equivalence of n dimensional roesser and fornasini marchesini models an equivalent roesser model is obtained for an arbitrary fornasini marchesini model in n dimensions and vice versa both the regular and singular cases are covered

walsh function analysis of 2 d generalized continuous systems the importance of the generalized or singular 2d continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables a technique is presented for solving these systems in terms of walsh functions the method replaces the solution of a two variable partial differential equation with the solution of a linear algebraic generalized 2d sylvester equation an efficient technique for the recursive solution of the latter equation is offered all the results apply also in the usual roesser 2d state space case

transformations of matrix pencils and implications in linear systems theory a new transformation of matrix pencils is proposed and its theory formally developed its restriction to generalized state space system matrix pencils is shown to be an appropriate generalization of the usual state space transformation and to represent a closed form expression in system matrix terms of verghese s concept of strong equivalence of such pencils

the stability for a one dimensional wave equation with nonlinear uncertainty on the boundary abstract in this work we are concerned with the boundary stabilization of a one dimensional wave equation subject to boundary nonlinear uncertainty the nonlinear uncertainty is first estimated in terms of the output and then canceled by its estimates we show that this strategy works well when the derivative of the uncertainty is bounded

matrix rank based conditions for reachability controllability of discrete linear repetitive processes abstract this paper uses both 2d and standard or 1d representations of the dynamics of discrete linear repetitive processes to characterise their reachability controllability properties the major new results are a 1d representation of constant dimensions and characterisations of reachability controllability in terms of matrix rank based conditions

matrix description of multivariable polynomials abstract a new multiway description of multivariable polynomials is presented applications to linear transformations of polynomial variables the cayley hamilton theorem and polynomial factorizability are given

analysis and control of the jump modes behavior of 2 d singular systems part i structural stability this paper considers the problem of structural stability of 2 d singular systems firstly some properties of structural stability of 2 d general singular systems are presented sufficient and necessary conditions for the structural stability of the 2 d singular systems are given then by extending the lyapunov approach for the structural stability of 1 d continuous singular systems to the discrete case a generalized lyapunov equation approach to the analysis of the structural stability of 2 d singular roesser models 2 d srm is proposed the existence of a solution to the generalized lyapunov equation gives a sufficient condition for the structural stability of the 2 d srm

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

analysis of modified smi method for adaptive array weight control the authors characterize the performance of the diagonally loaded sample matrix inverse smi algorithm versus the number k of snapshots used in the covariance matrix estimate by providing o 1 k statistics bias and variance of the array weights output powers and output power ratios such as signal to interference noise ratio sinr and inr the approach accommodates wideband signals monte carlo simulations verify the theoretical analysis

computing the state difference equations for discrete overdetermined linear m d systems we derive an algorithm that computes the state difference equations for a given set of poles of linear discrete overdetermined autonomous m d systems these difference equations allow the realization of the dynamical system by means of delay multiplication and addition elements in simulation diagrams in doing so we generalize the classical cayley hamilton theorem to multivariate polynomial ideals and provide a system theoretic interpretation to the notion of polynomial ideals leading monomials and grobner bases furthermore we extend the problem to include poles at infinity and so arrive at a description of overdetermined descriptor systems this results in a new state space description of autonomous m d descriptor systems in addition we discuss the separation of the state variables of singular m d systems into a regular and singular part a sufficient condition under which these two state vector parts can be interpreted as a forward evolving regular part and a backward evolving singular part is given the robustness and efficiency of the developed algorithms are demonstrated via numerical experiments

on the analysis of discrete linear time invariant singular systems the discrete singular equation over an interval can represent a two point boundary value problem or it can be considered as a dynamical relation developing forward in time a theory is provided by giving analytic solutions and discussing system properties in both cases that encompasses both interpretations the singular system fundamental matrix is used to provide analytic solutions to a time invariant discrete singular equation defined over an interval the two distinct cases in which the singular relation is interpreted as a two point boundary value problem or as a forward dynamical system on the interval are both considered also considered is the case in which the singular relation is considered as a backward dynamical system and the relationship between the index of nilpotence and the laurent series coefficients resulting from the solutions of certain state space equations is shown reachability and observability are discussed and the point is made that these properties are different depending on how the singular relation is interpreted

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

the linear quadratic optimal regulator for singular 2 d systems with variable coefficients the linear quadratic optimal regulator problem for singular 2 d linear systems with variable coefficients has been formulated sufficient conditions for the existence of a solution to the problem have been established an optimal sequence of input vectors can be found with slight modification the considerations can be extended for singular n d linear systems with variable coefficients

boundary value descriptor systems well posedness reachability and observability in this paper we introduce the class of two point boundary value descriptor systems tpbvds discrete time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system s interval of definition by introducing a standard form for regular pencils we obtain a new and simple generalized cayley hamilton theorem that simplifies our investigation of well posedness green s function solutions and reachability and observability for tpbvds there are two distinct notions of reachability and observability that one can define for tpbvds associated with processes that propagate inward from and outward toward the boundaries we investigate each of these in detail obtaining among other things far simpler forms for the reachability and observability results than found previously in the literature in addition we describe several methods for the efficient solution of tpbvds one involving recursions from each end of t

solutions to the output regulation problem of linear singular systems in this paper we revisit the output regulation problem for linear singular systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated we derive a necessary and sufficient condition for the regulation problem to be solvable via either full information feedback or error feedback then we show how full information feedback and error feedback controllers can be constructed explicitly

multidimensional realisation theory and polynomial system solving abstractmultidimensional systems are becoming increasingly important as they provide a promising tool for estimation simulation and control while going beyond the traditional setting of one dimen

convergence of the smi and the diagonally loaded smi algorithms with weak interference adaptive array approximations for the power levels at the output of an adaptive array that uses the diagonally loaded sample matrix inversion smi algorithm are derived diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion the authors examine how the signal to interference plus noise ratio sinr and signal to interference ratio sir at the array output vary with the number of samples taken when the input signals are continuous wave it is shown that positive loading produces more rapid convergence with a reduction in output sir negative loading provides an improved sir level but it is shown that positive loading produces more rapid convergence with a reduction in output sir negative loading provides an improved sir level but it is shown that the output power levels are erratic and slow to converge simulation results which verify the theoretical procedure are given

perfect observers for singular 2 d fornasini marchesini models a concept of the perfect observer for singular two dimensional 2 d fornasini marchesini models is proposed sufficient conditions are established for the existence of the perfect observer a procedure for design of the perfect observer is also derived and illustrated by a numerical example

a geometric approach to the theory of 2 d systems the authors develop a geometric approach to the theory of 2 d two dimensional systems defining in a suitable way the notion of a sub 1 2 b sub 1 2 invariant subspaces and of controlled invariant subspaces such subspaces are shown to have good computational and feedback properties which make them useful in application in particular sufficient conditions and constructive procedures are obtained for the solutions of disturbance decoupling and model matching problems moreover it is shown that certain structural properties of a 2 d system can be described by means of a set of indexes defined in geometric terms and that such structural indexes can be used to reformulate the sufficient condition for model matching

a review of 2 d implicit systems abstract the one dimensional notion of causality has no counterpart in the two dimensional plane where at best partial orderings of i j may be defined two dimensional implicit systems unlike the familiar state space 2 d models do not require any notion of causality or recursibility instead they require the milder notion of regularity thus the implicit models are more suited to the description of naturally occurring two dimensional systems such as are described by the hyperbolic equation and the heat equation as well as for applications in image processing this paper provides a brief summary of the current state of the theory of 2 d implicit systems

general response formula and minimum energy control for the general singular model of 2 d systems the general response formula for the general singular model of 2 d linear systems is derived the concepts of local reachability and local controllability are extended to the singular model necessary and sufficient conditions for local reachability and local controllability are established the minimum energy control problem for the singular model is formulated and solved

boundary recursion for descriptor variable systems it is shown that if an n dimensional descriptor variable system satisfies the properties of solvability and controllability the family of solutions is n dimensional and the set of two point boundary values that are consistent with the system can be expressed as the solutions to a linear system of equations involving only the boundary values this equation is termed a boundary mapping equation and it provides a compact representation of the system the boundary mapping generalizes the state transition matrix associated with state variable systems the author presents the boundary mapping theory describes the recursive processes required and applies both to some special cases including general linear time invariant systems and adjoint systems

local exponential stabilization of fisher s equation using the backstepping technique abstract this paper deals with the boundary stabilization problem for the 1d fisher s partial differential equation pde defined on a bounded interval which is a nonlinear unstable distributed parameter system the stabilizing controller derived using the backstepping technique for linear parabolic pdes associated with fisher s pde can be extended to the nonlinear case in the work we can prove that the boundary controller based on the linear backstepping synthesis approach can make the closed loop nonlinear fisher s system exponentially stable with any desired decay rate locally in both l 2 0 1 and h 1 0 1 respectively the effectiveness of the control synthesis approach is illustrated by a numerical simulation

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

stability analysis of the anti stable heat equation with uncertain disturbance on the boundary abstract in this paper we study the stability of the anti stable 1 d heat equation with uncertain disturbance on the boundary we first estimate the disturbance in terms of the output then we design some control strategy to stabilize the anti stable system

fundamental reachability and observability matrices for discrete descriptor systems this paper uses the fundamental matrix of a regular discrete descriptor system to derive expressions for descriptor reachability and observability matrices reachable and unobservable subspaces are defined it is shown that the natural space for analyzing descriptor system properties is r 2n where n is the dimension of the system not rnas is the case for state space systems solutions are provided for the descriptor open loop control and estimation problems

computation of the transfer function matrix and its laurent expansion of generalized two dimensional systems an algorithm is developed for the computation of the transfer function matrix of a two dimensional system which is given in its generalized form the algorithm is a recursion in terms of the original system matrix and does not require the inversion of a two variable polynomial matrix an algorithm for the evaluation of the laurent expansion of the inverse of a two variable polynomial matrix is also presented

the general state space model for a two dimensional linear digital system the general state space model for a 2 d linear digital system is presented a new definition of state transition matrix is given based on the definition it is easy to calculate the state transition matrix for any linear digital system the general response formula for a system follows simply from the definition a new definition of the characteristic function of a system and a theorem parallel to the cayley hamilton theorem are also given the presented results apply to any linear causal system

performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest diagonal loading is one of the most popular techniques to improve robustness in this paper we present a theoretical analysis of the signal to interference plus noise ratio sinr for the class of beamformers based on generalized i e not necessarily diagonal loading of the covariance matrix in the presence of random steering vector errors a closed form expression for the sinr is derived that is shown to accurately predict the sinr obtained in simulations this theoretical formula is valid for any loading matrix it provides insights into the influence of the loading matrix and can serve as a helpful guide to select it finally the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal sinr

descriptor systems expanded descriptor equation and markov parameters generalized concepts of solvability and conditionability are presented for descriptor systems and tests are given for these generalized properties an expression is derived for descriptor system markov parameters the notion of expanded descriptor equation is presented

rosenbrock models and their homotopy equivalence as is known the notion of homotopy equivalence is a fundamental notion of mathematics and was introduced in order to formalize a relation that is weaker than isomorphism in this note we define a homotopy equivalence of rosenbrock systems and show that it coincides with the classical equivalences of rosenbrock and fuhrmann next we show that the homotopy equivalence does preserve the important properties of a system including the properties at infinity when these are properly understood finally we define in a simple manner the states and motions of a system and claim that they are homotopy invariants

the singular general model of 2d systems and its solution a general singular model for 2d linear discrete systems with constant coefficients is defined necessary and sufficient conditions for the existence of a solution to the model are established the considerations of the author s previous work 1986 can be extended to singular models of 2d linear systems with variable coefficients

adaptive boundary control for unstable parabolic pdes part i lyapunov design we develop adaptive controllers for parabolic partial differential equations pdes controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain these are the first adaptive controllers for unstable pdes without relative degree limitations open loop stability assumptions or domain wide actuation it is the first necessary step towards developing adaptive controllers for physical systems such as fluid thermal and chemical dynamics where actuation can be only applied non intrusively the dynamics are unstable and the parameters such as the reynolds rayleigh prandtl or peclet numbers are unknown because they vary with operating conditions our method builds upon our explicitly parametrized control formulae to avoid solving riccati or bezout equations at each time step most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree

a fundamental notion of equivalence for linear multivariable systems a fundamental form of equivalence of polynomial matrix descriptions of linear multivariable systems is defined based on the existence of a bijective map between the finite and infinite solution sets of the differential equations describing the two systems the connection with the system matrix relationship of full system equivalence is established

infinite frequency structure preserving transformations for general polynomial system matrices a recent transformation proposed for polynomial matrices is extended to the systems theory case of general polynomial system matrices two such extensions are proposed depending on whether the system matrix or its normalized form is used the relationship between both these transformations is established and under them all finite and infinite frequency system zero and pole structure is shown to be invariant

a causal realization theory part i linear deterministic systems we study acausal linear systems their controllability and observability properties and the weighting patterns that they realize a complete classification is given of all minimal real analytic realizations of a given weighting pattern and of all minimal autonomous realizations of a stationary weighting pattern

fundamental equivalence of generalized state space systems this paper defines a fundamental form of equivalence between two generalized state space systems in terms of mappings of the solution sets of the describing differential equations together with mappings of the sets of restricted initial conditions properties of this equivalence relation are discussed and it is shown to be an alternative characterization of the system matrix relationship of complete system equivalence

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

control of 1 d parabolic pdes with volterra nonlinearities part i design boundary control of nonlinear parabolic pdes is an open problem with applications that include fluids thermal chemically reacting and plasma systems in this paper we present stabilizing control designs for a broad class of nonlinear parabolic pdes in 1 d our approach is a direct infinite dimensional extension of the finite dimensional feedback linearization backstepping approaches and employs spatial volterra series nonlinear operators both in the transformation to a stable linear pde and in the feedback law the control law design consists of solving a recursive sequence of linear hyperbolic pdes for the gain kernels of the spatial volterra nonlinear control operator these pdes evolve on domains t n of increasing dimensions n 1 and with a domain shape in the form of a hyper pyramid 0 x n x n 1 x 1 x 1 we illustrate our design method with several examples one of the examples is analytical while in the remaining two examples the controller is numerically approximated for all the examples we include simulations showing blow up in open loop and stabilization for large initial conditions in closed loop in a companion paper we give a theoretical study of the properties of the transformation showing global convergence of the transformation and of the control law nonlinear volterra operators and explicitly constructing the inverse of the feedback linearizing volterra transformation this in turn allows us to prove l 2 and h 1 local exponential stability with an estimate of the region of attraction where possible and explicitly construct the exponentially decaying closed loop solutions

elementary operations and equivalence of two dimensional systems this paper employs two dimensional elementary operations to construct a number of singular and standard roesser type state space realizations of two dimensional linear systems the main result consists of the development of the basic algorithm together with some algebraic properties

the active disturbance rejection control approach to stabilisation of coupled heat and ode system subject to boundary control matched disturbance we consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation subject to boundary control matched disturbance the active disturbance rejection control approach is applied to estimate in real time the disturbance with both constant high gain and time varying high gain the disturbance is cancelled in the feedback loop the closed loop systems with constant high gain and time varying high gain are shown respectively to be practically stable and asymptotically stable

further study on robust adaptive beamforming with optimum diagonal loading significant effort has gone into designing robust adaptive beamforming algorithms to improve robustness against uncertainties in array manifold these uncertainties may be caused by uncertainty in direction of arrival doa imperfect array calibration near far effect mutual coupling and other mismatch and modeling errors a diagonal loading technique is obligatory to fulfil the uncertainty constraint where the diagonal loading level is amended to satisfy the constrained value the major drawback of diagonal loading techniques is that it is not clear how to get the optimum value of diagonal loading level based on the recognized level of uncertainty constraint in this paper an alternative realization of the robust adaptive linearly constrained minimum variance beamforming with ellipsoidal uncertainty constraint on the steering vector is developed the diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique which provides loading on demand mechanism rather than fixed continuous or ad hoc loading we additionally enrich the proposed robust adaptive beamformers by imposing a cooperative quadratic constraint on the weight vector norm to overcome noise enhancement at low snr several numerical simulations with doa mismatch moving jamming and mutual coupling are carried out to explore the performance of the proposed schemes and compare their performance with other traditional and robust beamformers

the linear quadratic optimal regulator for descriptor systems in this paper we investigate the linear quadratic optimal regulator problem for the continuous time descriptor system e dot x ax bu where e is in general a singular matrix we solve first a general finite horizon problem by applying the calculus of variations to derive the optimal trajectory of the vector consisting of the concatenated descriptor codescriptor and control vectors from this trajectory the optimal feedback gain relating the control and descriptor variable can be computed by transforming to a coordinate system which can be computed by performing a singular value decomposition of e we derive several riccati differential equations all of which have the same solution this solution gives the optimal cost the steady state optimal feedback gain can be computed by solving an eigenvalue eigenvector problem formulated from the untransformed system parameters in general there does not exist a unique optimal feedback gain but rather the gain is constrained to lie in a linear variety whose dimension is equal to the number of inputs times the rank deficiency of e

algorithms for the computation of the transfer function matrix for two dimensional regular and singular general state space models the problem of computing the transfer function matrices for regular and singular discrete two dimensional general state space models 2d gm is discussed and some programmable algorithms are developed that generalize the well known leverrier algorithm to 2d systems of general form the results also show that the transfer function matrices for regular and singular 2d gm can also be formulated via the state transition matrices of the systems

on the control of linear systems whose coefficients are functions of parameters the stabilization and regulation of linear discrete time systems whose coefficients depend on one or more parameters is studied for linear systems whose coefficients are continuous functions of real or complex parameters respectively analytic or rational functions of real parameters it is shown that reachability of the system for all values of the parameters implies that the system can be stabilized using gains that are also continuous analytic rational functions of the parameters closed form expressions for a collection of stabilizing gains are given in terms of the reachability gramian for systems which are stabilizable for all values of the parameters it is shown that continuous analytic rational stabilizing gains can be computed from a finite time solution to a riccati difference equation whose coefficients are functions of the parameters these results are then applied to the problem of tracking and disturbance rejection in the case when both the plant and the exogenous signals contain parameters

the fornasini marchesini and the roesser models algebraic methods for recasting this paper is devoted to giving a new method for recasting the fornasini marchesini model of the two dimensional system to the roesser form endowed with an important feature that the dimensions of both models are the same the two dimensional similarity transformation and spectral transformations of the transfer function variables are used for this purpose both the standard and singular cases are considered

on the convergence of an extended state observer for nonlinear systems with uncertainty abstract the extended state observer first proposed by jingqing han in j q han a class of extended state observers for uncertain systems control decis 10 1 1995 85 88 in chinese is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering unfortunately there is no rigorous proof of convergence to date in this paper we attempt to tackle this long unsolved extraordinary problem the main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance for which the effect of total disturbance error is eliminated by the high gain

infinite elementary divisors of a matrix polynomial and implications a new characterization of infinite poles and zeros in terms of a natural extension of the idea of infinite elementary divisors of a matrix pencil to matrix polynomials is developed it is used to show that two previous descriptions of infinite frequency structure are equivalent subsequently a polynomial matrix transformation which simultaneously preserves the finite and infinite zero structure is presented

bounded real lemma and robust h control of 2 d singular roesser models abstract this paper discusses the problem of robust h control for linear discrete time two dimensional 2 d singular roesser models 2 d srm with time invariant norm bounded parameter uncertainties the purpose is the design of static output feedback controllers such that the resulting closed loop system is acceptable jump modes free stable and satisfies a prescribed h performance level for all admissible uncertainties a version of bounded realness of 2 d srm is established in terms of linear matrix inequalities based on this a sufficient condition for the solvability of the robust h control problem is solved and a desired output feedback controller can be constructed by solving a set of matrix inequalities a numerical example is provided to demonstrate the applicability of the proposed approach

local controllability reachability and reconstructability of the general singular model of 2d systems necessary and sufficient conditions for the local controllability reachability and reconstructability of the general singular model of 2d linear systems are established

finite sample size effect on minimum variance beamformers optimum diagonal loading factor for large arrays minimum variance beamformers are usually complemented with diagonal loading techniques in order to provide robustness against several impairments such as imprecise knowledge of the steering vector or finite sample size effects this paper concentrates on this last application of diagonal loading techniques i e it is assumed that the steering vector is perfectly known and that diagonal loading is used to alleviate the finite sample size impairments the analysis herein is asymptotic in the sense that it is assumed that both the number of antennas and the number of samples are high but have the same order of magnitude borrowing some results of random matrix theory the authors first derive a deterministic expression that describes the asymptotic signal to noise plus interference ratio sinr at the output of the diagonally loaded beamformer then making use of the statistical theory of large observations also known as general statistical analysis or g analysis the authors derive an estimator of the optimum loading factor that is consistent when both the number of antennas and the sample size increase without bound at the same rate because of that the estimator has an excellent performance even in situations where the quotient between the number of observations is low relative to the number of elements of the array

ude based robust boundary control for an unstable parabolic pde with unknown input disturbance a novel control strategy named uncertainty and disturbance estimator ude based robust control is applied to the stabilization of an unstable parabolic partial differential equation pde with a dirichlet type boundary actuator and an unknown time varying input disturbance the unstable pde is stabilized by the backstepping approach and the unknown input disturbance is compensated by the ude which constructs an estimation of the disturbance by filtering the system input and measurable state signals the proposed ude based robust boundary control only requires the spectrum information of the disturbance signal and one boundary output measurement stability analysis of the closed loop systems is carried out and a numerical example is provided to validate the proposed method

general response formula for two dimensional linear systems with variable coefficients a new definition of the transition matrix for a general 2 d system model with variable coefficients is presented the general response formula for the general 2 d system model with variable coefficients is derived solution to the first and the second fornasini marchesini models with variable coefficients are also given

acceptable input sequences for singular 2 d linear systems necessary and sufficient conditions for the acceptance of all input sequences on the given rectangle for singular 2 d linear systems are established a procedure based on elementary row operations for finding the set of acceptable input sequences is given and illustrated by numerical example

singular systems a new approach in the time domain a new approach in the time domain is developed for the study of singular linear systems of the form e dot x ax bu y cx with e singular central to the approach is the fundamental triple alpha e a 1 e alphae a 1 b c with a real number satisfying det alpha e a neq 0 controllability and observability matrices are expressed in terms of the fundamental triple new tests for impulse controllability and impulse observability are also established feedback control problems including pole placement decoupling and disturbance localization are studied by use of a modified proportional and derivative feedback of the state in the form of u f alpha x dot x v

fundamental equivalence of discrete time ar representations we examine the problem of equivalence of discrete time auto regressive representations dtarrs over a finite time interval two dtarrs are defined as fundamentally equivalent fe over a finite time interval 0 n if their solution spaces or behaviours are isomorphic we generalize the concept of strict equivalence se of matrix pencils to the case of general polynomial matrices and in turn we show that fe of dtarrs implies se of the underlying polynomial matrices

comments on 2 d descriptor systems abstract this paper discusses general 2 d descriptor systems of the form ex i 1 j 1 ax i j bx i 1 j cx i j 1 d 0 u i j d 1 u i 1 j d 2 u i j 1 solution formula and structural forms are developed for several large classes of 2 d descriptor systems the idea of a recursive chain is introduced it is shown that these systems include several types of behavior not discussed elsewhere in the literature

geometric theory for the singular roesser model a e b invariant and e a b invariant subspaces for the two dimensional singular roesser model are investigated these subspaces are related to the existence of the solutions when the boundary conditions are in these subspaces also the existence of a solution sequence in certain subspaces derived from the invariant subspaces is shown the boundary conditions that appear in the solution when some semistates in the solution are restricted to zero are also investigated

realization of noncausal 2 d systems based on a descriptor model it is shown that a class of linear discrete noncausal two dimensional systems can be represented by discrete descriptor systems whose coefficients are functions that admit laurent series expansions on the unit circle in the complex plane the basic idea is to obtain a conventional state space realization with coefficient functions for causal and anticausal subsystems in one direction and then view them as a descriptor system a single entity the resulting model is a 1 d descriptor system with coefficient functions defined on the unit circle in the complex plane some properties of this model concerning minimality are also investigated

using spectral estimation techniques in adaptive processing antenna systems improved spectral estimation techniques hold promise for becoming a valuable asset in adaptive processing array antenna systems their value lies in the considerable amount of additional useful information which they can provide about the interference environment utilizing a relatively small number of degrees of freedom dof the superresolution capabilities estimation of coherence and relative power level determination serve to complement and refine the data from faster conventional estimation techniques two conceptual application area examples for using such techniques are discussed partially adaptive low sidelobe arrays and fully adaptive tracking arrays for the partially adaptive area the information is utilized for efficient assignment of a limited number of dof in a beamspace constrained adaptive system in order to obtain a stable main beam retention of low sidelobes considerably faster response and reduction in overall cost these benefits are demonstrated via simulation examples computed for a 16 element linear array for the fully adaptive tracking array area the information is utilized in an all digital processing system concept to permit stable hulling of coherent interference sources in the main beam region efficient assignment control of the available dof and greater flexibility in time domain adaptive filtering strategy

an extension of wolovich s definition of equivalence of linear systems wolovich s classical definition of equivalence for linear systems 1974 is extended to the generalized study of linear systems it is shown that the resulting equivalence is an alternative characterization of the notion of full system equivalence underlying its fundamental role in the generalized study of linear systems

boundary feedback stabilization of an unstable heat equation in this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut x t uxx x t a x u x t this equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused mathematically due to the diffusive term uxx but also the destabilizing heat is generating mathematically due to the term a u with a 0 we show that for any given continuously differentiable function a and any given positive constant l we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of l this is a continuation of the recent work of boskovic krstic and liu ieee trans automat control 46 2001 pp 2022 2028 and balogh and krstic european j control 8 2002 pp 165 176

controllability of 2 d systems the concept of controllability of 2 d systems is introduced in a behavioral framework this property is defined as a systems concept and is characterized in terms of system representations state space realizations for controllable 2 d systems are presented the structure of state space systems is analyzed and the notions of trimness reachability and observability are introduced and characterized these realizations do not depend on any assumptions concerning causality

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors