design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

dissipativity based filtering for fuzzy switched systems with stochastic perturbation in this technical note the problem of the dissipativity based filtering problem is considered for a class of t s fuzzy switched systems with stochastic perturbation firstly a sufficient condition of strict dissipativity performance is given to guarantee the mean square exponential stability for the concerned t s fuzzy switched system then our attention is focused on the design of a filter to the t s fuzzy switched system with brownian motion by combining the average dwell time technique with the piecewise lyapunov function technique the desired fuzzy filters are designed that guarantee the filter error dynamic system to be mean square exponential stable with a strictly dissipative performance and the corresponding solvability condition for the fuzzy filter is also presented based on the linearization procedure approach finally an example is provided to illustrate the effectiveness of the proposed dissipativity based filter technique

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

matrix sum of squares relaxations for robust semi definite programs we consider robust semi definite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description on the basis of matrix sum of squares decompositions we suggest a systematic procedure to construct a family of linear matrix inequality relaxations for computing upper bounds on the optimal value of the corresponding robust counterpart with a novel matrix version of putinar s sum of squares representation for positive polynomials on compact semi algebraic sets we prove asymptotic exactness of the relaxation family under a suitable constraint qualification if the uncertainty region is a compact polytope we provide a new duality proof for the validity of putinar s constraint qualification with an a priori degree bound on the polynomial certificates finally we point out the consequences of our results for constructing relaxations based on the so called full block s procedure which allows to apply recently developed tests in order to computationally verify the exactness of possibly small sized relaxations

convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

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

on stability and h control of switched systems with random switching signals abstract in this paper the stability analysis and h control problems for a class of continuous time switched systems with a random switching signal are addressed the dwell time of the switched systems is characterized with a fixed part and a random part a new stability criterion which is equivalent to a necessary and sufficient condition developed previously is established first and then it is reformulated in terms of linear matrix inequalities based on the stability analysis result l 2 gain performance analysis and h control problems are studied several numerical examples are given to illustrate the effectiveness of our results

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

stability and stabilization of periodic piecewise linear systems a matrix polynomial approach abstract in this paper new conditions of stability and stabilization are proposed for periodic piecewise linear systems a continuous lyapunov function is constructed with a time dependent homogeneous lyapunov matrix polynomial the exponential stability problem is studied first using square matricial representation and sum of squares form of homogeneous matrix polynomial constraints on the exponential order of each subsystem used in previous work are relaxed state feedback controllers with time varying polynomial controller gain are designed to stabilize an unstable periodic piecewise system the proposed stabilizing controller can be solved directly and effectively which is applicable to more general situations than those previously covered numerical examples are given to illustrate the effectiveness of the proposed method

adaptive coded modulation for fading channels we apply coset codes to adaptive modulation in fading channels adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable therefore trellis and lattice codes designed for additive white gaussian noise awgn channels can be superimposed on adaptive modulation for fading channels with the same approximate coding gains we first describe the methodology for combining coset codes with a general class of adaptive modulation techniques we then apply this methodology to a spectrally efficient adaptive m ary quadrature amplitude modulation mqam to obtain trellis coded adaptive mqam we present analytical and simulation results for this design which show an effective coding gain of 3 db relative to uncoded adaptive mqam for a simple four state trellis code and an effective 3 6 db coding gain for an eight state trellis code more complex trellis codes are shown to achieve higher gains we also compare the performance of trellis coded adaptive mqam to that of coded modulation with built in time diversity and fixed rate modulation the adaptive method exhibits a power savings of up to 20 db

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

classification and characteristics of floquet factorisations in linear continuous time periodic systems this article has two purposes firstly the article is devoted to collecting basic facts about the floquet theorem and various floquet factorisation algorithms claimed for finite dimensional linear continuous time periodic fdlcp systems secondly the article presents a unified representation framework for various floquet factorisations in fdlcp systems while structural and analytic characteristics about them are examined as well more precisely the following aspects are considered i algorithms for floquet factorisations ii characteristics of floquet factors iii relationships and properties among floquet factorisations most results are reported for the first time while the others are generalised versions of existing ones

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

a product formula for spherical representations of a group of automorphisms of a homogeneous tree i let g aut t be the group of automorphisms of a homogeneous tree t and let be a lattice subgroup of g let be the tensor product of two spherical irreducible unitary representations of g we give an explicit decomposition of the restriction of to we also describe the spherical component of explicitly and this decomposition is interpreted as a multiplication formula for associated orthogonal polynomials

stability and l1 gain analysis of linear periodic piecewise positive systems this paper investigates the stability stabilization and l1 gain of linear periodic piecewise positive systems the monotonicity of linear periodic piecewise positive systems is first studied then a time varying co positive lyapunov function for periodic piecewise positive systems is employed and a sufficient condition for the asymptotic stability of the system is established based on the provided co positive lyapunov function and the sufficient stability condition a state feedback periodic piecewise controller to stabilize the system is formed and an upper bound of l1 gain of the system is given finally numerical examples are given to illustrate the theoretical results

nonconservative lifted convex conditions for stability of discrete time switched systems under minimum dwell time constraint in this note a novel conception called virtual clock which is defined by an artificial timer over a finite cycle is introduced for stability analysis of discrete time switched linear systems under minimum dwell time constraint two necessary and sufficient conditions associated with a virtual clock with a sufficient length are proposed to ensure the global uniform asymptotic stability of discrete time switched linear systems for the two nonconservative stability criteria the lifted version maintains the convexity in system matrices based on the lifted convex conditions the extensions to ell 2 gain computation and mathcal h infty control problems are presented in the sequel in particular a novel virtual clock dependent controller is designed which outperforms the traditional mode dependent and common gain controllers several numerical examples are provided to illustrate our theoretic results

uniform tube based stabilization of switched linear systems with mode dependent persistent dwell time in this note the stabilization problem for a class of discrete time switched linear systems with additive disturbances is investigated the considered switching signals are of mode dependent persistent dwell time mpdt property and the disturbances are assumed to be amplitude bounded by constructing a quasi time varying qtv lyapunov function a qtv stabilizing controller is designed for the nominal system such that the resulting closed loop system is globally uniformly asymptotically stable in the presence of bounded additive disturbances a mpdt robust positive invariant set is determined for the error system between the nominal system and disturbed system a concept of generalized robust positive invariant grpi set under admissible mpdt switching is further proposed for the error system it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the mpdt grpi set that can be regarded as the cross section of a uniform tube of the disturbed system a numerical example is provided to verify the theoretical findings

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

grassmannian packings from operator reed muller codes this paper introduces multidimensional generalizations of binary reed muller codes where the codewords are projection operators and the corresponding subspaces are widely separated with respect to the chordal distance on grassmannian space parameters of these grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for binary reed muller codes the subspaces are associated with projection operators determined by pauli matrices appearing in the theory of quantum error correction and this connection with quantum stabilizer codes may be of independent interest the grassmannian packings constructed here find application in noncoherent wireless communication with multiple antennas where separation with respect to the chordal distance on grassmannian space guarantees closeness to the channel capacity it is shown that the capacity of the noncoherent multiple input multiple output mimo channel at both low and moderate signal to noise ratio snr under the constraint that only isotropically distributed unitary matrices are used for information transmission is closely approximated by these packings

linear precoding gain for large mimo configurations with qam and reduced complexity in this paper the problem of designing a linear precoder for multiple input multiple output mimo systems in conjunction with quadrature amplitude modulation qam is addressed first a novel and efficient methodology to evaluate the input output mutual information for a general mimo system as well as its corresponding gradients is presented based on the gauss hermite quadrature rule then the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the mimo input output mutual information for qam systems with relatively moderate mimo channel sizes the proposed methodology is next applied in conjunction with the complexity reducing per group processing technique to both perfect channel state information csi at the transmitter as well as statistical csi statistical csi scenarios with large transmitting and receiving antenna sizes and for constellation size up to m 64 we show by the numerical results that the precoders developed offer significantly better performance than the configuration with no precoder as well as the maximum diversity precoder for qam with constellation sizes m 16 32 and 64 and for mimo channel size up to 100 times 100

l and l 2 semi global stabilisation of continuous time periodic linear systems with bounded controls this article is concerned with l and l 2 semi global stabilisation of continuous time periodic linear systems with bounded controls two problems namely l semi global stabilisation with controls having bounded magnitude and l 2 semi global stabilisation with controls having bounded energy are solved based on solutions to a class of periodic lyapunov differential equations pldes resulting from the problem of minimal energy control with guaranteed convergence rate under the assumption that the open loop system is asymptotically null controllable with constrained controls periodic feedback are established to solve the concerned problems the proposed plde based approaches possess the advantage that the resulting controllers are easy to implement since the designers need only to solve a linear differential equation a numerical example is worked out to illustrate the effectiveness of the proposed approach

group presentation p adic analytic groups and lattices in mathrm sl _2 mathbf c groups by using their pro p completions this method is based on the observation that if x r is a presentation of the finitely generated f g group f then x r considered as a presentation for a pro p group is actually a presentation for t the pro p completion of f first we prove a generalization of a theorem of golod and shafarevich cf h theorem let g be a p adic analytic pro p group different from zp the p adic integers if x r is a minimal presentation of g then 1x 2 iri 2

trees and discrete subgroups of lie groups over local fields let k be a locally compact field and g a simple at group g g k a discrete subgroup t of g is called a lattice if g f carries a finite g invariant measure it is a uniform or cocompact lattice if g t is compact and nonuniform otherwise when the jrf rank of g is greater than one margulis ma z proved that t is arithmetic establishing the conjecture of selberg and piatetskishapiro this remarkable work left open the case of rank one groups sli u contains continuous families of lattices the teichmuller spaces and in particular it contains nonarithmetic lattices by the mostow rigidity theorem cf ml sli r is essentially the only real simple lie group which allows this phenomenon some other real rank one groups are known to have nonarithmetic lattices gromov and piatetski shapiro gps showed that so n 1 have such lattices earlier it was shown by makarov and vinberg for small n mostow m2 constructed nonarithmetic lattices in su 2 1 and together with deligne dm also in su 3 1 for the other rank one real groups su n 1 n 4 sp n 1 and f4 the problem is still open a related problem is the congruence subgroup problem which asked given t arithmetic are all its finite index subgroups congruence subgroups serre si conjectured that t has the congruence subgroup property csp if and only if rank g 2 the affirmative part of this conjecture was proved to a large extent but mainly for nonuniform lattices see ri r2 for precise results and history less is known for arithmetic lattices in real rank one groups it is easy to prove that none of the arithmetic lattices in psl2 r so 2 1 has csp the same holds for psl2 c so 3 1 see si for the nonuniform case and li for the uniform case for so n 1 general n it is known only for some of the lattices millson mi similarly kazdhan ka showed that some lattices in su n 1 do not have csp again nothing is known for sp n 1 and which are of rank one but have kazdhan property t like groups of higher rank in this note we will describe results on the structure of lattices in rank one groups over locally compact nonarchimedean fields as well as some

lattices of minimal covolume in sl 2 a nonarchimedean analogue of siegel s theorem μ π 21 a classical result of siegel si asserts that if g sl2 r and u is its haar measure appropriately normalized then mintj u f g 7r 21 where r runs over all the discrete subgroups of g the minimum is obtained for the triangle group 2 3 7 which is a cocompact lattice in g see also gr for g sl2 c meyerhoff me has shown recently that among the nonuniform lattices in g that is discrete subgroups of finite covolume but not cocompact the minimum volume is obtained with f sl2 3 where 3 is the ring of integers of q v 3 and it is approximately 0 0863 but there are cocompact lattices with smaller covolumes and the minimum is not known see egm th in this paper we address the analogue question for locally compact nonarchimedean fields our main result is let f be a locally compact field of characteristic p 0 with residue field of order q pa hence f is isomorphic to fq i t the field of laurent formal power series in l t

stability stabilization and l 2 gain analysis of periodic piecewise linear systems in this paper the stability stabilization and l 2 gain problems are investigated for periodic piecewise linear systems in which not all subsystems are hurwitz first some sufficient and necessary conditions for the exponential stability are established by employing a discontinuous lyapunov function with time varying lyapunov matrix stabilization and l 2 gain conditions of periodic piecewise linear systems are proposed by allowing the corresponding lyapunov function to be possibly non monotonically decreasing over a period a state feedback periodic piecewise controller is developed to stabilize the system and the corresponding algorithm is proposed to compute the controller gain the l 2 gain criteria with continuous time varying lyapunov matrix and piecewise constant lyapunov matrices are studied as well numerical examples are given to show the validity of the proposed techniques

a converse lyapunov theorem for linear parameter varying and linear switching systems we study families of linear time varying systems where time variations have to satisfy restrictions on the dwell time that is on the minimum distance between discontinuities as well as on the derivative in between discontinuities such classes of systems may be formulated as linear flows on vector bundles the main objective of this paper is to construct parameter dependent lyapunov functions which characterize the exponential growth rate this is possible in the generic irreducible case as an application the gelfand formula is generalized to the class of systems studied here in other words the maximal exponential growth rate may be approximated by only considering the periodic systems in the family of time varying systems a perspective on the question of continuous dependence of the exponential growth rate on the data is given

finite time stability analysis and stabilization by bounded linear time varying feedback abstract this paper studies finite time stability analysis and finite time stabilization of linear systems by bounded linear time varying feedback on the one hand both local and global finite time stability of general nonlinear time varying systems is investigated by the comparison principle and the notion of finite time escaping functions some lyapunov like stability theorems are established on the other hand finite time and prescribed time stabilization of linear systems by bounded linear time varying feedback are revisited based on the proposed finite time stability theorems two classes of new time varying high gain functions are proposed to reduce the regulation time some connections of the proposed results to existing results on lyapunov inequality based finite time stability analysis and nonlinear feedback based finite time stabilization are revealed the effectiveness of the proposed methods is illustrated by a numerical example

stability and stabilization of continuous time switched linear systems this paper addresses two strategies for the stabilization of continuous time switched linear systems the first one is of open loop nature trajectory independent and is based on the determination of a minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function to be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition including chattering is expressed being nonconvex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

analysis of low density parity check codes based on exit functions we exploit extrinsic information transfer functions of single parity check and repetition codes over the binary input additive white gaussian noise biawgn channel derived by the authors for asymptotic performance analysis of belief propagation decoding of low density parity check codes the approach is based on a gaussian approximation ga of the density evolution algorithm using the mutual information measure we show that this method allows more accurate prediction of the decoding threshold in the biawgn channel than the earlier known ga methods

stability analysis of continuous time switched systems with a random switching signal this technical note is concerned with the stability analysis of continuous time switched systems with a random switching signal the switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part the stochastic stability of such switched systems is studied using a lyapunov approach a necessary and sufficient condition is established in terms of linear matrix inequalities the effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition

ldpc codes for flat rayleigh fading channels with channel side information in this paper we design capacity approaching low density parity check ldpc codes in the low signal to noise ratio snr regime for flat rayleigh fading channels with channel side information at transmitter and receiver we use the structure advocated by caire et al which uses a single codebook with dynamic power allocation the extrinsic information transfer exit function method is used to design the ldpc codes which approach the channel capacities we also study the exit function properties of various demappers

periodic lyapunov equation based approaches to the stabilization of continuous time periodic linear systems this note is concerned with stabilization of continuous time periodic linear cpl systems with state feedback the design is based on solutions to a class of parametric periodic lyapunov differential equations pldes resulting from the problem of minimal energy control with guaranteed convergence rate by carefully studying the properties of the pldes and their solutions a continuous periodic state feedback is designed the plde based approach is effective in designing stabilizing controller for cpl systems as the designers need only to solve a linear differential equation whose solution can be obtained analytically if the system is relative simple and can be computed numerically by integration in general cases necessary and sufficient conditions on the free parameter in the plde are proposed to guarantee the stability of the closed loop system whose characteristic multiplier set can even be exactly computed accordingly a numerical example is worked out to show the effectiveness of the proposed approach

stability and l_2 synthesis of a class of periodic piecewise time varying systems in this paper the stability stabilization and l 2 gain problems are investigated for periodic piecewise systems with time varying subsystems continuous lyapunov function with time varying lyapunov matrix is adopted a condition guaranteeing the negative definiteness of a matrix polynomial deriving from the lyapunov derivative is first obtained based on such a condition an exponential stability condition is provided moreover a state feedback controller with time varying gain is developed to stabilize the unstable periodic piecewise time varying system the l 2 gain criterion for periodic piecewise time varying system is also studied numerical examples are given to show the validity of the proposed techniques

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

exit functions for binary input memoryless symmetric channels use of extrinsic information transfer exit functions characterizing the amplification of mutual information between the input and output of the maximum a posteriori map decoder significantly facilitates analysis of iterative coding schemes previously exit functions derived for binary erasure channels becs were used as an approximation for other channels here we improve on this approach by introducing more accurate methods to construct exit functions for binary input memoryless symmetric bms channels by defining an alternative pseudo map decoder coinciding with the map decoder over bec we provide an expression for the exit functions of block codes over bec furthermore we draw a connection between the exit function over bec and the exit function over the bms channel under certain conditions this is used for deriving accurate or approximate expressions of exit functions over bms channels in certain scenarios

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

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

lmi techniques for optimization over polynomials in control a survey numerous tasks in control systems involve optimization problems over polynomials and unfortunately these problems are in general nonconvex in order to cope with this difficulty linear matrix inequality lmi techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems this survey aims to provide the reader with a significant overview of the lmi techniques that are used in control systems for tackling optimization problems over polynomials describing approaches such as decomposition in sum of squares positivstellensatz theory of moments polya s theorem and matrix dilation moreover it aims to provide a collection of the essential problems in control systems where these lmi techniques are used such as stability and performance investigations in nonlinear systems uncertain systems time delay systems and genetic regulatory networks it is expected that this survey may be a concise useful reference for all readers

degrees of freedom in adaptive modulation a unified view we examine adaptive modulation schemes for flat fading channels where the data rate transmit power and instantaneous ber are varied to maximize spectral efficiency subject to an average power and ber constraint both continuous rate and discrete rate adaptation are considered as well as average and instantaneous ber constraints we find the general form of power ber and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions the optimal adaptation of these parameters is to increase the power and data rate and decrease the ber as the channel quality improves surprisingly little spectral efficiency is lost when the power or rate is constrained to be constant hence the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted

design of multi input multi output systems based on low density parity check codes we design serial concatenated multi input multi output systems based on low density parity check ldpc codes we employ a receiver structure combining the demapper detector and the decoder in an iterative fashion we consider the a posteriori probability app demapper as well as a suboptimal demapper incorporating interference cancellation with linear filtering extrinsic information transfer exit chart analysis is applied to study the convergence behavior of the proposed schemes we show that exit charts match very well with the simulated decoding trajectories and they help explain the impact of different mappings and different demappers it is observed that if the app demapper transfer characteristics are almost flat the ldpc codes optimized for binary input channels are good enough to achieve performance close to the channel capacity we also present a simple code optimization method based on exit chart analysis and we design a rate 1 2 ldpc code that achieves very low bit error rates within 0 15 db of the capacity of a two input two output rayleigh fading channel with 4 pulse amplitude modulation we next propose to use a space time block code as an inner code of our serial concatenated coding scheme by means of a simple example scheme using an alamouti inner code we demonstrate that the design optimization of the outer code e g ldpc code is greatly simplified

convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode dependent dwell time abstract alternative conditions for establishing dwell time stability properties of linear switched systems are considered unlike the hybrid conditions derived in geromel and colaneri 2006 the considered ones are affine in the system matrices allowing then for the consideration of uncertain switched systems with time varying uncertainties the low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state feedback control laws the resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped functionals previously considered in the literature the sums of squares conditions are also proven to 1 approximate arbitrarily well the conditions of geromel and colaneri 2006 and 2 be invariant with respect to time scaling emphasizing that the complexity of the approach does not depend on the size of the dwell time several comparative examples illustrate the efficiency of the approach

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

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

variable rate coding for slowly fading gaussian multiple access channels we consider a nonergodic multiple access gaussian block fading channel where a fixed number of independent and identically distributed i i d fading coefficients affect each codeword variable rate coding with input power constraint enforced on a per codeword basis is examined a centralized power and rate allocation policy is determined as a function of the previous and present fading coefficients the power control policy that optimizes the expected rates is obtained through dynamic programming and the average capacity region and the average capacity region per unit energy are characterized moreover we study the slope of spectral efficiency curve versus e sub b n sub 0 db and we quantify the penalty incurred by time division multiple access tdma over superposition coding in the low power regime

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

design of low density parity check codes for modulation and detection a coding and modulation technique is studied where the coded bits of an irregular low density parity check ldpc code are passed directly to a modulator at the receiver the variable nodes of the ldpc decoder graph are connected to detector nodes and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder the code is optimized by performing a curve fitting on extrinsic information transfer charts design examples are given for additive white gaussian noise channels as well as multiple input multiple output mimo fading channels where the receiver but not the transmitter knows the channel for the mimo channels the technique operates within 1 25 db of capacity for various antenna configurations and thereby outperforms a scheme employing a parallel concatenated turbo code by wide margins when there are more transmit than receive antennas

brief paper a novel stability analysis of linear systems under asynchronous samplings this article proposes a novel approach to assess the stability of continuous linear systems with sampled data inputs the method which is based on the discrete time lyapunov theorem provides easy tractable stability conditions for the continuous time model sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems an additional stability analysis is provided for the cases of multiple sampling periods and packet losses several examples show the efficiency of the method

new results on stability of slowly switched systems a multiple discontinuous lyapunov function approach in this technical note the problem of stability for a class of slowly switched systems is investigated by developing a novel multiple discontinuous lyapunov function approach and exploring the feature of mode dependent dwell time switching new stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems in particular stability conditions for linear switched systems are also given via choosing multiple discontinuous lyapunov functions in the quadratic form moreover stability criteria for the systems consisting of stable subsystems are also derived it is shown that our proposed results cover some existing ones in literature as special cases and provide tighter bounds on the dwell time finally some simulation results are provided to show the advantages of the theoretic results obtained

convex lifted conditions for robust l 2 stability analysis and l 2 stabilization of linear discrete time switched systems with minimum dwell time constraint stability analysis of discrete time switched systems under minimum dwell time is studied using a new type of lmi conditions these conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in geromel and colaneri 2006b the convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables the convexity of the conditions can be exploited to extend the results to uncertain systems control design and 2 gain computation without introducing additional conservatism several examples are presented to show the effectiveness of the approach