technical communique predictor based stabilization of discrete time varying input delay systems this paper adapts some literature results on stabilizing discrete time varying input delay systems to the case of having a predictor based controller the objective of the paper is showing that the incorporation of predictors to the referred results is relatively simple and by means of such predictors robustness against delay mismatch in the input channel may be improved in this way larger delay variation margins are proved with predictors when compared to standard memoryless state feedback as intuitively expected due to the extra past information available

casimir operators of the exceptional group f4 the chain b4 contained in implied by f4 contained in implied by d13 expressions are given for the casimir operators of the exceptional group f4 in a concise form similar to that used for the classical groups the chain b4 contained in implied by f4 contained in implied by d13 is used to label the generators of f4 in terms of the adjoint and spinor representations of b4 and to express the 26 dimensional representation of f4 in terms of the defining representation of d13 casimir operators of any degree are obtained and it is shown that a basis consists of the operators of degree 2 6 8 and 12

h sub spl infin control of systems under norm bounded uncertainties in all system matrices this paper concerns h sub spl infin control of systems under norm bounded uncertainties in all the system matrices this is an extension of the work by xie et al 1992 where only the a matrix is allowed to be uncertain it is found that the problem shares the same formulation with the h sub spl infin control problem for systems without uncertainties it can also be viewed as reducing the problem of dealing with systems with both structured uncertainties and unstructured uncertainties to one with unstructured uncertainties only

sending a bivariate gaussian source over a gaussian mac with feedback we study the power versus distortion tradeoff for the transmission of a memoryless bivariate gaussian source over a two to one gaussian multiple access channel with perfect causal feedback in this problem each of two separate transmitters observes a different component of a memoryless bivariate gaussian source as well as the feedback from the channel output of the previous time instants based on the observed source sequence and the feedback each transmitter then describes its source component to the common receiver via an average power constrained gaussian multiple access channel from the resulting channel output the receiver wishes to reconstruct each source component with the least possible expected squared error distortion we study the set of distortion pairs that can be achieved by the receiver on the two source components we present sufficient conditions and necessary conditions for the achievability of a distortion pair these conditions are expressed in terms of the source correlation and of the signal to noise ratio snr of the channel in several cases the necessary conditions and sufficient conditions are shown to agree in particular we show that if the channel snr is below a certain threshold then an uncoded transmission scheme that ignores the feedback is optimal thus below this snr threshold feedback is useless we also derive the optimal high snr asymptotics

sending a bivariate gaussian over a gaussian mac we study the power versus distortion tradeoff for the distributed transmission of a memoryless bivariate gaussian source over a two to one average power limited gaussian multiple access channel in this problem each of two separate transmitters observes a different component of a memoryless bivariate gaussian source the two transmitters then describe their source component to a common receiver via an average power constrained gaussian multiple access channel from the output of the multiple access channel the receiver wishes to reconstruct each source component with the least possible expected squared error distortion our interest is in characterizing the distortion pairs that are simultaneously achievable on the two source components we focus on the equal bandwidth case where the source rate in source symbols per second is equal to the channel rate in channel uses per second we present sufficient conditions and necessary conditions for the achievability of a distortion pair these conditions are expressed as a function of the channel signal to noise ratio snr and of the source correlation in several cases the necessary conditions and sufficient conditions are shown to agree in particular we show that if the channel snr is below a certain threshold then an uncoded transmission scheme is optimal moreover we introduce a source channel vector quantizer scheme which is asymptotically optimal as the snr tends to infinity

on the awgn mac with imperfect feedback new achievable rate regions are derived for the two user additive white gaussian multiple access channel with noisy feedback the regions exhibit the following two properties irrespective of the finite gaussian feedback noise variances the regions include rate points that lie outside the no feedback capacity region and when the feedback noise variances tend to zero the regions converge to the perfect feedback capacity region the new achievable regions also apply to the partial feedback setting where one of the transmitters has a noisy feedback link and the other transmitter has no feedback at all again irrespective of the finite noise variance on the feedback link the regions include rate points that lie outside the no feedback capacity region moreover in the case of perfect partial feedback i e where the only feedback link is noise free for certain channel parameters the new regions include rate points that lie outside the cover leung region this answers in the negative the question posed by van der meulen as to whether the cover leung region equals the capacity region of the gaussian multiple access channel with perfect partial feedback finally we propose new achievable regions also for a setting where the receiver is cognizant of the realizations of the noise sequences on the feedback links

casimir operators for f4 e6 e7 and e8 we construct explicitly algebraically independent generating sets for the casimir operators and the invariants of the weyl groups and adjoint groups of the exceptional lie algebras f4 e6 e7 and e8

from constants of motion to superposition rules for lie hamilton systems a lie system is a non autonomous system of first order differential equations possessing a superposition rule i e a map expressing its general solution in terms of a generic finite family of particular solutions and some constants lie hamilton systems form a subclass of lie systems whose dynamics is governed by a curve in a finite dimensional real lie algebra of functions on a poisson manifold it is shown that lie hamilton systems are naturally endowed with a poisson coalgebra structure this allows us to devise methods for deriving in an algebraic way their constants of motion and superposition rules we illustrate our methods by studying kummer schwarz equations riccati equations ermakov systems and smorodinsky winternitz systems with time dependent frequency

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

casimir operators of the exceptional group g2 degree 2 and 6 casimir operators of g2 are calculated in explicit form with the generators of g2 written in terms of the subalgebra a2

uncoded transmission is exactly optimal for a simple gaussian sensor network a single memoryless gaussian source is observed by many terminals subject to independent gaussian observation noises the terminals are linked to a fusion center via a standard gaussian multiple access channel the fusion center needs to recover the underlying gaussian source with respect to mean squared error in this correspondence a theorem of witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission i e each terminal s channel input is merely a scaled version of its noisy observation

a systematic construction of completely integrable hamiltonians from coalgebras a universal algorithm to construct n particle classical and quantum completely integrable hamiltonian systems from representations of coalgebras with casimir elements is presented in particular this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of hamiltonian systems with coalgebra symmetry in order to illustrate this general method the algebra and the oscillator algebra are used to derive new classical integrable systems including a generalization of gaudin calogero systems and oscillator chains quantum deformations are then used to obtain some explicit integrable deformations of the previous long range interacting systems and a non coboundary deformation of the 1 1 poincare algebra is shown to provide a new ruijsenaars schneider like hamiltonian

a criterion for completeness of casimir operators we give a criterion for a set of casimir operators of any semisimple lie algebra to be an algebraically independent generating set of the algebra of the casimir operators the criterion is applied to supply complete sets for the casimir operators of al bl cl and dl with the aid of a method to construct some casimir operators we then furnish complete sets for the casimir operators of the exceptional lie algebras using the criterion

1 1 schrodinger lie bialgebras and their poisson lie groups all lie bialgebra structures for the 1 1 dimensional centrally extended schrodinger algebra are explicitly derived and proved to be of coboundary type therefore since all of them come from a classical r matrix the complete family of schrodinger poisson lie groups can be deduced by means of the sklyanin bracket all possible embeddings of the harmonic oscillator extended galilei and gl 2 lie bialgebras within the schrodinger classification are studied as an application new quantum hopf algebra deformations of the schrodinger algebra including their corresponding quantum universal r matrices are constructed

stable transformations for control variable delayed systems a well known transformation containing a transport type integral induces a feedback controller for control variable delayed systems more recent numerical simulations based on the discretization of the transport type integral have cast doubt on the stabilizing property of this controller further investigation has revealed that the null space of the transport type integral is a potential source of a destabilizing input for the closed loop system this is the hidden input problem on the basis of the concept of a stable transformation a new feedback stabilizing controller is formulated to address the hidden input problem an additional benefit of the stable transformation theory is a quasi functional observer which allows the new feedback controller to be implemented as a constant multiple of an augmented state variable

solvable lie algebras with naturally graded nilradicals and their invariants the indecomposable solvable lie algebras with graded nilradical of maximal nilindex and a heisenberg subalgebra of codimension one are analysed and their generalized casimir invariants are calculated it is shown that rank one solvable algebras have a contact form which implies the existence of an associated dynamical system moreover due to the structure of the quadratic casimir operator of the nilradical these algebras contain a maximal non abelian quasi classical lie algebra of dimension 2n 1 indicating that gauge theories with ghosts are possible on these subalgebras

lk stability analysis of predictor based controllers for discrete time systems with time varying actuator delay abstract this paper extends the scaled small gain proposal in li and gao 2011 14 modifying the lyapunov krasovskii functional to analyze the robust stability of predictor based state feedback controllers for discrete time systems with model uncertainties and unknown time varying delays in the control input results show that the use of predictors improves the achieved robustness margin over static state feedback in some cases as expected due to the extra information available to the controller

a complete basis set of functionally independent invariants of continuous lie groups using the methods of differential equations the author has obtained the complete set of functionally independent bases of invariants for some continuous lie groups of mathematical physics i the conformal group ii the semi direct product of the weyl group and the one parameter group of psi translation iii the direct product of the poincare group and the one parameter group of psi scaling iv the weyl group v the 14 parameter maximal symmetry group of the schrodinger equation for the coulombic system of atoms and molecules and vi su 3 of elementary particle physics the first four groups are the only groups which together with the poincare group are the maximal symmetry groups of all forms of the non linear klein gordon equation

input output approach to stability and l2 gain analysis of systems with time varying delays abstract stability and l 2 l 2 gain of linear continuous time and discrete time systems with uncertain bounded time varying delays are analyzed under the assumption that the nominal delay values are not equal to zero the delay derivatives in the continuous time are not assumed to be less than q 1 an input output approach is applied by introducing a new input output model which leads to effective frequency domain and time domain criteria the new method significantly improves the existing results for delays with derivatives not greater than 1 which were treated in the past as fast varying delays without any constraints on the delay derivatives new bounded real lemmas brls are derived for systems with state and objective vector delays and norm bounded uncertainties numerical examples illustrate the efficiency of the new method

energy distortion tradeoffs in gaussian joint source channel coding problems the information theoretic notion of energy efficiency is studied in the context of various joint source channel coding problems the minimum transmission energy e d required to communicate a source over a noisy channel so that it can be reconstructed within a target distortion d is analyzed unlike the traditional joint source channel coding formalisms no restrictions are imposed on the number of channel uses per source sample for single source memoryless point to point channels e d is shown to be equal to the product of the minimum energy per bit ebmin of the channel and the rate distortion function r d of the source regardless of whether channel output feedback is available at the transmitter the primary focus is on gaussian sources and channels affected by additive white gaussian noise under quadratic distortion criteria with or without perfect channel output feedback in particular for two correlated gaussian sources communicated over a gaussian multiple access channel inner and outer bounds on the energy distortion region are obtained which coincide in special cases for symmetric channels the difference between the upper and lower bounds on energy is shown to be at most a constant even when the lower bound goes to infinity as d 0 it is also shown that simple uncoded transmission schemes perform better than the separation based schemes in many different regimes both with and without feedback

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

poisson maps and canonoid transformations for time dependent hamiltonian systems after a new presentation of the geometric theory of time dependent systems in the hamiltonian formulation using poisson structures a characterization of canonoid transformations with respect to a dynamical vector field is given the associated constants of motion and the generating functions of canonoid transformations are also studied the theory is illustrated with several examples

joint source channel coding with feedback this paper quantifies the fundamental limits of variable length transmission of a general possibly analog source over a memoryless channel with noiseless feedback under a distortion constraint we consider excess distortion average distortion and guaranteed distortion d semifaithful codes in contrast to the asymptotic fundamental limit a general conclusion is that allowing variable length codes and feedback leads to a sizable improvement in the fundamental delay distortion tradeoff in addition we investigate the minimum energy required to reproduce k source samples with a given fidelity after transmission over a memoryless gaussian channel and we show that the required minimum energy is reduced with feedback and an average rather than maximal power constraint

a new model transformation of discrete time systems with time varying delay and its application to stability analysis this technical note focuses on analyzing a new model transformation of uncertain linear discrete time systems with time varying delay and applying it to robust stability analysis the uncertainty is assumed to be norm bounded and the delay intervally time varying a new comparison model is proposed by employing a new approximation for delayed state and then lifting method and simple lyapunov krasovskii functional method are used to analyze the scaled small gain of this comparison model this new approximation results in a much smaller error than the existing ones based on the scaled small gain theorem new stability criteria are proposed in terms of linear matrix inequalities moreover it is shown that the obtained conditions can be established through direct lyapunov method two numerical examples are presented to illustrate the effectiveness and superiority of our results over the existing ones

energy distortion exponents in lossy transmission of gaussian sources over gaussian channels lossy transmission of gaussian sources over energy limited gaussian point to point and broadcast channels is studied under the infinite bandwidth regime i e when the number of channel uses is unlimited using previously known asymptotic achievability and converse results the energy distortion exponent defined as the rate of decay of the square error distortion as the available energy to noise ratio increases without bound is completely characterized for both the point to point and broadcast channel cases turning then to the scenario of zero delay transmission where outage events with arbitrarily small probability are allowed it is shown that the same energy distortion exponent as in the infinite delay case can be achieved in all the studied scenarios

casimir invariants for the complete family of quasisimple orthogonal algebras a complete choice of generators of the centre of the enveloping algebras of real quasisimple lie algebras of orthogonal type for arbitrary dimension is obtained in a unified setting the results simultaneously include the well known polynomial invariants of the pseudo orthogonal algebras as well as the casimirs for many non simple algebras such as the inhomogeneous the newton hooke and galilei type etc which are obtained by contraction s starting from the simple algebras the dimension of the centre of the enveloping algebra of a quasisimple orthogonal algebra turns out to be the same as for the simple algebras from which they come by contraction the structure of the higher order invariants is given in a convenient pyramidal manner in terms of certain sets of pauli lubanski elements in the enveloping algebras as an example showing this approach at work the scheme is applied to recovering the casimirs for the 3 1 kinematical algebras some prospects on the relevance of these results for the study of expansions are also given