transfer matrix approach to the structural block diagonal decoupling problem the block diagonal decoupling problem for structured systems is treated using the transfer matrix approach an associated graph which displays the internal structure of the system invariant and interconnection is used to establish necessary and sufficient conditions for the solution of the problem these conditions are expressed in the graph in terms of shortest input output paths which are related to the infinite structure of 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

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

block decoupling for linear systems over rings abstract this paper studies the block decoupling problem for injective linear systems defined over unique factorization domains and necessary and sufficient conditions for its solvability are obtained using the algebraic properties of transfer matrices further it is shown that if the problem is solvable the decoupling can be achieved by a biproper compensator and such a compensator can be realized by a regular static state feedback finally an example is given to illustrate the results

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

structured systems within the transfer matrix approach application to decoupling abstract we consider a new approach to structured systems within the transfer matrix framework we associate with such a structured system a graph which concentrates both knowledge on structural properties of independent subsystems and on their interconnections the analysis of this associated graph allows to conclude on the decouplability of structured systems

feedback representation of precompensators application to decoupling linear multi input multi output plants in this paper we examine the problem of internally stabilizing and simultaneously diagonally decoupling a linear multivariable system by two parameter compensation based on our earlier results boussaid and guerin 1996 we prove that any given plant p of full row rank can be decoupled with stability by the considered configuration computation of the decoupling compensators follows by easy constructions the decoupling problem with a minimum number of unstable zeros in the decoupled system is also formulated and solved in the generic case

decoupling with internal stability for unity output feedback systems abstract this paper presents for the first time a necessary and sufficient condition for solvability of the decoupling problem with internal stability for square plants by unit output feedback compensation it consists of some polynomial matrix coprimeness conditions and is concerned only with the greatest c divisor of the plant parameterizations of all decoupling compensators and achievable diagonal loop maps with internal stabilizability are given and the results are also generalized in a very natural way to the decoupling problem with arbitrary pole assignment examples are included for illustration

block decoupling with stability by unity output feedback solution and performance limitations abstract the block decoupling problem with stability using unity output feedback for possibly non square plants of full row rank is considered a necessary and sufficient condition for solvability of this problem is given and the set of all compensators solving the problem is characterized previous results on the diagonal decoupling problem for square plants are thus generalized moreover a class of plants is specified where decoupling does not impose additional performance limitations as compared with a synthesis without decoupling quite general performance measures involving the sensitivity function and the complementary sensitivity function are considered including weighted h and h 2 norms

complete decoupling of linear multivariable systems by means of linear static and differential state feedback the concept of complete decoupling is introduced in this paper we show in particular that for any linear controllable system with non singular transfer matrix there always exists a static and differential state feedback such that the closed loop system is completely decoupled

a unifying approach to the decoupling of linear multivariate systems a unifying approach to the decoupling problem diagonal triangular block decoupling is introduced the key element is the interactor a polynomial matrix of unique structure associated with the transfer matrix of the system necessary and sufficient conditions for block decoupling are derived and the stability questions are resolved using the block coupling zeros the results obtained for decoupling via state feedback state feedback plus input dynamics and constant output feedback are conceptually simple unify and expand those existing and easily lead to constructive decoupling algorithms

paper transfer matrix approach to the triangular block decoupling problem the triangular block decoupling problem for linear multivariable systems is studied via the transfer matrix approach this approach clearly separates the problem of admissible control laws from the one of desired decoupled system specifications necessary and sufficient triangular decoupling conditions are given for various control laws these conditions are expressed in a very simple way in terms of linear dependance among the transfer matrix rows it turns out that when the problem is solvable this can be done by static state feedback on a minimal realization of the system furthermore it is shown that whenever triangular block decoupling is possible it is also attainable with stability

solution of the static state feedback decoupling problem for linear systems with two outputs we give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem rdp in terms of some structural invariants a geometric characterization is also given which provides the least dynamical extension needed when rdp is not solvable

tradeoffs for language recognition on alternating machines the alternating machine having a separate input tape with k two way read only heads and a certain number of internal configurations am k is considered as a parallel computing model for the complexity measure time space parallelism tsp the optimal lower bounds n2 and n3 2 respectively are proved for the recognition of specific languages on am 1 and am k respectively for the complexity measure reversals space parallelism rsp the lower bound n1 2 is established for the recognition of a specific language on am k this result implies a polynomial lower bound on parallel time hardware of parallel ram s lower bounds on the complexity measures time space and reversals space of nondeterministic machines are direct consequences of the result introduced above all lower bounds obtained are substantially improved in the case that space n for 0 1 several strongest lower bounds for two way and one way alternating deterministic nondeterministic multihead finite automata are obtained as direct consequences of these results the hierarchies for the complexity measures tsp rsp ts and rs can be immediately achieved too

input output decoupling of hamiltonian systems the linear case in this note we give necessary and sufficient conditions for a linear hamiltonian system to be input output decouplable by hamiltonian feedback i e feedback that preserves the hamiltonian structure in a second paper we treat the same problem for nonlinear hamiltonian systems

linear feedback decoupling transfer function analysis the problem of linear system decoupling is examined based on recent results on linear feedback new insight is obtained through which resolution of the decoupliug problem is accomplished by calculations performed directly on the given transfer matrix computation of the decoupling compensators follows by easy constructions the problem of feedback block decoupling with internal stability is also formulated and resolved

a state space technique for the evaluation of diagonalizing compensators this note develops a technique for designing diagonalizing compensators based on state space descriptions the relationship with stable decoupling invariants is also explored

model matching and decoupling for continuous and discrete time linear time varying systems solutions to the exact model matching and block decoupling problems for both continuous and discrete time linear time varying systems are presented the parametrisation of the whole class of proper solutions is given for the decoupling the minimal delay problem is also considered in a time varying setting the approach is algebraic and based on the smith macmillan form at infinity of a transfer matrix of a time varying system which has been recently introduced in systems theory this avoids the difficulties related to the inversion of the transfer matrices with entries in non commutative fields over which the determinants of dieudonne or ore type are much more complicated the solutions presented here involve only standard matrix computations excluding direct matrix inversions and are thus easy to implement in practice examples are treated in detail to illustrate the theoretical results and the way in which the computations are done and a physical example is also shown

decoupling by dynamic measurement feedback with stability necessary and sufficient conditions the noninteracting control problem of linear time invariant multivariable systems by dynamic measurement feedback is solved in the state space geometric approach the generalization of w m wonham s edp 1979 is considered the problem of the reduction of compensator s order is not treated but the solution derived is able to solve simultaneous problems like the decoupling and the disturbance decoupling problems

parameterization of decoupling controllers in the generalized plant model a diagonal decoupling problem in linear multi variable systems is formulated for the most general setting a necessary and sufficient condition for the existence of a decoupling controller is presented and when a solution exists the class of all decoupling controllers is characterized in terms of free parameters of stable rational vectors

invariant spaces at infinity of linear systems application to block decoupling the dynamic state feedback block decoupling problem in the general case i e with singular or nonsingular input transformations is solved it is proven that the problem is solvable if the number of inputs is large enough the main tools for this study are some invariant spaces associated with the columns infinite behavior of a rational matrix it turns out that when the problem is solvable it is also solvable with stability

transfer function matrix approach to decoupling problem with stability a simple necessary and sufficient condition for solvability of decoupling with internal stability for unity output feedback for non singular plants is proposed

block decoupling by precompensation revisited the block decoupling problem by admissible dynamic precompensation for lti systems is considered admissibility refers to the preservation of the class of controlled output trajectories i e functional output controllability is concerned which is more demanding than just pointwise output controllability this problem has been solved by hautus and heyman within a transfer function matrix approach different new equivalent solvability conditions in terms of controllability subspaces transfer function matrices or matrix pencils are given one of these conditions expressed in the input space is at the origin of new necessary and sufficient conditions for block decoupling by general precompensation possibly non admissible and nonsquare in the wider sense of basile and marro

block decoupling and arbitrary pole assignment for a linear right invertible system by dynamic compensation abstract the block decoupling of a linear right invertible system by dynamic compensation is studied the system structure of the block decoupled system is clarified from the viewpoint of the closed loop poles a dynamic compensator that realizes block decoupling and arbitrary pole assignment is proposed two examples are given to illustrate the design procedure of the dynamic compensator and its effectiveness

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

decoupling of square singular systems via proportional state feedback necessary and sufficient conditions for the decoupling of a solvable square singular system ex t ax t bu t with output y t dx t through an admissible control law of the form u t kx t hr t where h is a square nonsingular matrix it has been shown that for a given singular system that satisfies these conditions a propagational state feedback exists for which the system s transfer function is a diagonal nonsingular and proper rational matrix the proofs of the main results are constructive and provide a procedure for computing an appropriate proportional state feedback

causal factorization and linear feedback an algebraic framework for the investigation of linear dynamic output feedback is introduced pivotal in the present theory is the problem of causal factorization i e the problem of factoring two systems over each other through a causal factor the basic issues are resolved with the aid of the new concept of latency kernels

wiener hopf factorization indices and infinite structure of rational matrices the relationship between the infinite structure and the wiener hopf factorization indices of polynomial matrix representations of controllable systems is investigated on the way local wiener hopf factorization indices must be defined in addition the finite and infinite structure of a rational matrix is characterized given its wiener hopf factorization indices

noninteracting control of 2 d systems necessary and sufficient conditions for the existence of a decoupling bicausal precompensator for multivariable 2 d systems are derived in state space and frequency domains in general the decoupling problem for 2 d systems can be solved by feedback compensators if suitable injectivity assumptions are introduced on the input state matrices the structure of dynamic compensators is derived for this case and the 2 d decoupling problem with stability is solved

geometric aspects of reduced order compensators for disturbance rejection the disturbance decoupling problem with stability constraint and pole placement is examined in a geometric framework two types of reduced order compensators are proposed one based on the observation scheme the other on the dual observation scheme the novelty lies mainly in these points 1 the avoidance of eigenspace computations in the syntheses as they rely on the determination of the maximum controlled invariant contained in a given subspace and its dual i e the minimum conditioned invariant containing a given subspace and pole assignability and 2 the concerted use of controlled and conditioned invariants which leads to a straightforward synthesis and also allows a clear interpretation of the dual compensation

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

factorization of linear systems a generalized framework abstract a generalized module theoretic framework for the study of linear time invariant systems is developed crucial in the present discussion are two new notions the generalized order and the adapted bases these notions form generalizations of the classical concepts of order or degree and of proper bases employed in the theory of linear systems the resulting framework is then applied to obtain explicit conditions for system factorization and to study output feedback systems in which the feedback compensator is stable

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

decoupling in the design and synthesis of singular systems abstract necessary and sufficient conditions for the decoupling of singular systems using p d proportional derivative feedback are determined given a system which satisfies these conditions the class of all feedback matrices which decouple the system is characterized this class is used to determine the number of closed loop pole zeros which can be specified for the decoupled system and to develop a synthesis technique for the realization of desired closed loop pole zero configurations

achieving diagonal interactor matrix for multivariable linear systems with uncertain parameters abstract the notion of interactor matrix or equivalently the hermite normal form is a generalization of relative degree to multivariable systems and is crucial in problems such as decoupling inverse dynamics and adaptive control in order for a system to be input output decoupled using static state feedback the existence of a diagonal interactor matrix must first be established for a multivariable linear system which does not have a diagonal interactor matrix dynamic precompensation or dynamic state feedback is required for achieving a diagonal interactor matrix for the compensated system such precompensation often depends on the parameters of system and is thus difficult to implement with accuracy when the system is subject to parameter uncertainty in this paper we characterize a class of linear systems which can be precompensated to achieve a diagonal interactor matrix without the exact knowledge of the system parameters more precisely we present necessary and sufficient conditions on the transfer matrix of the system under which there exists a diagonal dynamic precompensator such that the compensated system has a diagonal interactor matrix these conditions are associated with the so called non generic singularity of certain matrix related to the system structure but independent of the system parameters the result of this paper is expected to be useful in robust and adaptive designs

a simple existence condition of one degree of freedom block decoupling controllers a block decoupling problem in linear multivariable systems is treated for one degree of freedom controller configuration with unity output feedback the plant transfer matrix which may be non square is assumed to have unstable simple poles and zeros that may coincide a simple existence condition of a block decoupling controller is obtained by directional interpolation approaches

decoupling with stability for linear periodic systems in this paper the classical row by row decoupling problem with stability through the use of a dynamic compensator is studied for linear periodic discrete time systems the necessary and sufficient conditions for the existence of a solution are found and a design procedure of the dynamic compensator is provided by the sufficiency proof and also for the case of a dead beat requirement for the state free response

linear decoupling controllers for constrained dynamic systems linear decoupling controllers of proportional derivative pd type are considered for natural and robotic systems operating under holonomic constraints the dynamic system must be decomposed into orthogonal subspaces of motion and constraint the incremental motion of the system along the two hyper planes must be stable decoupling controllers including both non interacting and disturbance decoupling types are parameterized using a single matrix parameter the proof of stability is based on lyapunov function approach

block decoupling of generalized state space systems abstract the problem of input output block decoupling of generalized state space systems via a regular static state feedback law is studied for the first time the necessary and sufficient conditions for the problem to have a solution are established the necessary and sufficient conditions for block decoupling with simultaneous stabilizability and the necessary and sufficient conditions for block decoupling with simultaneous arbitrary assignment of the system poles are established 1997 elsevier science ltd

variants of equidistribution in arithmetic progression and the twin prime conjecture let mathcal h h 1 ldots h k be a fixed set of k distinct non negative integers we show that bombieri vinogradov type theorems for a certain class of functions f in arithmetic progressions can be extended to the product f n mu 2 n h 1 cdots mu 2 n h k up to almost the same level of distribution as that for f as an application of this result we show equidistribution of tuples of squarefree integers in arithmetic progressions with a level of distribution up to 2 3 this generalizes a result of orr j number theory 3 474 497 1971 we also formulate arithmetic progression analogues of the chowla conjecture on correlations of the mobius function we are able to prove this for some special cases thereby generalizing a result of siebert and wolke math z 122 4 327 341 1971 we also show the relevance of such conjectures to the twin prime problem

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature