instantaneous frequency estimation of nonlinear frequency modulated signals in the presence of multiplicative and additive noise this paper addresses the problem of estimating the instantaneous frequency if of monocomponent nonlinear not necessarily polynomial frequency modulated fm signals affected by stationary multiplicative and additive noise both noise processes are assumed to be complex circular gaussian and independent the peak of the polynomial wigner ville distribution pwvd is proposed here as an if estimator we derive analytical expressions for the bias and asymptotic variance of the estimator and propose an algorithm to select the optimal window length to resolve the bias variance tradeoff in the if estimation simulation results are presented to confirm the theoretical results

subspace based algorithm for parameter estimation of polynomial phase signals in this correspondence parameter estimation of a polynomial phase signal pps in additive white gaussian noise is addressed assuming that the order of the pps is at least 3 the basic idea is first to separate its phase parameters into two sets by a novel signal transformation procedure and then the multiple signal classification music method is utilized for joint estimating the phase parameters with second order and above in doing so the parameter search dimension is reduced by a half as compared to the maximum likelihood and nonlinear least squares approaches in particular the problem of cubic phase signal estimation is studied in detail and its simplification for a chirp signal is given the effectiveness of the proposed approach is also demonstrated by comparing with several conventional techniques via computer simulations

on the assignment of invariant factors by time varying feedback strategies abstract in this paper the realization of arbitrary invariant factors or cyclic components of the closed loop system matrix is discussed it is shown that the use of time varying feedback strategies enables one to realize arbitrary invariant factors in contrast with time invariant feedback control

use of the design freedom of time optimal control abstract a method for synthesizing a state feedback time optimal controller for linear n state r input discrete time systems is developed the nonuniqueness of the solution is organized in such a way as to select the controller with the minimum value of the frobenius norm of the feedback gain matrix k it is shown that among the rn design parameters in the parametric form of k only r n rp r need to be considered in the search technique where p r is the order of the smallest jordan block in the jordan form of the closed loop system

deadbeat algorithms for output controllers in discrete time multivariable systems abstract this paper studies the problem of designing output deadbeat controllers to force the state of discrete time multivariable systems to zero in a finite number of samples two algorithms are considered the first is based on the fact that the closed loop eigenstructure assignable by output feedback is constrained by the requirement that the left and right eigenvectors must be in certain subspaces in the second algorithm the output gain matrix is computed through the optimization of certain parameters of the controller while maintaining its structural constraints computer programs have been developed to realize the two algorithms and examples are given to illustrate the feasibility of the techniques

simultaneous deadbeat tracking controller synthesis abstract a direct and simple design algorithm for the problem of simultaneously deadbeat tracking a prespecified class of inputs by only one controller is presented this novel approach is based on polynomial algebra and the principle of system realizability without solving linear polynomial diophantine equations the proposed procedure consists of solving a set of linear equations depending on system dynamics and yields the deadbeat controller in a compact form well suited for system with inaccessible states and changeable reference signals since all solutions are described in a parametric form some performance criteria can be easily incorporated as well examples are presented to illustrate the usefulness and computational easiness of this simple design algorithm

the design of deadbeat controllers by state transition graph two kinds of deadbeat control problems are considered one is the state deadbeat control problem and the other is the pointwise minimum time deadbeat control problem a simple graph called the state transition graph of a matrix is introduced and simple algorithms based on it giving deadbeat controllers are presented the set of pointwise minimum time deadbeat controllers is characterized the set of output feedback deadbeat controller is also considered

dead beat control of linear discrete time systems the paper considers the problem of determining the various classes of state feed back dead beat controllers for linear multivariable discrete time systems unlike earlier work attention is not restricted to the special case of minimum time dead beat controllers a general dead beat control problem is posed and solved the solution is based principally on an approach of closed loop eigenstructure assignment the minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix the concept of the greatest minimum of free parameters is introduced finally the method is illustrated by a numerical example

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

comments on design of optimal dead beat controllers it is shown that the system considered in the numerical example of the above paper belongs to a class of systems with n states and r inputs for which the set of all minimum time dead beat mtdb controllers is parameterized by an arbitrary matrix of order lambda 1 r n x n lambda r where is the greatest integer less than the ratio n r since the example treats the case of n 3 r 2 the mdtb controller is parameterized by a single scalar element

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

output dead beat control for a class of planar polynomial systems output dead beat control for a class of nonlinear discrete time systems which are described by a single input output i o polynomial difference equation is considered the class of systems considered is restricted to systems with a two dimensional state space description it is assumed that the highest degree with which the present input appears in the equation is odd necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented we also design a minimum time output dead beat control algorithm feedback controller which yields stable zero dynamics whenever this is feasible a number of interesting phenomena are discussed and illustrated with examples

pole placement for linear discrete time systems by periodic output feedbacks abstract necessary and sufficient conditions for the existence of a solution to the pole placement problem by periodic output feedbacks for single input single output linear discrete time systems are established an algorithm for finding a sequence of output feedback gains is presented and illustrated by a simple numerical example

instantaneous frequency estimation of polynomial fm signals using the peak of the pwvd statistical performance in the presence of additive gaussian noise the peak of the polynomial wigner ville distribution pwvd has been previously proposed as an estimator of the instantaneous frequency if for a monocomponent polynomial frequency modulated fm signal in this paper we evaluate the statistical performance of this estimator in the case of additive white gaussian noise and provide an analytical expression for the variance we show that for a given pwvd order the estimator performance can be improved by a proper choice of the kernel coefficients in the pwvd a performance comparison between the pwvd based if estimator and another previously proposed one based on the high order ambiguity function haf is also provided simulation results show that for a signal to noise ratio larger than 3 db the proposed sixth order pwvd outperforms the haf in estimating the if of a third or fourth order polynomial phase signal evaluated at the central point of the observation interval

polynomial wigner ville distributions and their relationship to time varying higher order spectra the wigner ville distribution wvd has optimal energy concentration for linear frequency modulated fm signals this paper presents a generalization of the wvd in order to effectively process nonlinear polynomial fm signals a class of polynomial wvd s pwvd s that give optimal concentration in the time frequency plane for fm signals with a modulation law of arbitrary polynomial form are defined a class of polynomial time frequency distributions ptfd s are also defined based on the class of pwvd s the optimal energy concentration of the pwvd enables it to be used for estimation of the instantaneous frequency if of polynomial fm signals finally a link between pwvd s and time varying higher order spectra tvhos is established just as the expected value of the wvd of a nonstationary random signal is the time varying power spectrum the expected values of the pwvd s have interpretations as reduced tvhos

robust stabilization of uncertain systems by periodic feedback an uncertain control system described by a family parametrized by an unknown parameter that takes values in a known constraint set is considered the robust stabilization problem is defined as finding a dynamic output controller that globally stabilizes the uncertain system that is no matter what the parameter value chosen by nature the closed loop system is globally asymptotically stable it is shown that in the class of dynamic periodic controllers the solution to this problem exists under reasonable assumptions given for a general family of abstract non linear models those assumptions in the case of a family of linear finite dimensional models are equivalent to suitable stabilizability and detectability assumptions for this case insensitivity of the design with respect to small errors in the data is proved

highly concentrated time frequency distributions pseudo quantum signal representation distributions that are highly concentrated in the time frequency plane are presented since the idea for these distributions originated from the wigner representation in the quantum mechanics a review of this representation is done in the first part of the paper abstracting the physical sense of the quantum mechanics representation we defined the pseudo quantum signal representation on the basis of a signal the pseudo wave function with the corresponding pseudo particle having the pseudo momentum sub p spl planck sub f spl omega is generated by varying the value of spl planck sub f one is in a position to influence the concentration of the pseudo quantum time pseudo momentum signal s presentation while keeping its most important time frequency properties invariant from this reflection an efficient distribution for the time frequency time pseudo momentum signal analysis is obtained this distribution produces as high a concentration in the time frequency time pseudo momentum plane as the l wigner distribution however it may satisfy the marginal properties the theory is illustrated with examples

radar maneuvering target motion estimation based on generalized radon fourier transform the slant range of a radar maneuvering target is usually modeled as a multivariate function in terms of its illumination time and multiple motion parameters this multivariate range function includes the modulations on both the envelope and the phase of an echo of the coherent radar target and provides the foundation for radar target motion estimation in this paper the maximum likelihood estimators mle are derived for motion estimation of a maneuvering target based on joint envelope and phase measurement phase only measurement and envelope only measurement in case of high signal to noise ratio snr respectively it is shown that the proposed mles are to search the maximums of the outputs of the proposed generalized radon fourier transform grft generalized radon transform grt and generalized fourier transform gft respectively furthermore by approximating the slant range function by a high order polynomial the inherent accuracy limitations i e the cramer rao low bounds crlb and some analysis are given for high order motion parameter estimations in different scenarios finally some numerical experimental results are provided to demonstrate the effectiveness of the proposed methods

a fast algorithm for estimating the parameters of a quadratic fm signal this paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated fm signal the proposed algorithm is fast in that it requires only one dimensional 1 d maximizations the optimal maximum likelihood method by contrast requires a three dimensional 3 d maximization which can only be realized with an exhaustive 3 d grid search asymptotic statistical results are derived for all the estimated parameters the amplitude estimate is seen to be optimal whereas the phase parameters are in general suboptimal of the four phase parameter estimates two approach optimality as the signal to noise ratio snr tends to infinity the other two have mean square errors that are within 50 of the theoretical lower bounds for high snr simulations are provided to support the theoretical results extensions to multiple components and higher order fm signals are also discussed

a phase error analysis of multigrid methods for hyperbolic equations in this paper we study the effects of the coarse grid correction process on multigrid convergence for hyperbolic problems in one and two dimensions we approach this from the perspective of phase error which allows us to exploit the hyperbolic nature of the underlying pde in particular we consider three combinations of coarse grid operators and coarse grid solution approaches 1 inexact coarse grid solve with direct discretization 2 exact coarse grid solve with direct discretization and 3 exact coarse grid solve with galerkin coarse grid operator for all these approaches we show that the convergence behavior of multigrid can be precisely described by the phase error analysis of the coarse grid correction matrix and we verify our results by numerical examples in one and two dimensions

ordering effects on relaxation methods applied to the discrete one dimensional convection diffusion equation the authors present an analysis of relaxation methods for the one dimensional discrete convection diffusion equation based on norms of the iteration matrices in contrast to standard analytic techniques that use spectral radii these results show how the performance of iterative solvers is affected by directions of flow associated with the underlying operator and by orderings of the discrete grid points in particular for problems of size n relaxation against the flow incurs a latency of approximately n steps in which convergence is slow and red black relaxation incurs a latency of approximately n 2 steps there is no latency associated with relaxation that follows the flow these results are largely independent of the choice of discretization

regulation of time invariant discrete time descriptor systems time invariant discrete time descriptor systems of the form exk 1 axk buk where e and a are n n matrices and e may be singular are considered the problem is to find a feedback law uk kxk that drives the descriptor from x 0 to the origin in less than n time steps

finite settling time stabilisation for multivariable discrete time systems a polynomial equation approach the multivariable case of finite settling time stabilisation fsts of linear discrete time systems is considered in this paper an algebraic approach is adopted which leads to the solution of a polynomial matrix diophantine equation this gives rise to the parametrisation of all fsts controllers in a kucera youla bonjiorno sense and the fsts problem is further reduced to a linear algebra problem over the real numbers subsequently the family of all causal fsts controllers is parametrised and necessary and sufficient conditions for strong fsts stable controllers are derived the minimal mcmillan degree solution and minimal complexity controllers are examined and new bounds are given the analysis provides the means for the parametrisation of families of fsts controllers with certain complexity finally the problems of tracking disturbance rejection and partially assigned dynamics in fst sense are considered and conditions for their solvability are given

a computationally efficient technique for estimating the parameters of polynomial phase signals from noisy observations many real world applications are characterized by the presence of polynomial phase signals embedded in noise these applications include radar sonar telemetry communications and power systems in a significant number of these applications it is highly desirable to be able to accurately estimate the polynomial phase signal parameters this correspondence presents a computationally efficient method for estimating any or all of the parameters of polynomial phase signals in white gaussian noise and provides a first order statistical analysis of the technique simulations are also presented to support the theoretical analysis

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

deadbeat control of linear discrete time systems by periodic output feedback two deadbeat control problems for open loop time invariant linear discrete time multivariable systems by periodic output feedbacks are formulated and solved sufficient conditions for the existence of solutions to the problems are established procedures for finding solutions to the problems are presented and illustrated by numerical examples

fifo stable control systems abstract motivated by the dead beat and shortest correlation control strategies the paper introduces the notion of finite input finite output fifo stability for linear discrete time control systems a simple parametrization of all controllers that fifo stabilize a given plant is obtained the best controller is then chosen for various applications including h 2 optimization disturbance rejection and transfer function shaping

deadbeat error control of discrete multivariable systemsdagger abstract the main objective of this paper is to delineate conditions under which deadbeat error control can be achieved between a plant output and a discrete reference input signal all facets of this problem are considered in the linear multivariable case i e when the reference is any non diminishing signal whether the plant is truly discrete or a discretized continuous one and whether the initial conditions are zero or unknown the results presented can also be used to resolve the case of known non zero initial conditions on the state of the plant as well as the compensator

design of higher order polynomial wigner ville distributions the polynomial wigner ville distribution pwvd is a time frequency signal analysis tool for representing polynomial frequency modulated fm signals we present an optimization procedure to design pwvds and discuss the need for higher order pwvds

analysis of moving source characteristics using polynomial chirplet transform the received doppler signal of a stationary sensor as emitted by a transiting acoustic source is used to estimate source motion parameters including speed closest distance rest frequency and closest point of approach cpa time first the instantaneous frequency amplitude and cpa time are accurately estimated by the polynomial chirplet transform of the doppler signal thereafter the three other source motion parameters are obtained with a simplified amplitude weighted nonlinear least squares method the proposed scheme is successfully applied to the analysis of the characteristics of a moving truck

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

a direct computation of state deadbeat feedback gains a method for computing a feedback gain that achieves state deadbeat control is given from systems given in the staircase form this method derives the deadbeat gain in a numerically reliable way it is shown that the gain turns out to be lq optimal for some weightings

the effect of sampling period on the behaviour of systems incorporating state feedback an exposition of the effects of sampling on the controllability characteristics and the kronecker invariants of the plant and the input matrices of sampled data systems is presented in particular the effect of sampling period on the feedback matrix for time optimal control of sampled data systems is investigated in detail and it is shown that different classes of systems produce different response characteristics as the sampling period becomes large also simple expressions for a nt in terms of a t and b nt as a function of a t and b t are derived these expressions are computationally attractive and therefore facilitate the study of the effect of sampling period on system behaviour by applying these expressions the effects of sampling period on the feedback matrices for time optimal control of three classes of systems whose open loop plants are asymptotically stable marginally stable and unstable are illustrated by numerical examples

fast computation of multiphase flow in porous media by implicit discontinuous galerkin schemes with optimal ordering of elements we present a family of implicit discontinuous galerkin schemes for purely advective multiphase flow in porous media in the absence of gravity and capillary forces to advance the solution one time step one must solve a discrete system of nonlinear equations by reordering the grid cells the nonlinear system can be shown to have a lower triangular block structure where each block corresponds to the degrees of freedom in a single or a small number of cells to reorder the system we view the grid cells and the fluxes over cell interfaces as vertices and edges in a directed graph and use a standard topological sorting algorithm then the global system can be computed by processing the blocks sequentially using a standard newton raphson algorithm for the degrees of freedom in each block decoupling the system offers greater control over the nonlinear solution procedure and reduces the computational costs memory requirements and complexity of the scheme significantly in particular the first order version of the method may be at least as efficient as modern streamline methods when accuracy requirements or the dynamics of the flow allow for large implicit time steps

on the general solution of the state deadbeat control problem in this note the state deadbeat control problem is considered it is shown that after appropriate change of basis of input and state spaces the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix this result yields a very simple procedure for the calculation of a state feedback deadbeat control gain it also provides the number of free parameters which could be used for further design purposes the results are illustrated by an example at the end of the note

stabilizability and dead beat controllers for two classes of wiener hammerstein models two classes of block oriented models of the wiener hammerstein type are considered we prove that a generic condition is sufficient for a null controllable discrete time system of this form to have a stabilizing minimum time dead beat controller when the condition is violated we show how to design a nonminimum time stabilizing dynamic dead beat controller the result is used to obtain stabilizability conditions for these systems

random denoising and signal nonlinearity approach by time frequency peak filtering using weighted frequency reassignment abstracttime frequency peak filtering tfpf may efficiently suppress random noise and hence improve the signal to noise ratio however the errors are not always satisfactory when applying the tfpf to fast varying seismic signals we begin with an error analysis for the tfpf by using the spread factor of the phase and cumulants of noise this analysis shows that the nonlinear signal component and non gaussian random noise lead to the deviation of the pseudo wigner ville distribution pwvd peaks from the instantaneous frequency the deviation introduces the signal distortion and random oscillations in the result of the tfpf we propose a weighted reassigned smoothed pwvd with less deviation than pwvd the proposed method adopts a frequency window to smooth away the residual oscillations in the pwvd and incorporates a weight function in the reassignment which sharpens the time frequency distribution for reducing the deviation because the weight function is determined by the lateral coherence of seismic

characterization of polynomial functions and application to time frequency analysis we propose necessary and sufficient conditions for a function spl phi t to be a polynomial and establish a formula that allows us to compute the value of the derivative spl phi t of a polynomial at any point in terms of the values of this polynomial for this purpose we establish that any polynomial spl phi t of degree spl les q can be represented as a linear combination of spl phi t t sub 1 q t t sub q where t sub 1 t sub q denote arbitrary parameters a similar property is established for the derivative spl phi t some signal processing applications of these results are discussed

space time domain decomposition for parabolic problems we analyze a space time domain decomposition iteration for a model advection diffusion equation in one and two dimensions the discretization of this iteration is the block red black variant of the waveform relaxation method and our analysis provides new convergence results for this scheme the asymptotic convergence rate is super linear and it is governed by the diffusion of the error across the overlap between subdomains hence it depends on both the size of this overlap and the diffusion coefficient in the equation however it is independent of the number of subdomains provided the size of the overlap remains fixed the convergence rate for the heat equation in a large time window is initially linear and it deteriorates as the number of subdomains increases the duration of the transient linear regime is proportional to the length of the time window for advection dominated problems the convergence rate is initially linear and it improves as the the ratio of advection to diffusion increases moreover it is independent of the size of the time window and of the number of subdomains numerical calculations illustrate our analysis

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

ripple free deadbeat control for sampled data systems in this paper the ripple free deadbeat control problem for sampled data systems is considered this control objective is to settle the error to zero for all time after some finite settling time in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled data systems the necessary and sufficient conditions to solve this problem are derived and related to the system type and a method of constructing the ripple free deadbeat control system is presented

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

parametrized solution of the periodic dead beat control problem the dead beat control problem for linear periodic discrete time systems in presence of unmeasurable disturbances and external reference signals is considered using a polynomial method a parametrization of all causal output feedback controllers solving the problem is provided

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

deadbeat servoproblem for multivariable n d systems sufficient conditions are given for the existence of a solution to the deadbeat servoproblem for multivariable n d linear systems an algorithm is presented for finding matrices of an n d linear controller the algorithm is illustrated by a simple example

state deadbeat control of nonlinear systems construction via sets a geometric generalization of the discrete time linear deadbeat control problem is studied the proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of the deadbeat feedback law and tracker dynamics are provided for an example system based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given

aircraft flight parameter estimation based on passive acoustic techniques using the polynomial wigner ville distribution the acoustic signal from an overflying aircraft as heard by a stationary observer is used to estimate an aircraft s constant height ground speed range and acoustic frequency central to the success of this flight parameter estimation scheme is the need for an accurate estimate of the instantaneous frequency of the observed acoustic signal in this paper the polynomial wigner ville distribution is used in this application as the instantaneous frequency estimator its performance and the issue of the optimal time domain window length are addressed

generalized high order phase function for parameter estimation of polynomial phase signal the high order phase function hpf has been introduced recently to estimate the parameters of a polynomial phase signal pps in this correspondence we generalize the standard hpf by introducing multiple time instants thus the standard hpf can be treated as a special example of the generalized hpf with identical time instants we propose a procedure for finding time instants minimizing the mean square error mse the proposed method achieves better performances than the high order ambiguity function haf and polynomial wigner ville distribution pwvd the theoretical analysis as well as the monte carlo simulations verify the advantages such as lower mse and lower snr threshold for the pps

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

a note on dead beat controllability of generalised hammerstein systems necessary and sufficient conditions for dead beat and complete controllability for a class of generalised hammerstein systems are presented since the system s structure is very close to linear only linear algebra is used for the controllability test the test is very simple and easy to use a closed loop minimum time dead beat controller can be designed for a subclass of generalised hammerstein systems using the grobner basis method

on the polynomial matrix equation ax yb c in this note an algorithm for finding a unique solution x y of the bilateral polynominal matrix equation ax yb c is presented the solution is obtained by solving a set of linear equations relations between the bilateral polynomial equation and the unilateral one are also discussed

optimal hold functions for sampled data regulation abstract this paper investigates the use of generalized sampled data hold function control gshf to optimize quadratic measures of performance in sampled data control loops the idea of gshf control is to use sampled data feedback but consider the hold function as a design parameter explicit solutions are given for the gshf versions of the optimal lq and lqg regulators the questions of existence uniqueness and computation of optimal hold functions are treated an example is presented

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

extending the performance of the cubic phase function algorithm this paper details an algorithm for estimating the parameters of cubic phase signals embedded in additive white gaussian noise the new algorithm is an extension of the cubic phase cp function algorithm with the extension enabling performance at lower signal to noise ratios snrs this improvement in the snr performance is achieved by coherently integrating the cp function over a compact interval in the two dimensional cp function space the computation of the new algorithm is quite moderate especially when compared to the maximum likelihood ml technique above threshold the algorithm s parameter estimates are asymptotically efficient a threshold analysis of the algorithm is presented and is supported by simulation results a method for extending the capability of this algorithm to process higher degree phase signals is also presented furthermore the algorithm is applied to a real data signal

deadbeat ripple free tracking with disturbance rejection a polynomial approach the deadbeat ripple free tracking problem for sampled data systems is considered it is assumed that both the state and the output of the continuous time plant to be controlled are affected by external disturbances a polynomial approach is adopted and solvability conditions are given both in terms of the sampled system and of the original continuous time one

a crosswind block iterative method for convection dominated problems this paper is on a block iterative algorithm for convection dominated equations the algorithm uses crosswind thin blocks in a block gauss seidel method the relaxation sweep is carried out successively along the downwind direction and exact solvers are used for the block systems this method is efficient for convection dominated problems discretized by monotone finite element finite difference schemes such as the edge average finite element method an optimal partitioning and ordering algorithm tarjan s algorithm is used to partition the nodes into crosswind blocks and order the blocks in the downwind direction the convergence of this block iterative method is analyzed and exponential convergence rates are proved for both one and two dimensional cases on both structured and unstructured meshes our empirical and analytical studies indicate that crosswind grouping is essential for the rapid convergence of the method and merely ordering the nodes along the downwind direction is not good enough some numerical examples are given to illustrate the effectiveness of the proposed algorithm for convection dominated problems and to compare it with other popular algorithms

a general riccati equation solution to the deadbeat control problem it is well known that the state of a controllable system can be driven to zero in minimum time for arbitrary initial condition by the time varying kalman gain sequence computed via a singular riccati equation this paper shows how a constant deadbeat control feedback which will accomplish the same result in the same minimum time can always be found via the same riccati equation

on multigrid solution of high reynolds incompressible entering flows an approach is presented for effectively separating the solution process of the elliptic component of high reynolds incompressible steady entering flow for which classical multigrid techniques are well suited from that of the non elliptic part for which other methods are more effective it is shown by analysis and numerical calculations that such an approach is very effective in terms of asymptotic convergence as well as reduction of errors well below discretization level in a 1 fmg algorithm

brief paper multivariable closed loop deadbeat control a polynomial matrix approach the closed loop deadbeat servo problem cdsp considered in this paper consists of the synthesis of a linear output feedback controller such that the control signal and tracking error both vanish after a finite period of time for every reference sequence from a prespecified class and for every initial state of a plant and the controller the closed loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance a new theorem asserts that if an open loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class then cdsp is solvable and all desired control laws are found in an explicit parametric form by solving simple unilateral linear equations in polynomial matrices on the basis of this theorem a design algorithm is developed asymptotic stability of the closed loop system exhibiting deadbeat properties is demonstrated a numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented

closed loop expressions of minimum energy control for single input linear digital systems closed loop expressions for the minimum energy control of a single input linear digital system are described they are obtained by two different methods the optimal inputs are given by state feedback with the bounded variable gains the gains are independent of the initial state of the system