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

relating h sub 2 and h sub spl infin norm bounds for sampled data systems we relate the h sub spl infin and h sub 2 norms for multi input multi output sampled data feedback control systems where a continuous time plant is controlled by a digital compensator with hold and sampler upper bounds on both h sub 2 and h sub spl infin norms are obtained based on fundamental relations derived by two different approaches namely the hybrid state space approach and the fast sampling and lifting approach

auxiliary matrices for the six vertex model and the algebraic bethe ansatz we connect two alternative concepts of solving integrable models baxter s method of auxiliary matrices or q operators and the algebraic bethe ansatz the main steps of the calculation are performed in a general setting and a formula for the bethe eigenvalues of the q operator is derived a proof is given for states which contain up to three bethe roots further evidence is provided by relating the findings to the six vertex fusion hierarchy for the xxz spin chain we analyse the cases when the deformation parameter of the underlying quantum group is evaluated both at and away from a root of unity

quantization of models with non compact quantum group symmetry modular xxz magnet and lattice sinh gordon model we define and study certain integrable lattice models with non compact quantum group symmetry the modular double of including an integrable lattice regularization of the sinh gordon model and a non compact version of the xxz model their fundamental r matrices are constructed in terms of the non compact quantum dilogarithm our choice of the quantum group representations naturally ensures self adjointness of the hamiltonian and the higher integrals of motion these models are studied with the help of the separation of variables method we show that the spectral problem for the integrals of motion can be reformulated as the problem to determine a subset among the solutions to certain finite difference equations baxter equation and quantum wronskian equation which is characterized by suitable analytic and asymptotic properties a key technical tool is the so called operator for which we give an explicit construction our results allow us to establish some connections to related results and conjectures on the sinh gordon theory in continuous spacetime our approach also sheds some light on the relations between massive and massless models in particular the sinh gordon and liouville theories from the point of view of their integrable structures

spatio temporal patterns in population dynamics abstract the transient dynamics of interacting biological species extracted from two ecosystems is investigated we model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing we find noise induced effects such as enhanced temporal oscillations spatial patterns and noise delayed extinction for the model of two competing species we extend our analysis to an ecosystem of three interacting species namely one predator and two preys we find spatial patterns induced by the noise

sampled data h 2 optimization of systems with i o delays via analog loop shifting the problem of sampled data h2 control of systems with a single input delay is studied conventional solutions of sampled data optimal control problems begin with a conversion to a discrete time problem with input delays followed by a matching optimization method geared to handle delays we propose reversing that order and address the delay first by an analog loop transformation hence discretization and optimization involve no delays and are amenable to any standard method the proposed streamlined approach fits also previously unsolved problems where sampling and or hold functions are design parameters

on baxter s q operator for the xxx spin chain we discuss the construction of baxter s q operator the suggested approach leads to the one parametric family of q operators satisfying wronskian type relations also we have found the generalization of baxter operators which defines the nondiagonal part of the monodromy

induced norms for sampled data systems abstract in this paper we consider a general linear interconnection of a continuous time plant and a discrete time controller via sample and hold devices when the closed loop sampled data feedback system is internally stable bounded inputs produce bounded outputs we present some explicit formulae for the induced norm of the closed loop system with l i e peak value and 1 i e integral absolute norms on the input and output signals

effect of time delay on pattern dynamics in a spatial epidemic model time delay accounting for constant incubation period or sojourn times in an infective state widely exists in most biological systems like epidemiological models however the effect of time delay on spatial epidemic models is not well understood in this paper spatial pattern of an epidemic model with both nonlinear incidence rate and time delay is investigated in particular we mainly focus on the effect of time delay on the formation of spatial pattern through mathematical analysis we gain the conditions for hopf bifurcation and turing bifurcation and find exact turing space in parameter space furthermore numerical results show that time delay has a significant effect on pattern formation the simulation results may enrich the finding of patterns and may well capture some key features in the epidemic models

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

the periodic toda chain and a matrix generalization of the bessel function recursion relations the authors obtain the quantization conditions of the periodic toda lattice in the baxter form lambda u q u inq u i i nq u i lambda is the transfer matrix containing the information about the spectrum and q is an integral operator commuting with lambda the logarithms of the matrix elements of q are the generating functions of the canonical backlund transformation the requirement that q is analytic and vanishes when u goes to infinity completely determines the spectrum of lambda

fr operator approach to the h sub 2 analysis and synthesis of sampled data systems recently a frequency domain operator called frequency response fr operator was defined and shown to represent the transfer characteristics of a stable sampled data system using this novel frequency domain notion and introducing its extended notion called hybrid fr operator we define an h sub 2 norm for sampled data systems in this paper then sampled data h sub 2 control problems are formulated and solved whereby the usefulness of these frequency domain notions is demonstrated both in the analysis and synthesis aspects of sampled data systems for the case of sampled data systems with hybrid i e both continuous time and discrete time input and output signals the h sub 2 norm defined by a hybrid fr operator turns out to be slightly different from that defined in previous studies the source of the discrepancy is also identified

baxter s q operator for the homogeneous xxx spin chain applying the pasquier gaudin procedure we construct baxter s q operator for the homogeneous xxx model as an integral operator in the standard representation of sl 2 the connection between the q operator and the local hamiltonians is discussed we show that lipatov s duality symmetry operator arises naturally as the leading term of the asymptotic expansion of the q operator for large values of the spectral parameter

linear time varying h 2 optimal control of sampled data systems abstract the goal in this paper is twofold first it is shown that linear time varying control is in general superior to linear time invariant lti control for lti plants with an h 2 criterion an expression for the optimal performance using time varying control is derived and a condition under which there is no advantage in using linear time varying control over lti control is determined second the h 2 optimal control of continuous time systems is studied via dual rate sampled data controllers it is shown that such a problem can be recast via the lifting technique as a standard lti h 2 problem in discrete time a design procedure for the dual rate h 2 optimal controller is proposed

unitary representations of uq 2 ℝ the modular double and the multiparticle q deformed toda chain the paper deals with the analytic theory of the quantum q deformed toda chains the technique used combines the methods of representation theory and the quantum inverse scattering method the key phenomenon which is under scrutiny is the role of the modular duality concept first discovered by l faddeev in the representation theory of noncompact semisimple quantum groups explicit formulae for the whittaker vectors are presented in terms of the double sine functions and the wave functions of the n particle q deformed open toda chain are given as a multiple integral of the mellin barnes type for the periodic chain the two dual baxter equations are derived

a hybrid state space approach to sampled data feedback control this paper develops a state space theory for the study of linear shift invariant finite dimensional hybrid dynamical systems by hybrid system we mean an inputoutput operator relating hybrid signals that is signals which consist of two parts a continuous time part and a discrete time part we first introduce the hybrid state space model and show the closedness properties under the fundamental operations we next investigate the standard basic issues associated with this formalism reachability observability and internal stability we define the notion of hz norm of the hybrid system and show how to evaluate it since the analysis result can be applied to any hybrid system with the proposed hybrid state space model we apply the analysis result to the optimal digital control problem for standard four block configuration with h norm performance measure the solution with computational algorithm is derived for the time delay case

robust stability and performance analysis of sampled data systems the authors consider the robust stability and performance analysis of a general linear interconnection of a continuous time plant and a discrete time controller via sample and hold devices they obtain necessary and sufficient conditions for the robust stability of the feedback system consisting of an uncertain plant represented as a known linear time invariant nominal model with time varying norm bounded uncertainty and a shift invariant discrete time controller these results show that the condition arising from the small gain theorem is necessary and sufficient when the uncertainties belong to a class of linear systems also similar results are derived for a case of structured uncertainty both l sub 2 and l sub infinity signal norms are considered robust performance analysis problem is solved by converting it to a robust stability analysis problem

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

performance of periodically time varying controllers for sampled data control analyzes performance of periodically time varying sampled data controllers for l sub p deterministic and uniform disturbance rejection for a given linear periodic sampled data controller controlling a linear time invariant continuous time plant it is shown that a linear time invariant controller can be found to give better l sub p sampled data control than the time varying controller the performance analysis is in time domain using convexity properties of the l sub p signal space

on the l 2 induced norm of a sampled data system formulas are given for the norms of sg and gh g is a linear continuous time system s an ideal sampler and h a zero order hold the signal spaces are l2 continuous time and l2 z discrete time these formulas are then applied to problems of uniformly optimal control of sampled data systems

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

role of the noise on the transient dynamics of an ecosystem of interacting species abstract we analyze the transient dynamics of an ecosystem described by generalized lotka volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species we consider specifically three cases i two competing species ii three interacting species one predator two preys iii n interacting species the interaction parameter in case i is a stochastic process which obeys a stochastic differential equation we find noise delayed extinction of one of two species which is akin to the noise enhanced stability phenomenon other two noise induced effects found are temporal oscillations and spatial patterns of the two competing species in case ii the noise induces correlated spatial patterns of the predator and of the two preys concentrations finally in case iii we find the asymptotic behavior of the time average of the ith population when the ecosystem is composed of a great number of interacting species

quantifying stochastic outcomes a system consisting of two species in a fluctuating environment when the interspecies competition for resources is strong will have a stochastic outcome only one of the species will survive but there is no a priori way of knowing which one this will be it is natural in such a situation to ask what will be the probability of one or another of the species surviving this probability is calculated as a function of the average growth rates and the strengths of the interaction between the species and of the randomness this is an example of a class of stochastic problems in which multiple final states are available for occupation we refer to the choice of final states as state selection and the probabilities of final states being occupied as state selection probabilities the calculation of these probabilities is carried out in the context of a model of the system which consists of two coupled stochastic differential equations by reformulating these equations in terms of path integrals the powerful methods based on the use of optimal paths may be utilized to calculate the probability of one outcome or the other the analytical results obtained by using this technique agree well with numerical simulations when both species have the same growth rate although the method adopted rests on the assumption that the strength of the fluctuations d is small remarkably the analytic results are still found to be in good agreement with the numerical results when d is of order 1

a q operator for the twisted xxx model taking the isotropic limit 1 in a recent representation theoretic construction of baxter s q operators for the xxz model with quasi periodic boundary conditions we obtain new results for the xxx model we show that quasi periodic boundary conditions are needed to ensure convergence of the q operator construction and derive a quantum wronskian relation which implies two different sets of bethe ansatz equations one above the other below the equator of total spin sz 0 we discuss the limit to periodic boundary conditions at the end and explain how this construction relates to the trace functional introduced by boos et al in the context of correlation functions on the infinite lattice we also identify a special subclass of solutions to the quantum wronskian and numerically verify them up to spin chains of ten sites this special type of solutions might persist for longer chains

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

sampled data control of continuous time systems with an h optimality criterion abstract the synthesis of sampled data controllers for continuous time systems is studied in the context of h control theory the sampled data h optimal control problem consists of finding a sampled data controller which minimizes the l2 induced norm from the continuous time disturbance to the continuous time output the problem is here solved via a discrete system representation this is achieved by describing the closed loop system as a discrete system with finite state dimension and with a representation of the disturbance and the output signals of the discrete system as sequences of elements of certain infinite dimensional spaces via finite rank approximations of a compact integral operator associated with the system the sampled data h control problem can be solved to any degree of accuracy from the structure of the problem it follows that irrespective of the order of the approximation a feasible sampled data controller can be found which has the same order as the system

on the hankel singular values of linear continuous and sampled data multivariable systems abstract this paper considers the hankel singular values of the sample data systems obtained from continuous time models via standard sampling techniques it is shown that the hankel singular values of the sampled data system recover the hankel singular values of the continuous time system as the sampling period approaches zero a state space proof of this result is given

factorization of the transfer matrices for the quantum sl 2 spin chains and baxter equation it is shown that the transfer matrices of homogeneous sl 2 invariant spin chains with generic spin both closed and open are factorized into the product of two operators the latter satisfy the baxter equation that follows from the structure of the reducible representations of the sl 2 algebra

factorization of r matrix and baxter q operators for generic sl n spin chains we develop an approach for constructing the baxter operators for generic sl n spin chains the key element of our approach is the possibility of representing a solution of the yang baxter equation in the factorized form we prove that such a representation holds for a generic sl n invariant operator and find the explicit expression for the factorizing operators taking trace of monodromy matrices constructed of the factorizing operators one defines a family of commuting baxter operators on the quantum space of the model we show that a generic transfer matrix factorizes into the product of n baxter operators and discuss an application of this representation for a derivation of functional relations for transfer matrices

baxter s q operator for the w algebra wn the q oscillator representation for the borel subalgebra of the affine symmetry is presented by means of this q oscillator representation we give the free field realizations of baxter s q operator for the w algebra wn we give functional relations of the t q operators including the higher rank generalization of baxter s t q relation

asymptotic properties of the best sampled data control performance properties of the best achievable performance of sampled data control systems are investigated contrary to our intuition the best sampled data control performance does not always converge to the best continuous time control performance even as the sampling period approaches zero a counterexample is presented and a lifting based analysis is performed it is shown that the performance convergence is guaranteed if and only if a certain hankel norm and an aliasing effect computed from a specified antialiasing filter tend to vanish with a decreasing sampling period it is also shown that this condition is reduced to a simpler form if the specified filter has special forms these results can be generalized to a system involving a generalized hold

optimal and robust controllers for periodic and multirate systems the problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete time periodic systems the solution consists of solving an equivalent time invariant standard l sup 1 optimization problem subject to an additional constraint this constraint assures the causality of the resulting periodic controller by the duality theory the problem is shown to be equivalent to a linear programming problem which is no harder than the standard l sup 1 problem also it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems finally the results are applied to the problem of robust stabilization of periodic and multirate systems

sampled data optimal control of continuous systems for quadratic criterion function taking account of delayed control action this paper is concerned with the sampled data control of a continuous system in the situation where there exists delay for the control action after the measurement of the output at each sampling instant the optimal control with the quadratic criterion function defined for the continuous system is adopted in this control problem this paper shows that the problem can be transformed into the optimal control of a discrete system for the quadratic criterion function and the variation of the control law to the sampling period and to the delay of the control action is clarified the deterioration of cost performance with respect to delay is derived a numerical example is also presented

extensive theoretical numerical comparative studies on h2 and generalised h2 norms in sampled data systems abstractthis paper is concerned with linear time invariant lti sampled data systems by which we mean sampled data systems with lti generalised plants and lti controllers and studies their h2 norms from the viewpoint of impulse responses and generalised h2 norms from the viewpoint of the induced norms from l2 to l a new definition of the h2 norm of lti sampled data systems is first introduced through a sort of intermediate standpoint of those for the existing two definitions we then establish unified treatment of the three definitions of the h2 norm through a matrix function g defined on the sampling interval 0 h this paper next considers the generalised h2 norms in which two types of the l norm of the output are considered as the temporal supremum magnitude under the spatial 2 norm and norm of a vector valued function we further give unified treatment of the generalised h2 norms through another matrix function f which is also defined on 0 h through a close connection between g

ℋ2 optimisation of mimo sampled data systems with pure time delays this article considers the digital control of a mimo continuous time process when we have time delays at different locations in the control loop the controller has to be causal realisable and stabilising under these restrictions we search for the controller ensuring the minimal 2 norm of the closed loop using the parametric transfer function concept a constructive method for the solution of this problem is provided on the basis of these results a number of characteristic properties of the closed 2 optimal system are formulated which are important for practical applications

self regulation mechanism of an ecosystem in a non gaussian fluctuation regime we study a dynamical model for an ecological network of many interacting species we consider a malthus verhulst type of self regulation mechanism in the framework of the mean field theory we study the nonlinear relaxation in three different cases a towards the equilibrium state b towards the absorbing barrier c at the critical point we obtain asymptotic behavior in all different cases for the time average of the process the dynamical behavior of the system in the limit of infinitely many interacting species is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations textcopyright 1996 the american physical society

a new optimal multirate control of linear periodic and time invariant systems the optimal multirate design of linear continuous time periodic and time invariant systems is considered it is based on solving the continuous linear quadratic regulation lqr problem with the control being constrained to a certain piecewise constant feedback necessary and sufficient conditions for the asymptotic stability of the resulting closed loop system are given an explicit multirate feedback law that requires the solution of an algebraic discrete riccati equation is presented such control is simple and can be easily implemented by digital computers when applied to linear time invariant systems multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly compared to the classical single rate sampled data feedback in which the state is always sampled at the same rate the multirate system can provide a better response with a considerable reduction in the optimal cost in general the multirate scheme offers more flexibility in choosing the sampling rates

h sub spl infin type problem for sampled data control systems a solution via minimum energy characterization this paper aims at deriving a solution for h sub spl infin type problem for sampled data control systems the solution is given in terms of an equivalent discrete time h sub spl infin problem the reduction procedure is viewed and characterized from the viewpoint of minimum energy principle and j unitary transformations

adaptive robust sampled data control of a class of systems under structured perturbations robust adaptive sampled data control of a class of linear systems under structured perturbations is considered the controller is a time varying state feedback law having a fixed structure containing an adjustable parameter and operating on sampled values the sampling period and the controller parameter are adjusted with simple adaptation rules the resulting closed loop system is shown to be stable for a class of unknown perturbations the same result is also shown to be applicable to decentralized control of interconnected system

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

stability in a system subject to noise with regulated periodicity the stability of a simple dynamical system subject to multiplicative one side pulse noise with hidden periodicity is investigated both analytically and numerically the stability analysis is based on the exact result for the characteristic functional of the renewal pulse process the influence of the memory effects on the stability condition is analyzed for two cases i the dead time distorted poissonian process and ii the renewal process with pareto distribution we show that for fixed noise intensity the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

on an lmi approach to optimal sampled data state feedback control design the literature presents a large number of interesting and useful results on sampled data systems in this paper we deal with control design problems for this class of systems following a different route the novelty is that the optimal h2 and h state feedback control design problems for sampled data linear systems are solved in a unified and direct manner through linear matrix inequalities to this purpose the solution to a special two point boundary value problem is used to verify the stability and to evaluate the performance of the closed loop system these results are then generalised to cope with non uniform data rates the theory is illustrated by means of simple examples borrowed from the literature

frequency response of sampled data systems this paper develops a frequency domain theory that provides a method to analyze and design sampled data control systems including their intersample behaviors the key idea is to consider the signal space x x t x t n x xn exp j t jn st n x xn 2 where s is the sampling angular frequency it is shown that a stable sampled data system equipped with a strictly proper pre filter before the sampler maps x into x l2 in the steady state that mapping is denoted by q j and is referred to as an fr operator it is proved that the norm of the sampled data system as an operator from l2 to l2 is given by max q j 2 2 where 12 s 12 s a set of equations relating outputs of a closed loop system to its inputs in the frequency domain is derived and their solution is given in an explicit form based on that solution the sensitivity fr operator y j and the complementary sensitivity fr operator t j are defined for feedback control systems and it is shown that y j gives the improvement of the sensitivity of the transfer characteristics from the reference to the controlled output and also represents the ability of rejecting disturbances and that t j represents the degree of robust stability and at the same time gives the effect of detection noises it is also shown that y j t j i and thus a frequency domain paradigm for the design of sampled data control systems which is exactly parallel to the continuous time case is established

generalized sample hold functions frequency domain analysis of robustness sensitivity and intersample difficulties over the past 5 years there has been substantial interest in the use of generalized sample hold functions for control in this correspondence the authors use a tool which is novel in this context namely amplitude modulation theory the authors employ this tool to analyze the quantitative and qualitative features of the intersample behavior in a frequency domain setting this offers new theoretical and practical insights into the method the authors conclusion is that the perceived benefits come at substantial cost which makes its practical use questionable

best achievable tracking performance in sampled data systems via lti controllers in this paper we study the problem of tracking a step reference signal using sampled data control systems we are interested in the tracking performance defined as the integral square of the tracking error response between the system s output and the reference input this performance is deemed the best achievable by a sampled data controller with a linear time invariant discrete time compensator if it is the minimal attainable by all such controllers that stabilize the system our primary objective is to investigate the fundamental tracking performance limit in sampled data systems and to understand whether and how sampling and hold in a sampled data system may impose intrinsic barriers to performance we consider two tracking performance measures with one defined with respect to the unit step signal and another with respect to a delayed step signal and averaged over one sampling period we derive an analytical closed form expression in each case for the best achievable performance the results show that a performance loss is generally incurred in a sampled data system in comparison to the tracking performance achievable by analog controllers this loss of performance as so demonstrated by the expressions is attributed to the non minimum phase behaviors as well as the intersample effects generated by samplers and hold devices thus sampled data controllers do result in an additional performance limit which is seen as a necessary tradeoff for other advantages offered by this class of controllers

trichotomous noise controlled signal amplification in a generalized verhulst model abstract the long time limit of the probability distribution and statistical moments for a population size are studied by means of a stochastic growth model with generalized verhulst self regulation the effect of variable environment on the carrying capacity of a population is modeled by a multiplicative three level markovian noise and by a time periodic deterministic component exact expressions for the moments of the population size have been calculated it is shown that an interplay of a small periodic forcing and colored noise can cause large oscillations of the mean population size the conditions for the appearance of such a phenomenon are found and illustrated by graphs implications of the results on models of symbiotic metapopulations are also discussed particularly it is demonstrated that the effect of noise generated amplification of an input signal gets more pronounced as the intensity of symbiotic interaction increases

further results on the l 1 analysis of sampled data systems via kernel approximation approach abstractthis paper gives two methods for the l1 analysis of sampled data systems by which we mean computing the l induced norm of sampled data systems this is achieved by developing what we call the kernel approximation approach in the setting of sampled data systems we first consider the lifting treatment of sampled data systems and give an operator theoretic representation of their input output relation we further apply the fast lifting technique by which the sampling interval 0 h is divided into m subintervals with an equal width and provide methods for computing the l induced norm in contrast to a similar approach developed earlier called the input approximation approach we use an idea of kernel approximation in which the kernel function of an input operator and the hold function of an output operator are approximated by piecewise constant or piecewise linear functions furthermore it is shown that the approximation errors in the piecewise constant approximation or piecewise linear appro

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

a simple derivation of the h2 optimal sampled data controllers abstract this paper gives a simple and elementary derivation of the h 2 optimal sampled data control problem formulated and studied independently by khargonekar and sivashankar and by bamieh and pearson

linear and nonlinear experimental regimes of stochastic resonance we investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode the experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude we observe both a regime described by the linear response theory and the nonlinear deviation from it in the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density when these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input

l sub 1 analysis and design of sampled data systems the focus of this work is l sub 1 optimal control of sampled data systems a converging approximation procedure is derived to compute the l sub infinity induced norm of closed loop finite dimensional linear time invariant lti sampled data systems an approximation method is developed to synthesize l sub 1 optimal sampled data regulators finally an example is provided that illustrates the l sub 1 analysis and design techniques presented

upper lower bounds of generalized h2 norms in sampled data systems with convergence rate analysis and discretization viewpoint abstract this paper considers linear time invariant lti sampled data systems and studies their generalized h 2 norms they are defined as the induced norms from l 2 to l in which two types of the l norm of the output are considered as the temporal supremum magnitude under the spatial norm and 2 norm the input output relation of sampled data systems is first formulated under their lifting based treatment we then develop a method for computing the generalized h 2 norms with operator theoretic gridding approximation this method leads to readily computable upper bounds as well as lower bounds of the generalized h 2 norms whose gaps tend to 0 at the rate of 1 n with the gridding approximation parameter n an approximately equivalent discretization method of the generalized plant is further provided as a fundamental step to addressing the controller synthesis problem of minimizing the generalized h 2 norms of sampled data systems finally a numerical example is given to show the effectiveness of the computation method

a bound of conservativeness in sampled data robust stabilization and its dependence on sampling periods abstract this paper investigates conservativeness of the l 2 induced norm in a sampled data robust stabilization problem namely it is shown that possible conservativeness of the l 2 induced norm can be bounded by difference between the best achievable performance of time invariant continuous time controllers and that of sampled data controllers moreover this difference is proven to approach zero as a sampling period tends to zero which means the conservativeness above loses importance when a sampling period is small these results are important because robust stabilization based on the l 2 induced norm is computationally inexpensive compared with robust stabilization based on the non conservative robust stability index one key lemma plays an essential role in this paper and it should be interesting independently

descent algorithms for optimal periodic output feedback control periodic output feedback is investigated in the context of linear quadratic regulation for finite dimensional time invariant linear systems discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control the optimal solution is obtained in two steps by separating the continuous time from the discrete time structure first the optimal pole placement problem under periodic output feedback is solved explicitly under the assumption that the behavior at the sample times has been specified in terms of a gain matrix g then the minimum value which depends on g is substituted into the overall objective this results in a finite dimensional nonlinear programming problem over all admissible gain matrices g the solution defines the optimal periodic output feedback control via the formulas of the optimal pole placement problem a steepest descent and a direct iterative method for solving this problem are formulated and compared numerical examples show that the performance using periodic output feedback is almost equivalent to that using optimal continuous state feedback

robust strong stabilization via modified popov controller synthesis in this paper the authors merge the parameter dependent lyapunov function framework used to construct robust popov controllers with the a priori and a posteriori approaches for obtaining stable compensators specifically the authors derive constructive sufficient conditions that yield robust lyapunov and asymptotically stable stabilizing popov dynamic compensators

computation oriented expression of a non conservative condition for robust stability of sampled data systems a new expression of a non conservative robust stability condition is derived for sampled data systems taking into consideration its convenience in numerical computation our expression is described using a global maximum of a certain differentiable function while the conventional expression includes a global maximum of a structured singular value which is expensive to compute when the sampling period is long the advantages of our expression become clear a possible problem is that the maximized function may be multimodal however the conventional expression has the same problem and even a local maximum is shown to give useful information our expression is applicable to a fairly large class of systems including the multi input multi output additive and multiplicative perturbation models using an example we show how our expression is computed and make a comparison with the conventional expression

an lmi solution to the robust synthesis problem for multi rate sampled data systems in this paper we address the asynchronous multi rate sampled data h synthesis problem necessary and sufficient conditions are given for the existence of a controller achieving the desired performance and the problem is shown to be equivalent to a convex optimization problem expressed in the form of linear operator inequalities in the case where the sample and hold rates are synchronous these operator inequalities reduce to linear matrix inequalities for which standard numerical software is available

noise enhanced stability of periodically driven metastable states we study the effect of noise enhanced stability of periodically driven metastable states in a system described by piecewise linear potential we find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system we analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations

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

the h 2 problem for sampled data systems m for sampled data systems in this paper we pose and give a complete solution to an analog of the h2 problem for sampled data system we motivate and develop a natural generalization of the h2 cost to periodic systems which is then applied to the continuous time closed loop mapping in a sampled data control system it is shown that the cost criterion developed is actually a norm in an space of hilbert schmidt operator valued functions we give state space solutions to the optimal and suboptimal controllers synthesis problems in this new norm by establishing an equivalent standard h2 problem

linear quadratic optimal sampled data control problems convergence result and riccati theory we consider a general linear control system and a general quadratic cost where the state evolves continuously in time and the control is sampled i e is piecewise constant over a subdivision of the time interval this is the framework of a linear quadratic optimal sampled data control problem as a first result we prove that as the sampling periods tend to zero the optimal sampled data controls converge pointwise to the optimal permanent control then we extend the classical riccati theory to the sampled data control framework by developing two different approaches the first one uses a recently established version of the pontryagin maximum principle for optimal sampled data control problems and the second one uses an adequate version of the dynamic programming principle in turn we obtain a closed loop expression for optimal sampled data controls of linear quadratic problems

separation of variables for the ruijsenaars system we construct a separation of variables for the classical n particle ruijsenaars system the relativistic analog of the elliptic calogero moser system the separated coordinates appear as the poles of the properly normalised eigenvector baker akhiezer function of the corresponding lax matrix two different normalisations of the ba functions are analysed the canonicity of the separated variables is verified with the use of the r matrix technique the explicit expressions for the generating function of the separating canonical transform are given in the simplest cases n 2 and n 3 taking the nonrelativistic limit we also construct a separation of variables for the elliptic calogero moser system

h sub 2 optimal sampled data control the h sub 2 optimal control of continuous time linear time invariant systems by sampled data controllers is discussed two different solutions state space and operator theoretic are given in both cases the h sub 2 sampled data problem is shown to be equivalent to a certain discrete time h sub 2 problem other topics discussed include input output stability of sampled data systems performance recovery in digital implementation of analog controllers and sampled data control of systems with the possibility of multiple time delays

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

quantum integrable systems and elliptic solutions of classical discrete nonlinear equations in spite of the diversity of solvable models of quantum field theory and the vast variety of methods the final results display dramatic unification the spectrum of an integrable theory with a local interaction is given by a sum of elementary energies e sum limits i varepsilon left u i right 1 1 where u i obey a system of algebraic or transcendental equations known as bethe equations 1 2 the major ingredients of bethe equations are determined by the algebraic structure of the problem a typical example of a system of bethe equations related to a i type models with elliptic r matrix is e 4 eta nu frac phi left u j right phi left u j 2 right mathop pi limits k frac sigma left eta left u j u k 2 right right sigma left eta left u j u k 2 right right 1 2 where x is the weierstrass function and phi left u right mathop pi limits k 1 n sigma left eta left u y k right right 1 3

an approach for measuring corporation financial stability by econophysics and bayesian method abstract corporation financial stability was investigated by the method of econophysics and bayesian approach in this paper a stochastic predator prey model was built to describe the corporation financial condition the mean limiting extinction time was proposed to measure the corporation financial stability the model parameters were estimated by using bayesian approach with real corporation financial data experimental results show that i an increase of system risk corresponds to a decrease of the corporation stability ii the optimal initial financial condition enhances the corporation stability to its maximum extent iii under the optimal initial financial condition the optimal system parameters and system risk strength can be observed

h2 optimal controllers with measurement feedback for continuous time systems flexibility in closed loop pole placement for a general h 2 optimal control problem at first all h 2 optimal measurement feedback controllers are characterized and parameterized and then attention is focused on controllers with observer based architecture both full order as well as reduced order observer based h 2 optimal controllers are characterized and parameterized also systematic methods of designing them are presented an important problem coined as an h 2 optimal control problem with simultaneous pole placement is formulated and solved that is since in general there exist many h 2 optimal measurement feedback controllers utilizing such flexibility and freedom we can solve the problem of simultaneously placing the closed loop poles at desirable locations whenever possible while still preserving h 2 optimality all the design algorithms developed here are easily computer implementable

the reachability and observability of hybrid multirate sampling linear systems this paper investigates algebraic sufficient necessary and sufficient conditions for sampling time reachability and observability in hybrid multirate sampling data linear systems for the cases of fast input and fast output sampling rates some implications in the context of closed loop pole placement under both properties under multirate sampling are heuristically discussed

baxter q operator from quantum k theory abstract we define and study the quantum equivariant k theory of cotangent bundles over grassmannians for every tautological bundle in the k theory we define its one parametric deformation referred to as quantum tautological bundle we prove that the spectrum of operators of quantum multiplication by these quantum classes is governed by the bethe ansatz equations for the inhomogeneous xxz spin chain in addition we prove that each such operator corresponds to the universal elements of quantum group u sl 2 in particular we identify the baxter operator for the xxz spin chain with the operator of quantum multiplication by the exterior algebra tautological bundle the explicit universal combinatorial formula for this operator is found the relation between quantum line bundles and quantum dynamical weyl group is shown