the matching of a prescribed linear input output behavior in a nonlinear system in this paper we deal with the problem of finding a feedback under which the input output behavior of a nonlinear system becomes exactly the same as that of a specified linear model the solvability of this problem is shown to depend on a formal infinite zero structure associated with the system

the solution of diagonal decoupling problem by dynamic output feedback and constant precompensator the general case in this paper the solution to diagonal decoupling problem via dynamic output feedback and constant precompensator is presented in the general case the literature contains a number of particular solutions for this problem these solutions are valid for instance for square transfer matrices or they employ restricted dynamic output feedback schemes here we start with a nonsquare transfer matrix and consider a dynamic output feedback scheme where there is a proper compensator in the feedback loop accompanied by a constant gain precompensator in the feedforward path in this respect the problem being considered is the dynamic output feedback version of the well known morgan s problem the approach taken involves the characterization of open loop diagonalizers which admit a dynamic output feedback realization the key concepts involved in the solution are the generalized version of diagonal causality degree dominance and the set of attainable infinite zero orders an example is also included to illustrate the main result

on a necessary and sufficient condition for finite dimensionality of estimation ever since the technique of the kalman bucy filter was popularized there has been an intense interest in finding new classes of finite dimensional recursive filters in the late seventies the concept of the estimation algebra of a filtering system was introduced it has proven to be an invaluable tool in the study of nonlinear filtering problems in this paper a simple algebraic necessary and sufficient condition is established for an estimation algebra of a special class of filtering systems to be finite dimensional also presented is a rigorous proof of the wei norman program which allows one to construct finite dimensional recursive filters from finite dimensional estimation algebras

generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

parallel computations for yau filters in the early 1990s yau developed a new class of nonlinear filters called the yau filterswhich contain the kalman bucy filters and the benes filters as special cases it has been shown that from the lie algebraic point of view the yau filters are the most general finite dimensional filters yau and hu proved that the dmz equation for a yau filter can be reduced to a kolmogorov type partial differential equation and a system of linear differential equations they noticed that the pde is independent of the observed data and hence can be solved off line an efficient parallel algorithm for the system of odes would lead to fast solutions of yau filters and hence their suitability for real life applications in this paper we have proposed several parallel methods suitable for this system of odes

minimal structure in the block decoupling problem with stability abstract in this paper we consider the block decoupling problem with stability we characterize the minimal mcmillan degree achievable for the block decoupled system for this we introduce a new list of integers which are feedback invariant these integers are related in a simple way to the minimal number of unstable and infinite zeros of the block decoupled system

model matching and factorization for nonlinear systems a structural approach the model matching and the left factorization problems for nonlinear systems are investigated using an approach based on the structural algorithm sufficient conditions for the solvability of the f

on minimal compensators for decoupling control abstract the general construction of minimal regular compensators for decoupling a nonlinear system is given by means of vector subspaces which are generated by differential vectors of outputs and states and the minimal dimension of a decoupling compensator is expressed in intrinsic characterization the equivalence relation of all minimal regular compensators is established though these compensators may have different dynamic behavior from each other

a goodness of fit approach to inference procedures for the kappa statistic confidence interval construction significance testing and sample size estimation we propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome the procedure is based on a chi square goodness of fit test as applied to a model frequently used for clustered binary data the procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures the procedure also has use for significance testing and the planning of corresponding sample size requirements

maximum likelihood estimation of the kappa coefficient from models of matched binary responses we present an estimate of the kappa coefficient of agreement between two methods of rating based on matched pairs of binary responses and show that the estimate depends on the common intraclass correlation coefficient between the pairs via monte carlo simulation we investigate power of the test of significance on kappa and the large sample bias and variance of its maximum likelihood estimator

parallel algorithms for initial value problems for difference and differential equations abstract let yn be a trajectory defined sequentially by a nonlinear vector difference equation yn 1 fn 1 yn with y0 known a steffensen like iterative method is proposed which starts from a guessed sequence un 0 for the approximation of yn and allows certain computations to be performed in parallel the sequence u k 1 n is obtained from u k n by means of a formula of the form u k 1 n 1 v k 1 n 1 k 1 n 1 u k 1 n u k n here the vectors v k 1 n 1 and the matrices k 1 n 1 each require a function evaluation but can be computed in parallel with respect to n in a suitable interval nk mk the length of which depends on the number of processors available therefore for the algorithm to serve effectively the steffensen iteration must converge quickly and the machine used must possess a large number of processors finally note that the theory includes the case that the sequence yn is given by a one step ode solver

a transfer matrix approach to feedback invariants of linear systems application to decoupling abstract the transfer matrix approach allows one to exhibit fairly easily fundamental invariants of multivariable systems under the action of transformation groups these transformation groups include the classical state feedback state and input changes of coordinates then the solvability of numerous classical control problems e g decouplability disturbance rejection model following can be expressed directly in terms of these invariants in this expository paper we present in a unified way three lists of feedback invariants related to the infinite behavior of linear systems these invariants turn out to be crucial in studying feedback decoupling problems the main tools for this study are factorization of transfer matrices over the p i d of proper rational functions when dealing with stability we factor transfer matrices over the p i d of proper rational stable functions we illustrate the use of these invariants by studying some decoupling problems

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

structure at infinity revisited abstract the structure at infinity of an ordinary differential control system is a finite sequence of increasing integers ending with the differential output rank of the system namely the number of outputs that can be given as arbitrary functions of time when the inputs are unknown its definition and construction originally done for linear systems has been extended to affine nonlinear systems and used in order to study dynamic decoupling or model matching it essentially relies on a state representation the purpose of this paper is to make a critical examination of this concept and to modify it in order to avoid the state representation at the same time we extend it to nonlinear partial differential control systems by exhibiting a link with formal integrability a highly important concept in the formal theory of systems of partial differential equations that cannot be handled by means of a transfer matrix approach many explicit examples will illustrate the main results and the possibility to use computer algebra techniques will be pointed out

essential orders and the non linear decoupling problem abstract the concept of essential orders has recently been introduced into linear system theory and has been shown to be useful in the solution of static and dynamic decoupling problems commauit et al 1986 de luca et al 1985 this paper presents a non trivial extension to the class of non linear affine systems of some of these definitions and results it is shown that these invariant integers give the minimal order for a regular dynamic compensator that decouples a right invertible system

zeros at infinity for affine nonlinear control systems a definition of zeros at infinity for affine nonlinear control systems is proposed the definition is local which means that we exclude certain singularities we argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling in particular we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity

existence and uniqueness results for a third order implicit differential equation the purpose of this paper is to give sufficient conditions for the existence and uniqueness of solutions to the boundary value problem of a third order implicit differential equation as follows f t u t u t u t 0 email protected email protected 1u 0 u 0 u 1 0 the lower and upper solutions method maximum principle together with an iterative technique are employed an example illustrates the application of results obtained

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

minimality of dynamic input output decoupling for nonlinear systems in this note we study the strong dynamic input output decoupling problem for nonlinear systems using an algebraic theory for nonlinear control systems we obtain for a dynamic input output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

design of a minimal precompensator for the decoupling problem abstract for right invertible linear time invariant systems which cannot be decoupled row by row using regular static state feedback laws we propose a new algorithmic procedure for designing a minimal precompensator leading to a compensated system which can be decoupled by regular static state feedback

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

solution to morgan s problem a necessary and sufficient condition is presented for the solution of the row by row decoupling problem known as morgan s problem in the general case that is without any restrictive assumption added to the system to the feedback law u fx gy g may be noninvertible this is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system these integers are the infinite zero orders morse s list i sub 4 and the essential orders of the system which only depend on the input output behavior and morse s list i sub 2 of the system which depends on the choice of a particular state realization

a nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem the nonregular dynamic disturbance decoupling problem for nonlinear control systems is introduced a local solution is given by means of a constructive algorithm that is based on singh s algorithm and the clamped dynamics algorithm further studied is the nonlinear model matching problem that is defined as follows given a nonlinear control system to be referred to as the plant and another nonlinear control system to be referred to as the model can a compensator for the plant be found in such a way that the input output behavior of the compensated plant matches that of the model by proving that the solvability of the nonlinear model matching problem is equivalent to the solvability of an associated nonregular dynamic disturbance decoupling problem a complete local solution of this problem can be established

robust output regulation for invertible nonlinear mimo systems abstract the robust output regulation problem for a class of invertible nonlinear mimo systems is addressed in this paper under a mild assumption on the high frequency gain matrix and strongly minimum phase assumption a robust regulator is proposed with the combination of nonlinear internal model and a new extended high gain observer more explicitly the robust output regulation is achieved by employing a novel extended high gain observer based stabilizer such that the regulated system augmented with the nonlinear internal model is asymptotically stabilized the novelty of this approach consists in the use of an extended observer to estimate under mild assumptions all unmeasured terms

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

invertibility of observable multivariable nonlinear systems based on the algorithm of hirschorn 1 for obtaining inverses sufficient conditions for invertibility of observable multivariable nonlinear systems are derived for observable and invertible systems a static left inverse system is constructed for certain noninvertible systems the sufficient condition yields a characterization of input space on which the input output map is injective

reduced form of the interactor matrix some structural results about the interactor of a given right invertible system are presented an original form for this operator which directly exhibits structural information such as infinite zero structure or essential orders is provided moreover this form allows the linkage of the infinite and essential structures of a system

on implicit systems of differential equations abstract this article considers implicit systems of differential equations the implicit systems that are considered are given by polynomial relations on the coordinates of the indeterminate function and the coordinates of the time derivative of the indeterminate function for such implicit systems of differential equations we are concerned with computing algebraic constraints such that on the algebraic variety determined by the constraint equations the original implicit system of differential equations has an explicit representation our approach is algebraic although there have been a number of articles that approach implicit differential equations algebraically all such approaches have relied heavily on linear algebra the approach of this article is different we have no linearity requirements at all instead we rely on algebraic geometry in particular we use birational mappings to produce an explicit system the methods developed in this article are easily implemented using various computer algebra systems

a graph theoretic method for computing a formal representation of the largest controlled invariant subspace of a structured system the paper discusses a method to compute a kernel representation of the largest controlled invariant subspace in the kernel of the output mapping of a structured system the graph of the structured system is used to make the relevant equations and then a formula manipulation package can be used to compute a condensed kernel representation or even an image representation of the largest controlled invariant subspace

lq control of descriptor systems by cancelling structure at infinity this paper presents results concerning lq control of arbitrary descriptor systems and a numerical algorithm for achieving it the algorithm consists of two steps the first step is using the silverman algorithm orthogonal version transformation of the problem of lq control of descriptor system into a problem of lq control of a strictly proper system with singular or non singular new matrix 22 if new 22 is singular we perform the second step i e solving the lq singular control problem using again the silverman algorithm regarding the existing results on the lq singular control problem we have new results a counter example that this problem may not have a stable solution most general solvability conditions with or without stability and a new numerical algorithm based on using orthogonal matrices when stabilizability conditions are satisfied the algorithm places simultaneously stable poles in the closed loop system we show that the traditional riccati equation associated to this proble

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

an extended linearization approach to nonlinear system inversion the inversion problem for nonlinear systems is considered from both the internal viewpoint state equation representations and the external viewpoint volterra series representations in order to circumvent difficulties in the known exact inversion theory a method for obtaining what will be called a partial inverse system is proposed for a given nonlinear system a cascade system typically containing differentiators is found such that the overall nonlinear system has a family of constant operating points with inputs and outputs identical furthermore the linearization of the overall system about each of these constant operating points is the identity system

feedback block decoupling and infinite structure of linear systems abstract using factorizations at infinity of the transfer matrix two interesting necessary and sufficient conditions arc obtained for the block decoupling problem of linear systems by state feedback and a constant non singular input transformation these conditions are expressed in a very simple way in terms of integers which are feedback invariants for the system under consideration these feedback invariants are related either to the system infinite structure or to the reachability indices of the feedback reduced system

parallel ode solvers with stepsize control in this paper we propose a parallel implementation of one step methods with stepsize control for the numerical solution of ivps for odes of the form y t f t y t y t 0 y 0 the proposed implementation is based on the fact that any one step ode method on a mesh t 0 n y 0 known in a previous paper 1989 we introduced a paral iterative algorithm for the approximation of the trajectory y 0 y 1 y n in which a block of guessed values u 0 0 y 0 u 0 1 u 0 n is iterated concurrently with respect to the index n until an error proportional to a given iteration tolerance tol i t is reached here that parallel algorithm is developed further in order to perform the stepsize control strategy according to a given step tolerance tol s t moreover an analysis of the optimal ratio between tol i t and tol s t is given the paper ends with numerical examples and estimations of the attainable speedup

decoupling by restricted static state feedback the general case in this paper we tackle the general block decoupling problem for linear constant dynamical systems c a b with m inputs and p outputs with restricted static state feedback in other words with control laws of type u gfx gv we give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in 2 for the simple case k p leq m where k denotes the number of blocks to be decoupled

the matching of nonlinear models via dynamic state feedback it is well known that for linear systems the model matching problem is equivalent to a disturbance decoupling problem with disturbance measurement the solution of both problems can be expressed in terms of properties of invariant subspaces of the system and of the model in this paper it is shown that for nonlinear systems under appropriate hypotheses analogous results can be obtained the solvability of a model matching problem can be expressed in terms of properties of suitable invariant distributions it is also shown that as for linear systems those properties are related to the so called structures at infinity of the system and of the model

generalized linear systems with lumped or distributed parameters and differential vector spaces abstract by employing differential vector spaces we obtain results for linear systems with constant or varying coefficients and with lumped or distributed parameters which were only known for constant linear systems described by rational transfer matrices questions such as the characterization of input and output input output equivalence invertibility feedback decoupling and realization are investigated

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

new feedback invariants and the block decoupling problem a new list of feedback invariant integers is introduced we give several equivalent characterizations of these invariants within both geometric and transfer matrix approaches when solving the block decoupling problem it turns out that when decoupling is possible these integers represent the minimal mcmillan degree achievable for the blocks of the decoupled system

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

model reference adaptive and nonadaptive control of linear time varying plants we address the adaptive and nonadaptive model reference control problem for a class of multivariable linear time varying plants namely index invariant ones we show that under appropriate controllability and observability conditions this class of plants admits a fractional description in terms of polynomial differential operators and as such allows for a polynomial equation based controller design we also show that for a model reference control objective the controller can be designed by solving a set of algebraic equations further when the plant parameters are only partially known we employ a gradient based adaptive law with projection and normalization to update the controller parameters and establish the stability and tracking properties of adaptive closed loop plant finally we present a simple example to illustrate the design and realization of both the adaptive and nonadaptive control laws

testing the homogeneity of kappa statistics procedures are compared for testing the homogeneity of k or 2 independent kappa statistics in the case of two raters and a dichotomous outcome one of the procedures is based on the estimated large sample variance derived under a model frequently adopted for inferences concerning interobserver agreement the other is based on a goodness of fit approach to this model the results of a monte carlo simulation show that the two approaches have similar properties if the number of subjects in each sample is large 100 and the prevalence of the underlying trait of interest is not extreme while the goodness of fit approach is recommended for comparisons involving smaller numbers of subjects or in which the prevalence of the underlying trait is small 0 3

local nonlinear model matching from linearity to nonlinearity the model matching problem consists of designing a compensator for a given system called the plant in such a way that the resulting input output behaviour matches that of a prespecified model in this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback the main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model the generic conditions are identified they naturally appear in the solution of the dynamic input output decoupling problem for the plant the theory is illustrated by means of two examples

block noninteracting control with non regular static state feedback a complete solution abstract we consider linear time invariant systems c a b where the output map c is partitioned into k blocks c i we assume that the system are block right invertible i e the rank of c a b equals the sum of the ranks of the subsystems c i a b we give for the first time a necessary and sufficient condition for the solution of the block decoupling problem using static state feedbacks of the type u fx gv with g possibly nonregular for solving the decoupling problem we impose that the rank of the closed loop system equals that of c a b this is a structural condition in terms of invariant lists of integers the infinite zero orders the block essential orders and morse s list i 2 of c a b the main result theorem 3 generalizes that of our previous work for the so called morgan s problem i e the row by row decoupling problem

the block essential orders and the dynamic block decoupling problem abstract in recent papers 8 it has been pointed out that two invariant lists of integers the infinite zero orders and the essential orders play a key role in the solution of the so called morgan s problem i e the row by row decoupling problem the purpose of the present paper is to define the block essential orders of a linear system with respect to the block decoupling problem this is done through a new dynamic solution to the latter based upon a procedure which extends to the block case that previously given in 15 for morgan s problem this procedure is minimal in the sense that it leads to the least infinite zero structure for any decoupled system reachable from the original one

a definition of column reduced proper rational matrices the aim of this work is to develop analogue concepts of column reduced polynomial matrices for proper rational matrices a definition of column reducedness for a class of proper rational matrices is proposed and the properties of such matrices are studied in particular reduction to column reduced form by elementary operations over the ring of proper rational functions and the relationship between the degrees of the invariant factors of a column reduced matrix and the so defined column indices the physical significance of such matrices in terms of their finite structure is explained this interpretation completely complements the physical interpretation of a column reduced polynomial matrix an application of the properties of column reduced proper rational matrices to the decoupling problem is also presented the infinite structure which can be obtained while decoupling a linear multivariable system by non regular static state feedback is completely characterized

a complement about almost controllability subspaces abstract we show that for any almost controllability subspace there exist a maximal input chain and a family of state feedbacks which lead to the well known feedback chain expression for this subspace

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

decoupling and pole assignment of singular systems a frequency domain approach abstract a new approach to the row by row decoupling of singular systems via state feedback and regular input transformation is presented the proposed method is based on the matrix fraction description of the system and is an extension of the frequency domain method for strictly proper systems the solvability condition of the problem is readily obtained from the numerator matrix of a coprime and column reduced matrix fraction description of the given system pole placement and decoupling is also considered and the characterization of the fixed poles is given

on the structure at infinity of linear block decouplable systems the general case the aim of this note is to show that a linear system c a b is block decouplable by means of static state feedback laws f g with g invertible if and only if the infinite structure of c a b equals the union of the infinite structures of the subsystems c i a b extracted from the given output partition this result generalizes the ones recently obtained for morgan s problem 6 and for the particular cases of right invertible 7 or left invertibie 8 systems

2 x 2 kappa coefficients measures of agreement or association summary two general but different contexts in which kappa might be used are defined agreement and association two models one for agreement and one for utility of association are defined yielding different kappa coefficients and different sampling theory asymptotic results are derived for both models small sample evaluations are presented for the model for agreement

state feedback in linear control theory abstract the role of system invariants in solutions of classical control problems when regular state feedback is used is reviewed the structural modifications that arise when these problems are extended to the case of non regular state feedback are presented an interpretation of state feedback problems in terms of matrix pencils completion is also discussed

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

stabilization by output feedback of multivariable invertible nonlinear systems in this paper the problem of global stabilization of a rather general class of mimo nonlinear systems is addressed the systems considered in the paper are invertible have a trivial zero dynamics and possess a normal form in which certain multipliers are functions of the state vector of a special kind while special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization via full state feedback though the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability thus making the design of observers possible and to the property of uniform invertibility relations never established before in the literature as a result for this class of mimo nonlinear systems a dynamic output feedback law can be designed yielding semiglobal and even global under appropriate assumptions asymptotic stability

new results about morgan s problem some aspects of the nonsquare morgan s problem are considered in particular it is shown that the condition given by j descusse et al 1986 to solve this problem is not sufficient it is also shown that the essential orders are not necessarily preserved in the static decoupling problem a necessary and sufficient condition for static decoupling of a system without modifying the essential orders is given for the case k p 1 where p is the number of outputs and k is the rank at infinity of the proper part of the interactor

the row by row decoupling via state feedback a polynomial approach necessary and sufficient conditions for the row by row and integrator decoupling of a linear system x ax bu y cx via nonregular static state feedback are established a procedure is outlined to calculate one such gain

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

the nonlinear interactor and its application to input output decoupling the solvability of the input output decoupling problem via pure dynamic state feedback a special type of dynamic compensator without zeros at infinity is investigated a necessary and sufficient condition for the solvability of this problem is established in terms of a nonlinear interactor a new concept in the theory of nonlinear control

diagonal decoupling of linear systems by static state feedback a solution is presented to the long standing open problem of linear systems theory diagonal decoupling by static state feedback the earliest known investigation of system decoupling dates back to 1934 a state space formulation of the problem appeared in 1964 and a solution for square and invertible systems followed in 1967 the case of right invertible systems however has withstood all past efforts to obtain a solution save for several special cases the present formulation avoids restrictive hypotheses concerning system and decoupling feedback the existence of a solution is shown to depend on the existence of three lists of integers conditioned solely by system invariants with respect to the permissible transformations

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

output feedback disturbance decoupling graph interpretation for structured systems abstract in this paper we consider first the output feedback disturbance decoupling problem for linear systems we derive a set of new necessary or sufficient conditions for the solvability of this problem these conditions are expressed in terms of system structural invariants such as infinite zero orders and essential orders then we consider the output feedback disturbance decoupling problem for structured linear systems necessary or sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

a triangular canonical form for a class of 0 flat nonlinear systems this article proposes a triangular canonical form for a class of 0 flat nonlinear systems necessary and sufficient geometrical conditions are given in order to guarantee the existence of a local diffeomorphism to transform the studied nonlinear systems into the proposed 0 flat canonical form which enables us to compute the flat output as well

new decoupling invariants the essential orders the aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row by row decoupling problem several equivalent characterizations are provided within both the geometric and the transfer matrix approaches

fixed modes and nonlinear noninteracting control with stability the existence of a fixed internal dynamics inherent to the noninteraction requirement is identified when unstable this represents an obstruction to the achievement of noninteracting control with stability by means of static state feedback remarkably whenever one leaves the class of linear systems this obstruction cannot in general be removed by dynamic state feedback

set of open loop block diagonalizers of transfer matrices abstract the set of open loop right block diagonalizers of a given p m transfer matrix z with specified block sizes is studied a characterization of this set is obtained in terms of a maximal open loop block diagonalizer and a minimal proper basis of the kernel of z the relevance of the results to some non interacting control problems is pointed out in particular the results obtained yield a minimum delay solution to the block decoupling problem using dynamic state feedback

a modified algorithm for invertibility in nonlinear systems the algorithm of hirschorn 1 for the construction of inverses of nonlinear systems is modified and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained for the systems which do not satisfy the invertibility conditions a characterization of input space on which the input output map is injective is derived

graph theoretic methods for the computation of disturbance decoupling feedback matrices for structured systems abstract structured systems are considered for which the disturbance decoupling problem is known to be generically solvable it is recalled how this generic solvability is in one one correspondence with certain properties of the graph representing the structure of the system further a graph oriented method is derived for the efficient computation of a feedback that actually solves the disturbance decoupling problem it is believed that the method is especially useful in case of sparse system matrices the method may also be advantageous in case some of the entries in the system matrices have an unknown value since the influence of the various entries is easy to establish

functional reproducibility of general multivariable analytic non linear systems in this paper the functional reproducibility of a general multivariable analytic nonlinear system of the form x f x u y h x u will be discussed where the state space is a real analytic manifold a general inversion algorithm is presented for the system a sufficient and necessary condition for the functional reproducibility of the system is derived the construction of a right inverse system is also included

controllability distributions and systems approximations a geometric approach given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a taylor series approximation of it the value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant controllability distributions the relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation