minimal positive realizations of transfer functions with nonnegative multiple poles this note concerns a particular case of the minimality problem in positive system theory a standard result in linear system theory states that any nth order rational transfer function of a discrete time invariant linear single input single output siso system admits a realization of order n in some applications however one is restricted to realizations with nonnegative entries i e a positive system and it is known that this restriction may force the order n of realizations to be strictly larger than n a general solution to the minimality problem i e determining the smallest possible value of n is not known in this note we consider the case of transfer functions with nonnegative multiple poles and give sufficient conditions for the existence of positive realizations of order n n with the help of our results we also give an improvement of an existing result in positive system theory

blind ofdm channel estimation using fir constraints reduced complexity and identifiability in this correspondence blind channel estimators exploiting finite alphabet constraints are discussed for orthogonal frequency division multiplexing ofdm systems considering the channel and data jointly a joint maximum likelihood jml algorithm is described along with identifiability conditions in the noise free case this approach enables development of general identifiability conditions for the minimum distance md finite alphabet blind algorithm of zhou and giannakis both the jml and md algorithms suffer from high numerical complexity as they rely on exhaustive search methods to resolve a large number of ambiguities we present a substantially more efficient blind algorithm the reduced complexity minimum distance rmd algorithm by exploiting properties of the assumed finite length impulse response fir channel the rmd algorithm exploits constraints on the unwrapped phase of fir systems and results in significant reductions in numerical complexity over existing methods in many cases the rmd approach is able to completely eliminate the exhaustive search of the jml and md approaches while providing channel estimates of the same quality

reachability observability and realizability of continuous time positive systems this paper discusses reachability observability and realizability of single input single output linear time invariant systems in which state variables and or input output functions are restricted to be nonnegative to reflect physical constraints frequently encountered in real systems we define a set reachable from the origin with nonnegative inputs and also a set observable with nonnegative outputs we investigate geometrical structures of the sets through convex analysis and a duality relation between them is established next we consider positive realization of a given transfer function using the reachable set and the observable set we give a necessary and sufficient condition for positive realizability an example is given to demonstrate that a positive realizable transfer function does not in general have a jointly controllable and observable positive realization

an example of how positivity may force realizations of large dimension abstract a standard result of linear system theory states that an siso proper rational transfer function of degree n always has a realization of dimension n in some applications one is interested in having a realization with nonnegative entries and it is known that when the dominant poles display a specific pattern forcing nonnegativity leads to a system which is not jointly reachable and observable in this paper we show that the minimal dimension of a positive realization may be large even in the case of a single dominant pole more precisely we provide a family of transfer functions each of which is of degree n 3 such that for any integer n 3 the corresponding member of the family admits a minimal positive realization of state space dimension not smaller than n

advances on the reachability index of positive 2 d systems this work was supported by dgi grant mtm2010 18228 recommended by associate editor z wang

codes based on a trellis cut set transformation ii codes for noncoherent detection for pt i see ibid vol 46 p 610 20 1998 we continue the study of cut set trellis section t sub cb codes begun in part i and show that such codes are well suited for use with multiple symbol noncoherent detection and conventional two symbol differential detection the information bit assignment for a cut set trellis section can be modified to make the resulting code noncatastrophic for noncoherent detection by this procedure many existing two dimensional 2 d and multidimensional mpsk and qam trellis codes designed for coherent detection can be easily converted into codes for both coherent and noncoherent detection compared to m dpsk trellis codes it is shown that 2 d mpsk cut set trellis section codes have improved performance for multiple symbol noncoherent detection and comparable performance for conventional two symbol differential detection thus cut set trellis section codes are a class of universal channel codes since a single encoder performs well for coherent detection multiple symbol noncoherent detection and conventional two symbol differential detection

invariance of the approximately reachable set under nonlinear perturbations this paper considers nonlinear perturbations of control systems with linear dynamics and seeks to analyze whether the approximately reachable set may be left unchanged by this perturbation under suitable conditions it is shown that this analysis may be reduced to the presumably simpler analysis of such invariance for a family of affine perturbations interest centers on the context of infinite dimensional state spaces so the system may for example correspond to a hyperbolic or parabolic partial differential equation

invariance of the reachable set under nonlinear perturbations for the abstract controlled volterra equation qquad x t bar x t int 0 t boldsymbol psi t s phi s x s bf b s v s ds on 0 t we consider the reachable set mathcal k phi x t text for some v in mathfrak b viewing phi cdot cdot as a nonlinear perturbation of an otherwise linear control problem conditions are obtained under which mathcal k phi mathcal k 0 for a suitable class mathfrak f of such nonlinear perturbations phi whenever the linear problem is known to have a reachable set invariant under affine perturbations phi cdot cdot g in mathfrak z the results generalize those obtained by naito 7 for control of the heat equation

admissible controllability of vibrating systems with constrained controls we study the control of a vibrating string when the controls f x t are applied only on a limited subset of the string and constrained by continuous functions alpha x beta x as alpha x leqq f x t leqq beta x we find that it is possible to transfer almost all states of vibration into rest by a constrained control the higher space dimensional vibrating systems are also considered

some comments on existence of solutions of abstract nonlinear second order neutral functional integrodifferential equations we establish the existence of mild solutions for a class of abstract second order partial neutral functional integro differential equations with finite delay in a banach space using the theory of cosine families of bounded linear operators and schaefer s fixed point theorem

approximate controllability of second order distributed implicit functional systems abstract in this paper we study the approximate controllability of control systems with states and controls in hilbert spaces and described by a second order semilinear abstract functional differential equation with infinite delay initially we establish a characterization for the approximate controllability of a second order abstract linear system and in the last section we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system

rotational invariance of trellis codes i encoders and precoders we present a theoretical framework for rotational invariance of trellis codes the distinction between codes and encoders plays a pivotal role necessary and sufficient conditions for rotational invariance are derived under general assumptions and a construction is presented that obtains a rotationally invariant encoder for almost any rotationally invariant code independent of the code s algebraic structure encoders that use a differential precoder are considered as a separate case where a system theoretic characterization of precoding is used to find two alternative and slightly less general encoder constructions

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

controllability of second order semilinear neutral functional differential systems in banach spaces abstract sufficient conditions for controllability of semilinear second order neutral functional differential systems in banach spaces are established using the theory of strongly continuous cosine families the results are obtained by using the leray schauder alternative

approximate controllability of semilinear functional equations in hilbert spaces in this paper approximate and complete controllability for semilinear functional differential systems is studied in hilbert spaces sufficient conditions are established for each of these types of controllability the results address the limitation that linear systems in infinite dimensional spaces with compact semigroup cannot be completely controllable the conditions are obtained by using the schauder fixed point theorem when the semigroup is compact and the banach fixed point theorem when the semigroup is not compact

on the existence of a positive realization the positive realization problem for linear systems is to find conditions for a given transfer function with nonnegative impulse response to have a realization such that the resulting system is a positive system recently it has been shown that under a mild assumption on the long term behaviour of the impulse response this problem is related to the maximum modulus poles only in this paper necessary and sufficient conditions for positive realizability of discrete time systems are given they show that also nondominant poles play a role in the most general case positive realizability conditions for the continuous time case are also given

controllability of the second order differential inclusion in banach spaces abstract the purpose of this paper is to study the controllability for the second order differential inclusion in banach spaces we rely on a fixed point theorem for condensing maps due to martelli we consider the damping term x and find a control u such that the solution satisfies x t x1 and x t y1

controllability of neutral functional integrodifferential systems in banach spaces abstract sufficient conditions for controllability of neutral functional integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

multiple trellis coded modulation mtcm the authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation mtcm wherein more than one channel symbol per trellis branch is transmitted they have found simple two state trellis codes for symmetric mpsk multiple phase shift keying and am modulations that can achieve 3 db gain over uncoded modulation at very high signal to noise ratios without bandwidth expansion or reduction in information bit rate the gain of these codes with respect to previously reported two state trellis codes is between 1 and 2 db at very high signal to noise ratios depending on the number of bits per hertz transmitted these gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram the authors note that additional computations per branch are needed for the multiple trellis coding scheme the concept can be extended to a higher number of states and other types of modulations

bounds on the size of minimal nonnegative realizations for discrete time lti systems nonnegative linear time invariant lti state space models are characterized by the property that their state variables and outputs remain nonnegative whenever the initial state and the inputs are nonnegative necessary and sufficient conditions for the existence of a nonnegative state space realization of a given discrete time dt impulse response were obtained recently in this letter we look at minimal nonnegative realizations of dt impulse responses and develop bounds on the number of state variables that are necessary

topological theory of non autonomous parabolic evolution inclusions on a noncompact interval and applications in this paper we consider the topological structure of the solution set of non autonomous parabolic evolution inclusions with time delay defined on non compact intervals the result restricted to compact intervals is then extended to non autonomous parabolic control problems with time delay moreover as the applications of the information about the structure we establish the existence result of global integral solutions for non autonomous cauchy problems subject to nonlocal condition and prove the invariance of a reachability set for non autonomous control problems under single valued nonlinear perturbations finally some illustrating examples are supplied

complete controllability of one dimensional vibrating systems with bang bang controls this paper deals with the problem of controllability for one dimensional vibrating systems with controls which are scalar valued functions of time only we give some constraint sets of controls and prove exact controllability of vibrations in those constraint sets by studying the moment problem attached to this control problem precisely using these results and lyapunov s convexity theorem for vector measures we obtain complete controllability only with bang bang controls

on the reachable set for third order linear discrete time systems with positive control the case of complex eigenvalues abstract in this paper we study the geometrical properties of the set of reachable states of a single input third order discrete time linear system with positive controls this set is a cone and we give a complete geometrical characterization of this set when the system has a complex conjugate pair of eigenvalues more in detail we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations

the solution sets for second order semilinear impulsive multivalued boundary value problems a second order semilinear differential inclusion with some boundary continuous and impulse characteristics in a separable banach space is considered some existence theorems for mild solutions are given when the multivalued nonlinearity of the inclusion is only a locally integrably bounded upper caratheodory map with convex and weakly compact values then the compactness of the set of all mild solutions for the problem is proved the results are obtained by using the theory of continuous cosine families of bounded linear operators and a fixed point theorem for multivalued maps due to agarwal meehan and o regan a corresponding result for closed graph of composition is extended

controllability of sobolev type integrodifferential systems in banach spaces sufficient conditions for controllability of sobolev type integrodifferential systems in banach spaces are established the results are obtained using compact semigroups and the schauder fixed point theorem as an example is provided to illustrate the results

coding for the discretely phase ambiguous additive white gaussian channel communication over the additive white gaussian channel subject to a discrete phase ambiguity at the receiver is considered when this phase ambiguity is considered as a discretely distributed random variable the channel is termed the acoherent additive white gaussian aawg channel it is shown that the optimum decoder for the aawg channel is not practically implementable and a suboptimum decoder that is asymptotically optimum at high signal to noise ratio is developed the low signal to noise ratio performance of the suboptimum decoder is also examined by considering the structural possibilities for this decoder it is shown that one implementation leads to rotationally invariant codes other implementations based on a rotationally disjoint property lead to a variety of solutions that offer a general framework for communication over this channel some of these solutions use a parallel receiver configuration various solutions are compared in terms of implementation and performance

on the capacity of the blockwise incoherent mpsk channel the capacity of m ary phase shift keying mpsk over an additive white gaussian noise awgn channel with carrier phase unknown but constant over l symbols is investigated it is shown that capacity achieving channel inputs are uniformly distributed and independent mpsk symbols capacity over a range of signal to noise ratio snr and l is presented for binary phase shift keying bpsk and quaternary phase shift keying qpsk upper and lower easy to compute bounds on capacity are derived it is proven that for large l the coherent capacity is approached an analytic asymptotic expression for low l spl middot snr is derived exhibiting the expected quadratic dependence on the snr

minimal positive realizations of transfer functions with real poles a standard result of linear system theory states that a single input single output siso rational n th order transfer function always has a state space realization of the same order in some applications one is interested in having a realization with nonnegative entries i e a positive system and it is known that such constraints may lead to a minimal order positive realization of order much greater than the transfer function order n in this technical note necessary and sufficient conditions for a third order transfer function with distinct real poles to have a third order positive realization are given these conditions are expressed in terms of lower bounds for the first three samples of the impulse response and therefore are very easy to check this result is an extension of a previous result for transfer functions with distinct real positive poles

on the reachable set for third order linear discrete time systems with positive control abstract in this paper we study the geometrical properties of the set of reachable states of a single input third order discrete time linear system with positive controls this set is a cone and we give a complete geometrical characterization of this set when the system has all real eigenvalues more in detail we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations moreover we provide necessary and sufficient conditions for finite time reachability of every reachable state and characterize the minimum number of steps needed to reach every state in terms of eigenvalue locations

controllability of semilinear control systems dominated by the linear part while various equivalent conditions for controllability have been obtained in the case of linear control systems controllability problems of semilinear control systems usually require some complicated and limited assumptions in this paper we show the approximate controllability of an abstract semilinear control system under the assumption which has a simple form and can be easily checked in many examples

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

controllability of second order neutral functional differential inclusions in banach spaces in this paper we prove the controllability of second order neutral functional differential inclusions in banach spaces the result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to martelli

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative