almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

a new indirect adaptive control scheme for time varying plants structures are developed for the control and estimation parts of the indirect adaptive scheme which are more appropriate for time varying plants in contrast to the usual pointwise schemes the new controller structure can meet the control objective exactly for a wide class of plants with smooth but otherwise unrestricted parameter variations on the other hand the possibly available knowledge of the form or frequency of variation of the fast parameters is included in the new estimator structure so that for successful estimation the overall plant is not restricted to varying slowly with time the new estimator and control law are combined using the certainty equivalence principle to develop an indirect adaptive control scheme meeting the control objective for plants with time varying parameters whose fast varying parts are of known form and unknown parts are slow in the mean

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

novel all pass factorization all solutions to rational matrix equation and control application for an arbitrary rational matrix rm a new descriptor realization of its all pass factorization is presented the coefficients of the factors are expressed explicitly in the solution of a linear matrix inequality which is well known in control theory using the all pass factorization necessary and sufficient conditions for existence of a solution of an equation with rms where the unknown rm has its poles in the left closed complex half plane and it can be improper are presented as well as all solutions as an application of the latter result the notion of almost disturbance decoupling i e when the infimum of the mathscr h infty norm of the transfer matrix from the disturbance input to the controlled output over the stabilizing controllers is zero is generalized the generalization is such that instead of the whole frequency axis the frequency axis with excluded intervals of small lengths is considered the controller consists of output feedback plus disturbance feedforward designed independently a necessary and sufficient solvability condition is presented which is expressed in terms of the given data the three main results are illustrated by an example

brief adaptive control for linear slowly time varying systems using direct least squares estimation in this paper we propose a least squares based non recursive identification algorithm capable of dealing with slowly time varying parameters the minimized criterion is an l 2 norm of the identification error with forgetting factor the proposed estimation algorithm does not require explicit knowledge on the noise bound or the region where the true parameters lie finally a pole placement hybrid controller is designed and the system s state is shown to be bounded

the generalized tp model transformation for t s fuzzy model manipulation and generalized stability verification this paper integrates various ideas about the tensor product tp model transformation into one conceptual framework and formulates it in terms of the takagi sugeno t s fuzzy model manipulation and control design framework several new extensions of the tp model transformation are proposed such as the quasi and full compact and rank reduced higher order singular value decomposition based canonical form of t s fuzzy models and the bilinear multi pseudo convex partial tp model transformations all of these extensions together form the generalized tp model transformation which provides an effective tool to freely and readily manipulate the antecedent sets and rules of t s fuzzy models and also provides main fuzzy rule component analysis as well as a means for complexity and accuracy tradeoffs it is demonstrated in this paper that the proposed manipulation forms a new effective and necessary optimization step of t s fuzzy or polytopic models and linear matrix inequality based control design and can also decrease conservativeness identification techniques are typically constructed according to the available data and measurement set as well as the type of system to be identified as a result they may not always provide good representations for control design frameworks this paper demonstrates that the proposed tp model transformation is unique in that it bridges between various soft computing based identification techniques and t s fuzzy model based approaches finally this paper proposes the multi tp model transformation which is a tractable and nonheuristic framework to verify the stability of the result of fuzzy or various soft computing based control designs the multi tp model transformation could provide an answer to the frequently emerging criticisms regarding the lack of mathematical stability verification techniques in the soft computing based control design control examples are provided in this paper

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

the extended j spectral factorization for descriptor systems in this paper we study an extended j spectral factorization problem i e j spectral factorization problem for descriptor systems which may not have full column normal rank and may exhibit poles and zeros on the extended imaginary axis we present necessary and sufficient solvability conditions and develop a numerically reliable method for the underlying problem our method is implemented by using only orthogonal transformations and has an acceptable computational complexity

new results and application of singular control we reconsider the singular control problem with marginal stability of the closed loop system when the transfer matrix from the input to the output can have linearly dependent columns and zeros on the extended imaginary axis we present a new theoretical existence result and a new numerical algorithm based on finding an orthogonal transformation of the matrix pencil associated to the euler lagrange differential equations into a block triangular form we present an application in linear quadratic control of descriptor systems under the constraints of physical realizability of the control and impulse free and marginally stable closed loop system

impulse controllability and observability of rectangular descriptor systems the presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered it is shown that the equivalence between impulse controllability observability and the existence of an impulse eliminating semistate feedback output injection gain although true for square descriptor systems does not hold for rectangular descriptor systems in general hence necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback output injection gain are presented

brief adaptive control of linear time varying systems single input single output uncertain linear time varying systems are considered which are affected by unknown bounded additive disturbances the uncertain time varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds the output which is the only measured variable is required to track a given smooth bounded reference trajectory the undisturbed system is assumed to be minimum phase and to have known and constant relative degree known sign of the high frequency gain known upper bound on the system order an adaptive output feedback control algorithm is designed which assures i boundedness of all closed loop signals ii arbitrarily improved transient performance of the tracking error iii asymptotically vanishing tracking error when parameter time derivatives are l 1 signals and disturbances are l 2 signals

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

adaptive control of linear time varying plants a new model reference controller structure the problem of developing a control law which can force the output of a linear time varying plant to track the output of a stable linear time invariant reference model is discussed it is shown that the standard model reference controller used for linear time invariant plants cannot guarantee zero tracking error in general when the plant is time varying a new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time varying plants with known parameters when the time varying plant parameters are unknown but vary slowly with time it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean the assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters

analyzing the stability of switched systems using common zeroing output systems this paper introduces the notion of common zeroing output systems czos to analyze the stability of switched systems the concept of czos allows one to verify weak zero state detectability it characterizes a common behavior of any individual subsystem when the output signal for each subsystem is approaching zero heuristically speaking it removes the effect of switching behavior and thus enables one to analyze stability properties in systems with complex switching signals with the help of czos the krasovskii lasalle theorem can be extended to switched nonlinear time varying systems with both arbitrary switching and more general restricted switching cases for switched nonlinear time invariant systems the needed detectability condition is further simplified leading to several new stability results particularly when a switched linear time invariant system is considered it is possible to generate a recursive method which combines a krasovskii lasalle result and a nested matrosov result to find a czos if it exists the power of the proposed czos is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions

constructive solutions to spectral and inner outer factorizations with respect to the disk we use state space realizations to solve the spectral and inner outer factorization problems with respect to the unit disk formulated for a completely general rational matrix the algorithm is based on orthogonal transformations and standard reliable procedures for solving stein and riccati equations the formulas apply in particular to general descriptor systems or polynomial matrices the main novelty is that we allow for arbitrary rank poles and zeros on the unit circle or at infinity

a new iterative method for solving the coefficient inverse problem of the wave equation on donne la definition de l equation operateur non lineaire du probleme inverse coefficient de l equation d onde dans le domaine des variables d espace et de temps sans les transformees de laplace et de fourier

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

algorithms for optimal control with invariant zeros on the extended imaginary axis abstract we transform an control problem with invariant zeros on the extended imaginary axis into a regular problem then using the nevanlinna pick theorem we find necessary and sufficient existence conditions for the original control problem an algorithm and examples with invariant zeros on the extended imaginary axis are given by the same approach we also solve the singular 2 control problem

a parabolic inverse problem arising in a mathematical model for chromatography in this paper the problem of determining an unknown coefficient for some parabolic equation is considered this problem arises from an engineering model of gel permeation chromatography which is a fundamental technique in measuring the size of molecules it is shown that under some assumptions the uniqueness of the coefficient holds

numerical recovery of the layered medium from the surface data abstract in this paper an inverse problem is formulated and its numerical solution is given the problem is of interest for example in geophysics numerical results show that the algorithm is efficient for noisy data practical recommendations are given the problem consists of finding n z the refraction coefficient of the medium given the surface data u x k x p x x3 0 and all k 0 k0 where k0 0 is an arbitrary small wave number the governing equation is 2 k2n z u x x x1 x2 z analytical solution to this inverse problem is given a numerical implementation is suggested and the results of the numerical experiments are reported

finite data rate feedback stabilization of switched and hybrid linear systems we study the problem of asymptotically stabilizing a switched linear control system using sampled and quantized measurements of its state the switching is assumed to be slow enough in the sense of combined dwell time and average dwell time each individual mode is assumed to be stabilizable and the available data rate is assumed to be large enough but finite our encoding and control strategy is rooted in the one proposed in our earlier work on non switched systems and in particular the data rate bound used here is the data rate bound from that earlier work maximized over the individual modes the main technical step that enables the extension to switched systems concerns propagating over approximations of reachable sets through sampling intervals during which the switching signal is not known a novel algorithm is developed for this purpose our primary focus is on systems with time dependent switching switched systems but the setting of state dependent switching hybrid systems is also discussed

brief paper almost disturbance decoupling and pole placement we revisit here the almost disturbance decoupling problem addp willems 1981 by state feedback with the objective to solve addp and simultaneously place the maximal number of poles in the closed loop solution indeed when addp is solvable we show that whatever be the choice of a particular feedback solution the obtained closed loop system always has a set of fixed poles we characterize these fixed poles of addp the other non fixed poles can be placed freely and we characterize the optimal solutions in terms of ad hoc subspaces and feedbacks which allow us to solve addp with maximal pole placement from our contribution which treats the most general case for studying addp with maximal usually partial pole placement directly follow the solutions of addp with complete pole placement when there are no addp fixed poles and addp with internal stability when all the fixed poles of addp are stable without requiring the use of stabilizability subspaces as in willems 1981 we extend the concept of self bounded controlled invariant subspaces basile marro 1992 to almost ones an example is proposed that illustrates our contributions

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

supervisory control of uncertain linear time varying systems we consider the problem of adaptively stabilizing linear plants with unknown time varying parameters in the presence of noise disturbances and unmodeled dynamics using the supervisory control framework which employs multiple candidate controllers and an estimator based switching logic to select the active controller at every instant of time time varying uncertain linear plants can be stabilized by supervisory control provided that the plant s parameter varies slowly enough in terms of mixed dwell time switching and average dwell time switching the noise and disturbances are bounded and small enough in terms of l infinity norms and the unmodeled dynamics are small enough in the input to state stability sense this work extends previously reported works on supervisory control of linear time invariant systems with constant unknown parameters to the case of linear time varying uncertain systems a numerical example is included and limitations of the approach are discussed

adaptive control of a class of slowly time varying plants abstract an adaptive control system of the type considered earlier by the author which is designed to be stable under the assumption that the unknown plant parameters are constant is shown to maintain stability when the plant parameters are slowly time varying

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

robust state dependent switching of linear systems with dwell time a state dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty a lyapunov function in quadratic form is assigned to each subsystem such that it is non increasing at the switching instants during the dwell time this function varies piecewise linearly in time after the dwell the system switches if the switching results in a decrease in the value of the lf the method proposed is also applicable to robust stabilization via state feedback it is further extended to guarantee a bound on the l2 gain of the switching system it is also used in deriving state feedback control law that robustly achieves a prescribed l2 gain bound

robust adaptive control a slowly varying systems approach in this paper we characterize a class of indirect adaptive controllers that can stabilize a time invariant system subjected to both parametric and l to l bounded unstructured uncertainty pertaining to this class of controllers a particular indirect adaptive scheme is proposed and an a priori computable upper bound on the size of the unstructured uncertainty for which stability is ensured is provided

kalman yakubovic popov lemma for descriptor systems abstract for a given descriptor realization of para hermitian rational matrix s we present a generalization of kalman yakubovic popov lemma i e necessary and sufficient conditions for 0 on the imaginary axis in terms of an inequality with constant matrices the result is quite general since can have poles and zeros on the extended imaginary axis hence the nonstrict inequality j 0 r can hold instead of the strict inequality can be singular the descriptor realization is required to be only impulse controllable and controllable or stabilizable and det 0 a spectral factorization of is given by the above mentioned constant matrices three consequences of the generalized kyp lemma and an illustrative numerical example are given

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

inverse scattering in 1 d nonhomogeneous media and recovery of the wave speed the inverse scattering problem for the 1 d schrodinger equation d2 dx2 k2 k2p x q x is studied this equation is equivalent to the 1 d wave equation with speed 1 1 p x in a nonhomogeneous medium where q x acts as a restoring force when q x is integrable with a finite first moment p x 1 and bounded below and satisfies two integrability conditions p x is recovered uniquely when the scattering data and q x are known some explicitly solved examples are provided

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

on uniqueness of an inverse problem for a 1 d wave equation from transmission data this paper concerns the uniqueness of a coefficient inverse problem for a one dimensional wave equation we allow the unknown coefficient under consideration to be discontinuous this type of inverse problem arises in seismology corresponding to the case in which the medium to be detected has discontinuous interfaces by virtue of spectra theory of the sturm liouville problem and asymptotics of the green function we prove that the discontinuous coefficient can be uniquely recovered from the source function f in l 1 0 infty and the response function g furthermore lemma 6 in this paper corrects some mistakes in t kimura and t suzuki siam j appl math 53 1993 pp 1747 1761 about the asymptotics of the green function this correction means that some related parts in the aforementioned article also need to be rectified correspondingly

parameter and state estimation of nonlinear systems using a multi observer under the supervisory framework we present a hybrid scheme for the parameter and state estimation of nonlinear continuous time systems which is inspired by the supervisory setup used for control state observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant which provides state and parameter estimates assuming that a persistency of excitation condition holds the convergence of the parameter and state estimation errors to zero is ensured up to a margin which can be made as small as desired by increasing the number of observers to reduce the potential computational complexity of the scheme we explain how the sampling of the parameter set can be dynamically updated using a zoom in procedure this strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy the results are shown to be applicable to linear systems and to a class of nonlinear systems we illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model

brief hysteresis based switching algorithms for supervisory control of uncertain systems we address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers we present a new hysteresis based switching logic designed specifically for this purpose and derive a bound on the number of switches produced by this logic on an arbitrary time interval the resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

h optimization without assumptions on finite or infinite zeros explicit algebraic conditions are presented for the suboptimality of some parameter in the h infty optimization problem by output measurement control apart from two strict properness conditions no artificial assumptions restrict the underlying system in particular the plant may have zeros on the imaginary axis or at infinity these suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability

h sub spl infin observer design for lipschitz nonlinear systems the problem of observer design for lipschitz nonlinear systems is considered a new dynamic framework which is a generalization of previously used lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented the equivalence between this condition and an h sub spl infin optimal control problem which satisfies the standard regularity assumptions in h sub spl infin optimization theory is shown and a parameterization of all possible observers is also presented a design procedure which is less restrictive than the existing design approaches is proposed and a simulation example is given to illustrate the observer design

synthesis of dissipative systems using quadratic differential forms part ii the problem discussed is that of designing a controller for a linear system that renders a quadratic functional nonnegative our formulation and solution of this problem is completely representation free the system dynamics are specified by a differential behavior and the performance is specified through a quadratic differential form we view control as interconnection a controller constrains a distinguished set of system variables the control variables the resulting behavior of the to be controlled variables is called the controlled behavior the constraint that the controller acts through the control variables only can be succinctly expressed by requiring that the controlled behavior should be wedged in between the hidden behavior obtained by setting the control variables equal to zero and the plant behavior obtained by leaving the control variables unconstrained the main result is a set of necessary and sufficient conditions for the existence of a controlled behavior that meets the performance specifications the essential requirement is a coupling condition an inequality that combines the storage functions of the hidden behavior and the orthogonal complement of the plant behavior

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail