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

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

degrees of freedom of two hop wireless networks everyone gets the entire cake we show that fully connected two hop wireless networks with k sources k relays and k destinations have k degrees of freedom both in the case of time varying channel coefficients and constant channel coefficients in which case the result holds for almost all values of constant channel coefficients our main contribution is a new achievability scheme which we call aligned network diagonalization this scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations thus being received free of interference by their intended destination in addition we extend our scheme to multihop networks with fully connected hops and multihop networks with mimo nodes for which the degrees of freedom are also fully characterized

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

primal dual strategy for constrained optimal control problems an algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed it is based on an active set strategy involving primal as well as dual variables for discretized problems sufficient conditions for convergence in finitely many iterations are given numerical examples are given and the role of the strict complementarity condition is discussed

on maximum linearly achievable degrees of freedom region of 2 times 2 times 2 interference network with arbitrary antenna configurations we obtain the exact maximum degrees of freedom dof region achieved by linear transceivers without symbol extensions of the 2 times 2 times 2 multiple input multiple output mimo interference network which is comprised of two sources two relays and two destinations each with arbitrary number of antennas we prove that the maximum achievable dof region for the networks under some antenna configurations coincide with the cut set bound of the networks while there is only one dof gap from the bound for the networks under other configurations which can not be bridged by linear transceivers the basic idea of the proof is to construct a two tier transceiver where the first tier decomposes the general networks to several basic networks with special configurations and the second tier achieves the maximal dof tuples for these basic networks a mechanism for constructing the second tier transceiver is proposed which is referred to as channel scaling assisted interference elimination combined with interference avoidance at sources and interference cancelation at destinations depending on the antenna configurations interference free transmission can be ensured

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

local error estimates for supg solutions of advection dominated elliptic linear quadratic optimal control problems we derive local error estimates for the discretization of optimal control problems governed by linear advection diffusion partial differential equations pdes using the streamline upwind petrov galerkin supg stabilized finite element method we show that if the supg method is used to solve optimization problems governed by an advection dominated pde the convergence properties of the supg method is substantially different from the convergence properties of the supg method applied for the solution of an advection dominated pde the reason is that the solution of the optimal control problem involves another advection dominated pde the so called adjoint equation whose advection field is just the negative of the advection of the governing pdes for the solution of the optimal control problem a coupled system involving both the original governing pde as well as the adjoint pde must be solved we show that in the presence of a boundary layer the local error between the solution of the supg discretized optimal control problem and the solution of the infinite dimensional problem is only of first order even if the error is computed locally in a region away from the boundary layer in the presence of interior layers we prove optimal convergence rates for the local error in a region away from the layer between the solution of the supg discretized optimal control problems and the solution of the infinite dimensional problem numerical examples are presented to illustrate some of the theoretical results

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

non commutative discretize then optimize algorithms for elliptic pde constrained optimal control problems abstract in this paper we analyze the convergence of several optimize then discretize and discretize then optimize algorithms based on either a second order or a fourth order finite difference discretization for solving elliptic pde constrained optimal control problems to ensure the convergence of a discretize then optimize algorithm one well accepted criterion is to design the discretization scheme such that the resulting discretize then optimize algorithm commutes with the corresponding optimize then discretize algorithm in other words both algorithms should give rise to exactly the same discrete optimality system however such a restrictive criterion is not trivial to fulfill by investigating a distributed control problem governed by an elliptic equation we first show that enforcing such a stringent condition of commutative property is only sufficient but not necessary for achieving the desired convergence we then introduce some suitable h 1 semi norm penalty regularization terms to recover the lost convergence due to the inconsistency caused by the loss of commutativity numerical experiments are carried out to verify our theoretical analysis and also validate the effectiveness of our proposed regularization techniques

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

multigrid methods for pde optimization research on multigrid methods for optimization problems is reviewed optimization problems considered include shape design parameter optimization and optimal control problems governed by partial differential equations of elliptic parabolic and hyperbolic type

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

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

capacity bounds for the gaussian interference channel the capacity region of the two user gaussian interference channel ic is studied three classes of channels are considered weak one sided and mixed gaussian ics for the weak gaussian ic a new outer bound on the capacity region is obtained that outperforms previously known outer bounds the sum capacity for a certain range of channel parameters is derived for this range it is proved that using gaussian codebooks and treating interference as noise are optimal it is shown that when gaussian codebooks are used the full han kobayashi achievable rate region can be obtained by using the naive han kobayashi achievable scheme over three frequency bands equivalently three subspaces for the one sided gaussian ic an alternative proof for the sato s outer bound is presented we derive the full han kobayashi achievable rate region when gaussian codebooks are utilized for the mixed gaussian ic a new outer bound is obtained that outperforms previously known outer bounds for this case the sum capacity for the entire range of channel parameters is derived it is proved that the full han kobayashi achievable rate region using gaussian codebooks is equivalent to that of the one sided gaussian ic for a particular range of channel parameters

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

the approximate capacity of the many to one and one to many gaussian interference channels recently etkin tse and wang found the capacity region of the two user gaussian interference channel to within 1 bit s hz a natural goal is to apply this approach to the gaussian interference channel with an arbitrary number of users we make progress towards this goal by finding the capacity region of the many to one and one to many gaussian interference channels to within a constant number of bits the result makes use of a deterministic model to provide insight into the gaussian channel the deterministic model makes explicit the dimension of signal level a central theme emerges the use of lattice codes for alignment of interfering signals on the signal level

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

crank nicolson schemes for optimal control problems with evolution equations crank nicolson methods are often used for the simulation of initial boundary value problems for parabolic partial differential equations in this paper we present a family of discretizations for parabolic optimal control problems based on crank nicolson schemes with different time discretizations for state y and adjoint state p so that discretization and optimization commute one of these methods can also be explained as a stormer verlet scheme in the context of geometric numerical integration of hamiltonian systems two of the schemes may also be obtained as a galerkin method with quadrature further we investigate the schemes for a variable time step size and prove second order convergence for this case if the time step size is chosen with respect to an arbitrary sufficiently smooth mesh generating function

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

runge kutta methods in optimal control and the transformed adjoint system the convergence rate is determined for runge kutta discretizations of nonlinear control problems the analysis utilizes a connection between the kuhn tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle this connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function

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

optimal control of the convection diffusion equation using stabilized finite element methods in this paper we analyze the discretization of optimal control problems governed by convection diffusion equations which are subject to pointwise control constraints we present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case moreover the in general different approaches optimize then discretize and discretize then optimize coincide for the proposed discretization scheme this allows for a symmetric optimality system at the discrete level and optimal order of convergence

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

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

control of an elliptic problem with pointwise state constraints this paper deals with a quadratic control problem for elliptic equations with pointwise state constraints existence and uniqueness of the solution is proved optimality conditions are given and regularity of the optimal solution is investigated

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

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

high order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems high mixed order finite difference discretization of optimality systems arising from elliptic nonlinear constrained optimal control problems are discussed for the solution of these systems an efficient and robust multigrid algorithm is presented theoretical and experimental results show the advantages of higher order discretization and demonstrate that the proposed multigrid scheme is able to solve efficiently constrained optimal control problems also in the limit case of bang bang control

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

accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system the finite difference multigrid solution of an optimal control problem associated with an elliptic equation is considered stability of the finite difference optimality system and optimal order error estimates in the discrete l2 norm and in the discrete h1 norm under minimum smoothness requirements on the exact solution are proved sharp convergence factor estimates of the two grid method for the optimality system are obtained by means of local fourier analysis a multigrid convergence theory is provided which guarantees convergence of the multigrid process towards weak solutions of the optimality 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

brief paper a unified framework for the numerical solution of optimal control problems using pseudospectral methods a unified framework is presented for the numerical solution of optimal control problems using collocation at legendre gauss lg legendre gauss radau lgr and legendre gauss lobatto lgl points it is shown that the lg and lgr differentiation matrices are rectangular and full rank whereas the lgl differentiation matrix is square and singular consequently the lg and lgr schemes can be expressed equivalently in either differential or integral form while the lgl differential and integral forms are not equivalent transformations are developed that relate the lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem the lg and lgr discrete costate systems are full rank while the lgl discrete costate system is rank deficient the lgl costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the lgl discrete costate system an example is considered to assess the accuracy and features of each collocation scheme

structured lattice codes for some two user gaussian networks with cognition coordination and two hops we study a number of two user interference networks with multiple antenna transmitters receivers mimo transmitter side information in the form of linear combinations over an appropriate finite field of the information messages and two hop relaying we start with a cognitive interference channel cic where one of the transmitters noncognitive has knowledge of a rank 1 linear combination of the two information messages while the other transmitter cognitive has access to a rank 2 linear combination of the same messages this is referred to as the network coded cic since such linear combination may be the consequence of some random linear network coding scheme implemented in the backbone wired network for such channel we develop an achievable region based on a few novel concepts precoded compute and forward pcof with channel integer alignment cia combined with standard dirty paper coding we also develop a capacity region outer bound and find the symmetric generalized degrees of freedom gdof region of the network coded cic through the gdof characterization we show that knowing mixed data linear combinations of the information messages provides a unbounded spectral efficiency gain over the classical cic counterpart if the ratio in decibel of signal to noise snr to interference to noise is larger than certain threshold then we consider a gaussian relay network having the two user mimo ic as the main building block we use pcof with cia to convert the mimo ic into a deterministic finite field ic then we use a linear precoding scheme over the finite field to eliminate interference in the finite field domain using this unified approach we derive the symmetric sum rate of the two user mimo ic with coordination cognition and two hops we also provide finite snr results not just dof which show that the proposed coding schemes are competitive against state of the art interference avoidance scheme based on orthogonal access for standard randomly generated rayleigh fading channels

on interference networks over finite fields we present a framework to study linear deterministic interference networks over finite fields unlike the popular linear deterministic models introduced to study gaussian networks we consider networks where the channel coefficients are general scalars over some extension field fpm scalar m th extensionfield models m m diagonal matrices over fp m symbol extension ground field models and m m general non singular matrices mimo ground field models we use the companion matrix representation of the extension field to convert m th extension scalar models into mimo ground field models where the channel matrices have special algebraic structure for such models we consider the 2 2 2 topology two hops two flow and the 3 user interference network topology we derive achievability results and feasibility conditions for certain schemes based on the precoding based network alignment pbna approach where intermediate nodes use random linear network coding i e propagate random linear combinations of their incoming messages and non trivial precoding decoding is performed only at the network edges at the sources and destinations furthermore we apply this approach to the scalar 2 2 2 complex gaussian ic with fixed channel coefficients and show two competitive schemes outperforming other known approaches at any snr where we combine finite field linear precoding decoding with lattice coding and the compute and forward approach at the signal level as a side result we also show significant advantages of vector linear network coding both in terms of feasibility probability with random coding coefficients and in terms of coding latency with respect to standard scalar linear network coding in pbna schemes

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

second order runge kutta approximations in control constrained optimal control in this paper we analyze second order runge kutta approximations to a nonlinear optimal control problem with control constraints if the optimal control has a derivative of bounded variation and a coercivity condition holds we show that for a special class of runge kutta schemes the error in the discrete approximating control is o h2 where h is the mesh spacing

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

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

worst case additive noise in wireless networks a classical result in information theory states that the gaussian noise is the worst case additive noise in point to point channels meaning that for a fixed noise variance the gaussian noise minimizes the capacity of an additive noise channel in this paper we significantly generalize this result and show that the gaussian noise is also the worst case additive noise in wireless networks with additive noises that are independent from the transmit signals more specifically we show that if we fix the noise variance at each node then the capacity region with gaussian noises is a subset of the capacity region with any other set of noise distributions we prove this result by showing that a coding scheme that achieves a given set of rates on a network with gaussian additive noises can be used to construct a coding scheme that achieves the same set of rates on a network that has the same topology and traffic demands but with non gaussian additive noises

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

linear degrees of freedom of the x channel with delayed csit we establish the degrees of freedom dof of the two user x channel with delayed channel knowledge at transmitters i e delayed channel state information at the transmitters csit assuming linear coding strategies at the transmitters we derive a new upper bound and characterize the linear dof of this network to be 6 5 the converse builds upon our development of a general lemma that shows that if two distributed transmitters employ linear strategies the ratio of the dimensions of received linear subspaces at the two receivers cannot exceed 3 2 due to delayed csit as a byproduct we also apply this general lemma to the three user interference channel with delayed csit thereby deriving a new upper bound of 9 7 on its linear dof this is the first bound that captures the impact of delayed csit on the dof of this network under the assumption of linear encoding strategies

approximately achieving gaussian relay network capacity with lattice based qmf codes recently a new relaying strategy quantize map and forward qmf scheme has been demonstrated to approximately achieve within an additive constant number of bits the gaussian relay network capacity universally i e for arbitrary topologies channel gains and snrs this was established using gaussian codebooks for transmission and random mappings at the relays in this paper we develop structured lattice codes that implement the qmf strategy the main result of this paper is that such structured lattice codes can approximately achieve the gaussian relay network capacity universally again within an additive constant in addition we establish a similar result for half duplex networks where we demonstrate that one can approximately achieve the capacity using fixed transmit receive tx rx schedules for the relays with no transmit power optimization across the different tx rx states of the network

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

interference networks with no csit impact of topology we consider partially connected k user interference networks where the transmitters have no knowledge about the channel gain values but they are aware of network topology we introduce several linear algebraic and graph theoretic concepts to derive new topology based outer bounds and inner bounds on the symmetric degrees of freedom of these networks we evaluate our bounds for two classes of networks to demonstrate their tightness for most networks in these classes quantify the gain of our inner bounds over benchmark interference management strategies and illustrate the effect of network topology on these gains

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

from finite differences to finite elements a short history of numerical analysis of partial differential equations abstract this is an account of the history of numerical analysis of partial differential equations starting with the 1928 paper of courant friedrichs and lewy and proceeding with the development of first finite difference and then finite element methods the emphasis is on mathematical aspects such as stability and convergence analysis