so 3 times mathbb r 3 guaranteeing global exponential stability of the zero estimation error thereafter we propose an observer based attitude tracking control scheme guaranteeing global exponential stability the second approach consists of introducing an auxiliary dynamical system that generates the necessary damping in the absence of the velocity we prove that the proposed auxiliary system based hybrid controller guarantees global exponential stability as well

an algorithm for counting short cycles in bipartite graphs let g u spl cup w e be a bipartite graph with disjoint vertex sets u and w edge set e and girth g this correspondence presents an algorithm for counting the number of cycles of length g g 2 and g 4 incident upon every vertex in u spl cup w the proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as o gn sup 3 where n max u w

smooth lyapunov functions for hybrid systems part ii pre asymptotically stable compact sets it is shown that pre asymptotic stability which generalizes asymptotic stability of a compact set for a hybrid system satisfying mild regularity assumptions is equivalent to the existence of a smooth lyapunov function this result is achieved with the intermediate result that asymptotic stability of a compact set for a hybrid system is generically robust to small state dependent perturbations as a special case we state a converse lyapunov theorem for systems with logic variables and use this result to establish input to state stabilization using hybrid feedback control the converse lyapunov theorems are also used to establish semiglobal practical robustness to slowly varying weakly jumping parameters to temporal regularization to the insertion of jumps according to an ldquoaverage dwell timerdquo rule and to the insertion of flow according to a ldquoreverse average dwell timerdquo rule

which codes have 4 cycle free tanner graphs let c be an n k d binary linear code with rate r k n and dual c perp in this correspondence it is shown that c can be represented by a 4 cycle free tanner graph only if pdperples lfloorradicnp p 1 n2 4 n 2 rfloorwhere p n k and dperp is the minimum distance of c perp by applying this result it is shown that 4 cycle free tanner graphs do not exist for many classical binary linear block codes

stability and performance of siso control systems with first order reset elements we consider set point regulation and l2 robust stability properties of a class of reset control systems consisting of a minimum phase relative degree one linear siso plant controlled by a novel first order reset element fore these results rely on necessary and sufficient conditions for exponential and l2 finite gain stability of a class of planar reset systems consisting of a scalar linear plant controlled by the novel fore we show that the l2 gain of the planar reset system decreases to zero as the pole and or the gain of the fore are increased to infinity a number of stability results including lyapunov conditions for lp and exponential stability for a larger class of reset and hybrid systems are presented and used to prove our main results

global stabilization of spherical orientation by synergistic hybrid feedback with application to reduced attitude tracking for rigid bodies in this paper we propose a hybrid feedback based on a synergistic potential function that achieves global asymptotic stabilization of a desired orientation on the n sphere with a nominal robustness to measurement disturbances a task that is not possible by classical feedback be it smooth nonsmooth periodic or any combination thereof due to the topological structure of the sphere we extend this basic result to a tracking controller for the reduced attitude or pointing direction of a rigid body and provide a method to remove jumps in the controlled torque by backstepping the proposed hybrid feedback is compared with a similar smooth feedback in simulation where it is illustrated that the hybrid feedback overcomes performance limitations inherent to the smooth feedback we provide two examples of a synergistic potential function one defined on a general sphere and the other on the unit circle

impulse differential inclusions a viability approach to hybrid systems impulse differential inclusions are introduced as a framework for modeling hybrid phenomena connections to standard problems in the area of hybrid systems are discussed conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion for sets that violate these conditions methods are developed for approximating their viability and invariance kernels that is the largest subset that is viable or invariant under the action of the impulse differential inclusion the results are demonstrated on examples

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

separation principles for input output and integral input to state stability we present new characterizations of input output to state stability this is a notion of detectability formulated in the iss input to state stability framework equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and output signals these results provide a set of separation principles for input output to state stability characterizations of the property as conjunctions of weaker stability notions when applied to the notion of integral iss these characterizations yield analogous results

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

recurrence principles and their application to stability theory for a class of stochastic hybrid systems in this paper we establish results similar in nature to the invariance principle for a class of stochastic hybrid systems modeled by set valued mappings in particular we characterize the set to which bounded random solutions converge in terms of a new concept called weak total recurrence a refinement of the result under the existence of a non increasing on average lyapunov like function is also established a comparison between weak total recurrence and the frequently studied invariance concepts are presented finally application of the main results to establish weak sufficient conditions for certifying stochastic stability properties like uniform global asymptotic stability in probability for compact sets and uniform global recurrence for open bounded sets are discussed

on singular perturbations due to fast actuators in hybrid control systems a stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators if a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted or equivalently are infinitely fast then the same compact set is semiglobally practically asymptotically stable in the finite speed of the actuator dynamics this result which generalizes classical results for differential equations justifies using a simplified plant model that ignores fast but continuous actuator dynamics even when using a hybrid feedback control algorithm

fourier reconstruction in tomography we give an asymptotic error analysis of the fourier reconstruction algorithm and show that a modified algorithm is asymptotically optimal we compare the modified algorithm with standard fourier and with filtered backprojection using a mathematically generated chest phantom

on pseudocodewords and decision regions of linear programming decoding of hdpc codes in this paper we explore the decision regions of linear programming lp decoding we compare the decision regions of an lp decoder a belief propagation bp decoder and the optimal maximum likelihood ml decoder we study the effect of minimal weight pseudocodewords on lp decoding we present global optimization as a method for finding the minimal pseudoweight of a given code as well as the number of minimal weight generators we present a complete pseudoweight distribution for the 24 12 8 extended golay code and provide justifications of why the pseudoweight distribution alone cannot be used for obtaining a tight upper bound on the error probability

on restoring band limited signals the problem of reconstruction of band limited signals from discrete and noisy data is studied the reconstruction schemes employing cardinal expansions are proposed and their asymptotical properties are examined in particular the conditions for the convergence of the mean integrated squared error are found and the rate of convergence is evaluated the main difference between the proposed reconstruction scheme and the classical one is in treating the sampling rate and the reconstruction rate differently this distinction is necessary to ensure consistency of the reconstruction scheme in the presence of noise

hybrid feedback control and robust stabilization of nonlinear systems in this paper we show for any nonlinear system that is asymptotically controllable to a compact set that a logic based hybrid feedback can achieve asymptotic stabilization that is robust to small measurement noise actuator error and external disturbance the construction of such a feedback hinges upon recasting a stabilizing patchy feedback in a hybrid framework by making it dynamic with a discrete state while insisting on semicontinuity and closedness properties of the hybrid feedback and of the resulting closed loop hybrid system the robustness of stability is then shown as a generic property of hybrid systems having the said regularity properties auxiliary results give uniformity of convergence and of overshoots for hybrid systems and give a characterization of asymptotic stability of compact sets

input output to state stability tools for hybrid systems and their interconnections we present results for the analysis of input output properties of a general class of hybrid systems given by a flow set a flow map a jump set a jump map and an output map for this class of systems the notion of input output to state stability is introduced in the first part of the technical note under mild assumptions on the functions and sets defining a hybrid system sufficient conditions for this notion in terms of lyapunov functions are derived equivalences between lyapunov functions for input output to state stability for asymptotic and exponential decay rates are established the sufficient conditions and equivalences are linked to the existence of norm observers for hybrid systems these results are used in the second part of the technical note to study interconnections of hybrid systems an interconnection result in terms of a lyapunov based small gain theorem is also presented examples illustrate the results

a nonsmooth hybrid invariance principle applied to robust event triggered design we first propose a nonsmooth hybrid invariance principle with relaxed conditions stemming from the fact that flowing solutions evolve only in the tangent cone and complete jumping solutions cannot jump outside the jump and flow sets we then show an application consisting in the design of event triggered rules to stabilize a class of uncertain linear control systems the event triggering rule depends only on local information that is it uses only the output signals available to the controller the approach proposed combines hybrid and sampled data tools the proposed design conditions are formulated in terms of linear matrix inequalities lmis ensuring global robust asymptotic stability of the closed loop system a tunable parameter is also available to guarantee an adjustable dwell time property of the solutions the effectiveness of the approach is evaluated through an example borrowed from the literature

improved random redundant iterative hdpc decoding an iterative algorithm for soft input soft output siso decoding of classical algebraic cyclic block codes is presented below inspired by other approaches for high performance belief propagation bp decoding this algorithm requires up to 10 times less computational complexity than other methods that achieve similar performance by utilizing multiple bp decoders and using random permutation taken from the permutation group of the code this algorithm reaches near maximum likelihood performance a computational complexity comparison of the proposed algorithm versus other methods is presented as well this includes complexity versus performance analysis allowing one to trade between the former and the latter according to ones needs

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

transactions letters random redundant iterative soft in soft out decoding this letter presents an iterative soft in soft out siso decoding algorithm based on redundant tanner graphs that is applicable to arbitrary linear block codes the proposed algorithm utilizes the permutation group of a code in order to efficiently and randomly generate redundant parity checks