pole placement by parametric output feedback abstract this note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m p n where n m and p are the number of states inputs and outputs respectively the approach is based upon parametric eigenstructure assignment of linear time invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations thus the resulting analytical solution explicitly offers all remaining m p n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping minimizing the norm of the feedback matrix and robust control respectively

robust linear regulator design for discrete time systems under polyhedral constraints the robust linear constrained regulation problem for uncertain linear discrete time systems a b is investigated using the theory of positively invariant polyhedral sets closed and bounded polyhedral uncertain domains are considered involving parameters of both a and b matrices and polyhedral constraints on both state and control vectors new sufficient conditions for the solvability of the regulation problem are presented for computational solution of the regulation problem a linear programming approach is proposed where the constraints are given by the solvability conditions and the performance index represents a guaranteed trade off between the closed loop stability margin and the level of control effort

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

parametric output feedback controller design abstract a parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters the set of n closed loop system eigenvalues and a set of mr n design parameters for n state r input m output systems the free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed loop eigenvectors under the condition m r n the principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria an illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth order pilot plant evaporator model

eigenstructure assignment based robust stability conditions for uncertain systems with multiple time varying delays the problem of robust stability of dynamical systems with multiple time varying delays and structured state space uncertainties is discussed based on the fact that the dynamic response of a multivariable control system can be modified by means of eigenstructure assignment a method is presented whereby a new sufficient condition for robust stability of such uncertain time delay systems is derived the new robust stability condition is a sum of terms each of which involves the ith right eigenvector the ith left eigenvector and the real part of the ith eigenvalue and is shown to be less conservative than the earlier result reported in the control literature here each time varying delay is assumed only to be any bounded continuous non negative function and the derived robust stability condition is independent of the delay therefore our results are also applicable to systems with perturbed delays finally a numerical example is given to demonstrate the validity of the results

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

eigenstructure assignment for componentwise ultimate bound minimization in discrete time linear systems this technical note presents a feedback design approach to minimise state ultimate bounds ubs in linear time invariant discrete time systems subject to non vanishing bounded disturbances a target closed loop eigenstructure is first constructed to achieve the lowest possible ubs for one or more state components of the system structural conditions on the system matrices are then derived to guarantee that the target eigenstructure can be assigned by state feedback when the required structural conditions are satisfied an eigenvector assignment procedure can be applied to simultaneously minimise multiple ubs in systems with multiple inputs the results are illustrated by a numerical example drawn from a distributed voltage control problem in inverter based microgrids

eigenvalue generalized eigenvector assignment by output feedback this note generalizes the previous results of the closed loop eigenstructure assignment via output feedback in linear multivariable systems necessary and sufficient conditions for the closed loop eigenstructure assignment by output feedback are presented some known results on entire eigenstructure assignment are deduced from this result

single input single output h control with time domain constraints standard h optimization cannot handle specifications or constraints on the time response of a closed loop system exactly in this paper the problem of h optimization subject to time domain constraints over a finite horizon is considered following an idea from helton and sideris 1989 ieee trans aut control ac 34 427 434 the problem is transformed into a finite dimensional optimization program that is shown to be convex although generically nondifferentiable the objective function is constructed via state space methods and several properties of the optimal constrained controller are discussed together with a robust algorithm for computation it is shown how satisfying the constraints over a finite horizon can imply overall good behavior

sufficient lmi conditions for output feedback control problems the authors present linear matrix inequality lmi conditions for output feedback control problems the results are based on sufficient conditions because they are dependent on the particular state space representation used for describing the system nevertheless the conditions are not sensitive to a certain class of state space transformations and if the control problem is feasible then there exists some state space transformation leading the conditions to be necessary and sufficient for the problem the authors approach can be used for designing decentralized controllers and is easily extended to h sub 2 h sub spl infin and mixed h sub 2 h sub spl infin problems via standard lmi techniques the continuous and discrete time cases are considered and numerical examples are given to illustrate the results

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

motivic periods and grothendieck arithmetic invariants abstract we construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers for the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective showing that a suitable betti de rham realization of 1 motives is fully faithful we can verify this period conjecture in several cases the divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical grothendieck period conjecture for algebraic cycles on smooth and proper schemes these divisibility properties are treated in an appendix by b kahn extending previous work of bloch and colliot thelene raskind

mixed l 1 h controllers for siso discrete time systems abstract in this paper we present a methodology for designing mixed l 1 h controllers these controllers allow for minimizing the worst case peak output due to a persistent disturbance while at the same time satisfying an h norm constraint upon some closed loop transfer function of interest thus they are of interest for applications dealing with mixed time frequency domain performance specifications the main result of the paper shows that suboptimal mixed l 1 h controllers can be obtained by solving a sequence of problems each one consisting of a finite dimensional convex optimization and a standard unconstrained h problem

convergence of optimal control problems with an h norm constraint this paper considers the problem of computing a stabilizing controller for a multivariable plant so that the performance objective defined on a closed loop transfer matrix is minimized while the h norm of possibly another transfer matrix is constrained in other words the problem is one of keeping the induced l2 to l2 norm from an input vector to an output vector below some pre specified level e g for guaranteeing robust stability against unstructured perturbations while achieving the best possible performance as measured by a function defined over a closed loop transfer matrix such a problem is referred to as a mixed optimization problem and includes h2 h l1 h and time domain constrained h control as special cases the approach in this paper is to approximate the mixed problem which is infinite dimensional by one involving a finite number of variables the performance achieved by a solution to the finite problem can be arbitrarily close to the optimal performance of the mixed problem moreover given a level of suboptimality the number of variables involved in the optimization can be bounded a priori in terms of the data the theory is illustrated by briefly discussing two examples

parametric eigenstructure assignment by output feedback control the case of multiple eigenvalues this paper deals with closed loop eigenstructure assignment by output feedback control in linear multivariable systems for the general case of multiple eigenvalues the approach is algebraic in nature and operates directly on the closed loop characteristic equation using fundamental properties of determinants and their derivatives a compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non uniqueness of the solution of the eigenvalue assignment problem some of these parameter vectors assume restricted forms while others are free a computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least square error sense an illustrative numerical example is included

static output feedback controllers stability and convexity the main objective of this paper is to solve the following stabilizing output feedback control problem given matrices a b sub 2 c sub 2 with appropriate dimensions find if one exists a static output feedback gain l such that the closed loop matrix a b sub 2 lc sub 2 is asymptotically stable it is known that the existence of l is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs hence this paper provides a new sufficient but not necessary condition for the solvability of the above stabilizing output feedback control problem as a natural extension we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index some examples borrowed from the literature are solved to illustrate the theoretical results

a reduced order framework applied to linear systems with constrained controls a major issue in the control of dynamical systems is the integration of both technological constraints and some dynamic performance requirements in the design of the control system the authors show in this work that it is possible to solve a class of constrained control problems of linear systems by using a reduced order system obtained by the projection of the trajectories of the original system onto a subspace associated with the undesirable open loop eigenvalues the class of regulation schemes considered uses full state feedback to guarantee that any trajectory emanating from a given polyhedral set of admissible initial states remains in that set this set of admissible states is said to be positively invariant with respect to the closed loop system the authors also address the important issues of numerical stability and complexity of the computations

transmission zero assignment using semistate descriptions the problem of finite infinite transmission zero assignment is examined by squaring a system from the outputs to the inputs in particular this problem is studied in two cases state accessible systems and partially state accessible systems it is shown that the problem of transmission zero assignment for state accessible state variable systems is equivalent to a pole placement problem with state feedback for a generalized system which always has a solution in the case of partially state accessible systems it is shown that the transmission zero assignment problem is equivalent to a pole placement problem with output feedback for a generalized system in both cases the block hessenberg form of the system and the extended lower triangular hessenberg form are exploited to formulate the problem

feedback control of linear discrete time systems under state and control constraints in this paper the problem of stabilizing linear discrete time systems under state and control linear constraints is studied based on the concept of positive invariance existence conditions of linear state feedback control laws respecting both the constraints are established these conditions are then translated into an algorithm of linear programming

an eigenstructure assignment approach for constrained linear continuous time singular systems abstract this paper establishes necessary and sufficient algebraic conditions for positive invariance of convex polyhedra with respect to some linear continuous time singular systems they can be considered as an extension for linear singular systems of the classical positive invariance relations for regular linear systems for a stabilizable and impulse controllable singular system with constrained inputs a stabilizing state feedback control guaranteeing the closed loop positive invariance of some polyhedral sets determined from the feedback matrix is studied an analysis of the closed loop positive invariance relations is thus presented in terms of eigenstructure and stability properties an eigenstructure assignment technique is proposed depending on the number of stable finite poles of the singular system

realisation l adique des motifs triangules geometriques ii for geometrical triangulated motives with rational coefficients over a ground field of characteristic zero which is embeddable into mathbb c huber j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 has constructed a realization functor with values in the category of mixed realization of huber mixed motives and their realization in derived categories lecture notes in mathematics vol 1604 springer berlin 1995 in this sequel to ivorra doc math 12 607 671 2007 we prove that the l adic realization functor obtained in theorem 4 3 of ivorra doc math 12 607 671 2007 is the same up to a canonical isomorphism as the l adic component of a huber s construction in this way ivorra in doc math 12 607 671 2007 might be viewed as an integral generalization to all noetherian separed schemes of the work huber in j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 as far as the l adic setting is concerned we also prove a comparison theorem with the classical l adic cycle class map over a perfect field using a naive motivic cycle class map

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

brief paper optimal control for linear systems with state equality constraints this paper deals with the optimal control problem for linear systems with linear state equality constraints for deterministic linear systems first we find various existence conditions for constraining state feedback control and determine all constraining feedback gains from which the optimal feedback gain is derived by reducing the dimension of the control input space for systems with stochastic noises it is shown that the same gain used for constraining the deterministic system also optimally constrains the expectation of states inside the constraint subspace and minimizes the expectation of the squared constraint error we compare and discuss performance differences between unconstrained using penalty method projected and constrained controllers for both deterministic and stochastic systems finally numerical examples are used to demonstrate the performance difference of the three controllers

positively invariant polyhedral sets of discrete time linear systems the problem of the existence of positively invariant polyhedral sets for linear discrete time dynamical systems is studied in the first part of the paper necessary and sufficient conditions for a

constrained regulation of linear systems abstract in this paper the linear constrained regulation problem without an assigned set of initial states is investigated this problem consists of the determination of a linear state feedback control law and of a set of admissible initial states d so that every trajectory of the resulting closed loop system which emanates from the set converges asymptotically to the origin without violation of the control constraints by applying well known results on the positive invariance of polyhedral sets an eigenstructure assignment approach to this problem is established if the number of unstable open loop eigenvalues does not exceed the number of control variables then this approach enables one to derive a linear state feedback stabilizing control law which makes the set of states where the control constraints are respected positively invariant this positively invariant set is the maximal admissible set of initial states for the control law under consideration for the case where the number of control variables is greater than the number of the unstable open loop eigenvalues a modified algorithm is proposed

design of l q regulators for state constrained continuous time systems a new methodology to the design of lq regulators for continuous time systems subject to linear state constraints is proposed consisting of two parts in the first one the positive invariance of the polyhedron defined by the constraints in the state space is imposed guaranteeing thereby that the constraints will not be violated furthermore the admissible constrained controllers are parameterized via the determination of the elements which are fixed in the state feedback matrix this parameterization enables in a second part the l q regulator to be obtained from the solution of a parameter optimization problem subject to linear constraints for which it is proposed a specialized feasible directions method

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

constrained stabilization of continuous time linear systems in this paper we consider the stabilization problem for linear continuous time systems under state and control constraints we show that the largest domain of attraction to the origin can be arbitrarily closely approximated by a polyhedral domain of attraction associated to a certain continuous feedback stabilizing control and we show how to use existing numeric procedures for discrete time systems to solve the continuous time problem we propose a new discontinuous stabilizing control law for scalar input systems which has the advantage of being successfully applicable to systems with quantized control

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

lmi approach to an h sub spl infin control problem with time domain constraints over a finite horizon the discrete time h sub spl infin control problem is considered with time domain constraints over a finite horizon it is shown that a solution of this problem can be obtained from a system of linear matrix inequalities

output feedback eigenstructure assignment using a new reduced orthogonality condition this paper presents a new method of output feedback eigenstructure assignment a new reduced orthogonality condition is derived which is less restrictive on the design degrees of freedom than others in the literature from this a novel general formulation for the gain matrix is admitted which utilizes a two stage design process in the first stage a subset of desired eigenvectors is assigned either left or right in the second stage a dual set is assigned which adheres to the necessary and sufficient conditions for output feedback eigenstructure assignment proved earlier in the paper a numerical example is presented to illustrate the whole procedure

polytopic control lyapunov functions for robust stabilization of a class of nonlinear systems abstract we develop a method for computing a region in state space over which a nonlinear system is guaranteed by a given polytopic control lyapunov function to be stable in closed loop under some appropriate control law for systems which are nonlinear in only a few state variables the procedure is computationally tractable the computation time required to evaluate stability over each cone comprising a level set of the lyapunov function is exponential in the number of nonlinear states but otherwise polynomial in the dimension of the full state space control constraints and robustness to bounded disturbances are easily incorporated

multistage parametric eigenstructure assignment by output feedback control this paper develops an efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output feedback control the sets of closed loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages this allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions the number of effective free parameters beyond eigenvalue assignment is determined and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced numerical examples are included to demonstrate the design procedure

some necessary and sufficient conditions for eigenstructure assignment abstract some necessary and sufficient conditions for closed loop eigenstructure assignment by output feedback in time invariant linear multivariable control systems are presented a simple condition on a square matrix necessary and sufficient for it to be the closed loop plant matrix of a given system with some output feedback is the basis of the paper some known results on entire eigenstructure assignment are deduced from this the concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors

output feedback eigenstructure assignment using two sylvester equations the eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p m n the main tool used is the concept of c a b invariance and two coupled sylvester equations the solution of which leads to the computation of an output stabilizing feedback a computationally efficient algorithm for the solution of these two coupled equations which leads to the computation of a desired output feedback is presented

mixed l sub 1 h sub spl infin control of mimo systems via convex optimization we present a methodology for designing mixed l sub 1 h sub spl infin controllers for mimo systems these controllers allow for minimizing the worst case peak output due to persistent disturbances while at the same time satisfying an h sub spl infin norm constraint upon a given closed loop transfer function therefore they are of particular interest for applications dealing with multiple performance specifications given in terms of the worst case peak values both in the time and frequency domains the main results of the paper show that 1 contrary to the h sub 2 h sub spl infin case the l sub 1 h sub spl infin problem admits a solution in l sub 1 and 2 rational suboptimal controllers can be obtained by solving a sequence of problems each one consisting of a finite dimensional convex optimization and a four block h sub spl infin problem moreover this sequence of controllers converges in the l sub 1 topology to an optimum

quadratic characterization and use of output stabilizable subspaces this note treats the problem of stabilization of linear systems by static output feedback using the concept of c a b invariant subspaces the work provides a new characterization of output stabilizable c a b invariant subspaces through two coupled quadratic stabilization conditions an equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by static output feedback an algorithm is provided and numerical examples are reported to illustrate the approach

simple lp type criteria for positively invariant polyhedral sets let s be a convex polyhedral set in the state space of a linear dynamical system a new proof of an algebraic condition for the set s to be positively invariant is given by the dual set of s the condition obtained in this correspondence can be examined by solving a set of standard lp type formulas it is also shown that the conventional algebraic conditions have redundancies in the lp type formulas discrete time systems as well as continuous time systems are considered

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

on the positive invariance of polyhedral sets for discrete time systems abstract in this note necessary and sufficient conditions for a polyhedral set to be a positively invariant set of a linear discrete time system are established

eigenstructure assignment for state constrained linear continuous time systems abstract linear state constraints define a polyhedron in the state space of a dynamical system if this polyhedron can be made positively invariant by state feedback the constraints are satisfied all along the trajectory for any initial point in this polyhedron in the context of continuous time linear systems some algebraic positive invariance conditions are established for unbounded symmetrical polyhedra the existence of a solution to the corresponding set of equations and inequalities depends on the structural properties of an associated input output system in particular the number of zeros of this system should be appropriate and they should be stable if these conditions are satisfied the problem can easily be solved by eigenvalue and eigenvector assignment

eigenvalue assignment robustness the analysis for autonomous system matrices abstract new techniques are presented for the analysis of eigenvalue assignment robustness the basic idea is to use a root locus approach to ensure that the eigenvalues of a dynamic system under parameter perturbations are restricted in the distinct desired regions no restriction is imposed on the shapes of the specified regions both the norm bound and the element bound for the allowable perturbations are obtained scaling techniques are proposed to increase the allowable element bound the proposed methods are applicable to the continuous time case as well as to the discrete time case when the eigenvalues are just required to locate in the stable region the proposed criteria will become the stability robustness criteria

nonquadratic lyapunov functions for robust control abstract this paper deals with the problem of controlling a linear continuous time system with structured time varying parameter uncertainties and input disturbances with a lyapunov function approach in contrast with most of the previous results in the literature we do not confine our attention to the class of quadratic lyapunov functions conversely the basic motivation of this paper is to determine whether there exist other functions that can be conveniently used as candidate lyapunov functions this question has a positive answer the proposed class is that of polyhedral norms or more generally of polyhedral minkowski functionals we show that the class of these functions is universal in the sense that if the problem of ultimately bounding the state in an assigned convex set via state feedback control can be solved via a lyapunov function and a continuous state feedback compensator then it can be solved via a polyhedral lyapunov function and a possibly different continuous control moreover we show that the control can be piecewise linear a numerical technique for constructing the controller is presented for the case in which the uncertainty constraint sets are polyhedral

constrained stabilization via smooth lyapunov functions abstract we consider the problem of stabilizing a dynamic system by means of bounded controls we show that the largest domain of attraction can be arbitrarily closely approximated by a smooth domain of attraction for which we provide an analytic expression such an expression allows for the determination of a non linear control law in explicit form

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

robust eigenstructure assignment for the extended medium range air to air missile abstract a new sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty is presented this sufficient condition is a sum of terms each of which involves the ith right eigenvector the ith left eigenvector and the real part of the ith eigenvalue this new robustness result is less conservative than an earlier result which involves the modal matrix and the real part of the eigenvalue which is closest to the imaginary axis in the complex plane a robust design is computed for the extended medium range air to air missile and the new design is compared with an earlier orthogonal projection eigenstructure assignment design the new design method uses the matlabtm optimization toolbox to minimize the integral of the deviations of the integrated roll rate which is approximately the bank angle from zero the integral is approximated by a sum of discrete samples of the integrated roll rate while normalizing the integration width to unity constraints are placed on the real part of the dutch roll and roll mode eigenvalues the damping ratios of the dutch roll and roll mode the aileron and rudder deflection rates and the sufficient condition for robust stability the new design satisfies the robustness condition while also yielding an improved transient response

further results on the optimal rejection of persistent bounded disturbances the problem of designing controllers that optimally reject persistent disturbances is studied the focus is on the case where the plant to be controlled has either zeros or poles on the stability boundary i e the unit circle in the discrete time case and the extended j omega axis in the continuous time case for the discrete time case the problem of minimizing a cost functional of the form f rg sub 1 where the transform g of g has some unit circle zeros is studied a previously published dual problem formulation is extended and it is shown that an optimal controller need not exist the construction of a sequence of suboptimal controllers whose performance approaches the unattainable infimum of the cost function is studied it is shown that two results which hold in the case of h sub infinity optimization do not hold in the presented situation specifically the introduction of unit circle zeros can increase the value of the infimum even when every unit circle zero of g is also a zero of f and a sequence of controllers constructed in an obvious fashion fails to be an optimizing sequence similar results are obtained for the continuous time case

weil etale cohomology over finite fields we calculate the derived functors r for the base change from the weil etale site to the etale site for a variety over a finite field for smooth and proper varieties we apply this to express tate s conjecture and lichtenbaum s conjecture on special values of functions in terms of weil etale cohomology of the motivic complex n

the regulator problem for class of linear systems with constrained control abstract this paper deals with the regulator problem for a class of linear discrete time systems with nonsymmetrical constrained controls for such a class a nonsymmetrical set of positive invariance and global attractivity exists this allows a globally asymptotically stable regulator to be obtained despite the existence of the constrained controls

optimal solution and approximation to the l sub 1 h sub spl infin control problem this paper addresses the l sub 1 h sub spl infin optimal control problem for a system described by linear time invariant finite dimensional discrete time equations it is shown that a solution to this problem exists and can be approximated arbitrarily by real rational transfer matrices perhaps more interesting from a computational point of view a bound on the order of a spl delta suboptimal solution is also given

perturbation theory of output feedback pole assignment perturbation theory for output feedback eigenstructure assignment is considered the analysis is based on general conditions for eigenstructure assignment together with the well known perturbation theory for the pseudo inverse of a matrix this enables us to present a variety of sensitivity analyses for this problem and to indicate some precautions when choosing eigenvectors in the pole assignment problem

a new approach to eigenstructure assignment by output feedback the eigenstructure assignment problem for a linear time invariant multi input multi output system using output feedback is considered a new approach is developed which identifies the eigenspaces for the desired set of all the closed loop eigenvalues for the assignment of this desired set necessary and sufficient conditions are established these conditions contain two coupled sylvester matrix equations one of which is proven to be a reduced order square sylvester matrix equation this results in an efficient analytical procedure numerically superior to known techniques for the determination of the output feedback gain matrix

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

exact pole assignment with regularity by output feedback in descriptor systems part 2 in this paper the first of two we examine the problem of modal control of linear time invariant multivariable descriptor systems in particular for systems satisfying a certain inequality we will give necessary and sufficient conditions for the existence of an output feedback matrix possibly complex which exactly assigns an arbitrary set of r the number of independent semi state variables of the system distinct complex numbers to a generalized eigenspectrum of the closed loop system while ensuring that the resulting system has a unique smooth solution for each admissible initial condition furthermore it is shown that if the set of proposed poles contains only real elements the assignment can be carried out using real feedback next we present conditions that are necessary and sufficient for pole assignability by real feedback of a self conjugate set of complex numbers provided that the system satisfies a further inequality

constrained regulation of linear continuous time dynamical systems abstract in this paper the linear constrained regulation problem lcrp for continuous time dynamical systems is studied the first part of the paper deals with the existence of linear state feedback control laws that transfer asymptotically to the origin all initial states belonging to a given polyhedral subset of the state space while respecting linear constraints on both state and control vectors then the lcrp is formulated as an optimization problem which can be solved by applying linear programming techniques

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

a bilinear formulation for the output feedback problem in linear systems this note ties together a geometric theory and previous algebraic results for the closed loop eigenstructure assignment by output feedback in multivariable systems necessary and sufficient conditions for the closed loop stabilization eigenstructure assignment are presented in terms of a bilinear sylvester equation the solutions of which completely characterize the closed loop eigenstructure problem with output feedback some preliminary results for the solution of this bilinear equation are presented

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem

siso controller design to minimize a positive combination of the l 1 and the h 2 norms abstract we consider the problem of minimizing a given positive linear combination of the l1 norm and the square of the h 2 norm of the closed loop over all internally stabilizing controllers the problem is analysed for the discrete time siso linear time invariant case it is shown that a unique optimal solution always exists and can be obtained by solving a finite dimensional convex optimization problem with an a priori determined dimension it is also established that the solution is continuous with respect to changes in the coefficients of the linear combination