exact and inexact lqg model matching problems the design of discrete time lqg linear quadratic gaussian controllers that yield closed loop systems that match a provided model is addressed the solution is in the form of a two degree of freedom controller having feedback and feedforward paths that independently provide the optimal actions for disturbance rejection and model matching exact and approximate model matching cases are discussed in a unified fashion

an h minimax approach to the design of robust control systems abstract a realistic feedback design problem is posed based on the minimization of a weighted combination of the sensitivity and complementary sensitivity matrices a solution is obtained which makes use of the recently proposed methods for minimizing the sensitivity function alone

krein space approach to h sup spl infin mixed sensitivity minimization for a class of infinite dimensional systems motivated by the computation of the h sup spl infin optimal performance and optimal mixed sensitivity for a class of infinite dimensional systems the author considers the explicit computation of the norm and minimal symbols of a class of hankel plus toeplitz type operators with irrational symbols using the krein space approach the author shows how to explicitly compute the norm and parameterize all the minimal symbols the results are used to obtain a complete solution to the h sup spl infin optimal mixed sensitivity synthesis problem for a class of infinite dimensional systems an explicit formula for computing the h sup spl infin optimal performance and explicit parameterization of all optimal and suboptimal mixed sensitivities an illustrative example is given

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

a hamiltonian based solution to the two block h problem for general plants in h and rational weights a complete skew toeplitz type solution to the two block h 1 problem for innite dimensional stable plants with rational weights is derived with a basis free proof the solution consists of one riccati equation with a rank criterion for a transcendental function of a certain hamiltonian this gives a natural extension of the well known formula for the one block case an example is given to illustrate the result c 2000 elsevier science b v all rights reserved

a hyperchaotic system from the rabinovich system this paper presents a new 4d hyperchaotic system which is constructed by a linear controller to the 3d rabinovich chaotic system some complex dynamical behaviors such as boundedness chaos and hyperchaos of the 4d autonomous system are investigated and analyzed a theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a lienard like oscillatory motion around a hypersaddle stationary point at the origin the corresponding bounded hyperchaotic and chaotic attractors are first numerically verified through investigating phase trajectories lyapunov exponents bifurcation path and poincare projections finally two complete mathematical characterizations for 4d hopf bifurcation are rigorously derived and studied

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

a simple inequality for the von neumann jordan and james constants of a banach space abstract let c nj x and j x be the von neumann jordan and james constants of a banach space x respectively we shall show that c nj x j x where equality holds if and only if x is not uniformly non square this answers affirmatively to the question in a recent paper by alonso et al j alonso p martin p l papini wheeling around von neumann jordan constant in banach spaces studia math 188 2008 135 150 this inequality looks quite simple and covers all the preceding results in particular this is much stronger than maligranda s conjecture c nj x j x 2 4 1

a note on essential spectra and norms of mixed hankel toeplitz operators in this brief hankel toeplitz operators which occur in feedback theory e g in the minimization of mixed h sensitivity and complementary sensitivity will be considered a method of computing their spectra eigenvectors and norms will be presented for infinite dimensional systems subject to continuous weightings

on the stable exact model matching problem abstract the stable exact model matching problem semmp is investigated we state and prove a number of equivalent necessary and sufficient conditions for the existence of proper solutions to the exact model matching problem that are also stable i e have no poles inside a symmetric forbidden subset of the finite complex plane c these results can be viewed as the counterpart of the results in 3 and 9 for the case of the ring of proper and stable rational functions

the four block adamjan arov krein problem abstract this paper is concerned with the mixed sensitivity h design in the most general i e the four block case this problem involves in a crucial manner the so called four block operator the norm of which is the achievable feedback tolerance our objective in this paper is to provide an interpretation for all singular values of these singular values are given an adamjan arov krein interpretation in terms of the l distance of an l function to h l intuitively the singular values of are the various tolerance levels that can be achieved if we allow a various number of unstable poles in the closed loop we finally provide an upper bound on the number of singular values

fast computation of achievable feedback performance in mixed sensitivity h design the computational bottleneck of the h infty design has been recognized to be the e iteration a computationally demanding direct search of the minimum achievable h infty performance verma and jonckheere showed that the optimal h infty performance can be characterized as the spectral radius of the so called toeplitz plus hankel operator even before the appearance of the toeplitz plus hankel operator in the h infty setting the same operator had already been shown to play a crucial role in the spectral theory of the linear quadratic problem developed by jonckheere and silverman in this paper we exploit this common toeplitz plus hankel operator structure shared by the seemingly unrelated linear quadratic and h infty problems and we construct fast state space algorithms for evaluating the spectral radius of the toeplitz plus hankel operator the salient feature of the algorithm is that the spectral radius can be evaluated with an accuracy predicted by an identifiable error bound from the antistabilizing solution of the algebraic riccati equation of the linear quadratic problem associated with the h infty design

frequency domain conditions for parameter convergence in multivariable recursive identification abstract a multivariable adaptive identifier is designed on the basis of a canonical form leading to a unique set of parameters to identify frequency domain conditions for parameter convergence are derived the sufficient condition to guarantee convergence in all cases is that n v distinct frequency components be present in each input of the plant where v is the maximum of the observability indices and n the order of the plant on the other hand the necessary condition requires n mv distinct frequency components distributed over the inputs where m is the number of inputs and at least v frequency components are in each separate input through examples it is shown that convergence may or may not occur for intermediate numbers of frequency components depending on their location and on the plant parameters

geometric mean and triangles inscribed in a semicircle in banach spaces we consider the triangles with vertices x x and y where x y are points on the unit sphere of a normed space using the geometric means of the variable lengths of the sides of these triangles we define two geometric constants for banach spaces these constants are closely related to the modulus of convexity of the space under consideration and they seem to represent a useful tool to estimate the exact values of the james and jordan von neumann constants of some banach spaces

a new hyperchaotic system from the lu system and its control this paper presents a 4d new hyperchaotic system which is constructed by a linear controller to a 3d lu system some complex dynamical behaviors such as hopf bifurcation chaos and hyperchaos of the simple 4d autonomous system are investigated and analyzed the corresponding hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories lyapunove exponents bifurcation path analysis of power spectrum and poincare projections furthermore the design is illustrated with both simulations and experiments finally the control problem of a new hyperchaotic system is investigated using negative feedback control ordinary feedback control dislocated feedback control and speed feedback control are used to suppress hyperchaos to an unstable equilibrium numerical simulations are presented to demonstrate the effectiveness of the proposed controllers

a multivariable self tuning controller based on pole placement design abstract the design problem of controller for discrete time linear multi input output systems is discussed the basic idea is to use pole placement approach a new pole placement tracking problem formulation and its solution is given the design of controller requires no a priori information either about stability or minimum phase of controlled plants the designed controller consists of a feedback part a feedforward part and a new precompensator and is suitable for self tuning control of continuous systems with differing and unknown dead times in each path the controller can have integral action the number of outputs can be different from the number of inputs of the controlled system a reference vector sequence and an effect of the initial state on the system output are given as a left matrix fraction the self tuning algorithm is based on identification of explicit plant model the self tuning algorithm is illustrated by examples

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

minimax lq stochastic tracking and servo problems it is proved that the separation between feedback and feedforward of the two degree of freedom linear quadratic lq stochastic controller reported by e mosca and g zappa ibid vol 34 p 240 2 1989 can be suitably extended when a linear controller is postulated to the minimax lq stochastic tracking and servo problems besides the relevance of the results the authors show that in some problems the wiener and the h sub infinity approaches can play a fruitful complementary role

fast iterative computation of optimal two block h sup infinity norm the two block h sup infinity optimization problem is discussed in which the most computationally demanding work is the computation of the optimal h sup infinity norm denoted by gamma sub 0 the problem of computing gamma sub 0 can be considered as that of finding a gamma such that mu gamma is equal to 1 some new properties of mu gamma are revealed and studied based on these properties and those found by c c chu and j doyle 1985 and z z wang and j b pearson 1984 a very fast computational algorithm for finding gamma sub 0 is proposed

the canonical diophantine equations with applications a fundamental relationship between appropriate pairs of polynomial matrices is presented this relationship termed canonical diophantine equations can be used to resolve a number of standard polynomial matrix problems here the general diophantine equation is constructively resolved in a unique minimal way in addition prime canonical factorizations of a system transfer matrix are derived from knowledge of any dual factorization

on the parametrization of the suboptimal solutions in generalized interpolation abstract we apply methods previously developed to give a explicit parametrization of the suboptimal solutions to the standard h generalized interpolation problem this gives in particular a simple parametrization of all the suboptimal controllers of the standard sensitivity minimization problem

continuous time lq regulator design by polynomial equations abstract the deterministic continuous time lq output regulation problem is solved by polynomial equations as an alternative to the usual riccati equation approach in particular it is shown that riccati based and polynomial methods are fully conceptually equivalent in steady state lq regulation

a spectral characterization of h optimal feedback performance and its efficient computation abstract we study the spectral properties of a toeplitz hankel operator which arises in the context of the mixed sensitivity h optimization problem and whose largest eigenvalue characterizes the optimal achievable performance 0 the existence of such an operator was first shown by verma and jonckheere 26 who also noted the potential numerical advantage of computing eo through its eigenvalue characterization rather than through the iteration here we investigate this operator in detail with the objective of efficiency computing its spectrum we define an adjoint linear quadratic problem that involves the same toeplitz hankel operator as shown by jonckheere and silverman 13 16 consequently a finite polynomial algorithm allows 0 to be characterized as simply as the largest root of a polynomial finally a computationally more attractive state space algorithm emerges from the h t 8 lq relationship this algorithm yields a very good accuracy evaluation of the performance 0 by solving just one algebraic riccati equation thorough exploitation of this algorithm results in a drastic computation reduction with respect to the standard e iteration

optimal model matching control systems minmax approach in this note the optimal interpolation theory is applied to deal with the model matching control problem with this approach we construct a best approximate model matching control in the sense of an h infty norm this approximation is constructed for the imperfect model matching case perfect model matching results whenever it is possible

some inequalities concerning the james constant in banach spaces abstract let a 2 x be the constant introduced by baronti casini and papini this paper discusses the constant a 2 x and states an estimate a 2 x 1 j x 1 in terms of the james constant the estimate enables us to improve an inequality between the james and von neumann jordan constants

an algorithm for the calculation of a nilpotent interactor matrix for linear multivariable systems a new algorithm for the calculation of the delay structure for a linear multivariable system is presented the algorithm evaluates a nilpotent interactor matrix from the matrix of coefficients of the numerator of a right matrix fraction description of the system the resulting nilpotent interactor is a product of first degree nilpotent polynomial matrices

on cancellation in h optimal controllers abstract this note clarifies the mechanism of pole zero cancellations that appeared in the derivation of the h optimal controller via a solution of the corresponding model matching problem the cancellable factor is explicitly expressed using chain scattering matrix descriptions a simple state space formula of the sub optimal controller is also presented based on the chain scattering forms and we show that there is a mixed sensitivity problem that can be solved by calculating a solution of only one riccati equation in each iteration

optimal h multivariable robust controllers and the relationship to lqg design problems a new solution for the multivariable minimax optimal robust design problem is presented the relationship between lqg and h design methods is considered and the h solution is obtained from the solution of a related lqg problem the approach provides insights into the relationship between the h and lqg design philosophies the h solution involves the same type of steps which are involved in the polynomial based solutions of the lqg problem namely spectral factorization and the solution of linear diophantine equations a simplified design procedure is described which requires only the solution of a standard eigenvalue eigenvector problem

an algorithm for super optimal h design the two block case abstract in this paper we consider the strengthened h optimization problem in the two block case an algorithm for the super optimal solution is proposed it is based on results by the authors ieee trans aut control ac 33 833 1988 for the less practical one block case it uses state space models and is numerically implementable a feature of the procedure is an optimality criterion which is a natural generalization of that used in the iterative scheme of doyle lecture notes in advances in multivariable control onr honeywell workshop minneapolis u s a 1984 for the unstrengthened problem

on a new geometric constant related to the von neumann jordan constant abstract the von neumann jordan constant c nj x is computed for x being l 2 l 1 and l l 1 space by introducing a new geometric constant x t these partly give an answer to an open question posed by kato et al some basic properties of this new coefficient are investigated moreover we obtain a new class of banach spaces with uniform normal structure

on the polynomial equations for the mimo lq stochastic regulator the role played by three polynomial equations in the lq stochastic regulation problem is discussed the emphasis is on establishing conditions under which the lq regulator can be obtained via the solution of a single uncoupled diophantine equation nevertheless the authors do not claim that there is any advantage in solving a single uncoupled equation in place of two coupled diophantine equations

a hyperchaos generated from lorenz system abstract this paper presents a four dimension hyperchaotic lorenz system obtained by adding a nonlinear controller to lorenz chaotic system the hyperchaotic lorenz system is studied by bifurcation diagram lyapunov exponents spectrum and phase diagram numerical simulations show that the new system s behavior can be convergent divergent periodic chaotic and hyperchaotic when the parameter varies

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

model following using measured output feedback this article considers the partial state feedback model following problem psfmfp introduced by howze et al 5 here we give a more general statement of this problem and show that its solution is closely related to the existence of certain d a invariant controllability subspaces where d is an output map connected with the measurable output we also give a procedure for the synthesis of a dynamic compensator using less integrators than in 5

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

when do the c0 1 k x spaces determine the locally compact subspaces k of the real line r abstract let x be a finite dimensional space and k a locally compact subspace of the real line r without isolated points the space c 0 1 k x will stand for the banach space of all x valued continuously differentiable functions f such that f and f vanish at infinity endowed with the norm f max f f it is shown that if there is an isomorphism t c 0 1 k x c 0 1 s x satisfying t t 1 x and t t 1 then k and s are homeomorphic where x is a parameter introduced by jarosz in 1989 and t is the norm of t when c 0 1 k x and c 0 1 s x are considered as subspaces of c 0 k x and c 0 s x respectively

on james and von neumann jordan constants and sufficient conditions for the fixed point property abstract in this paper we prove that a banach space x and its dual space x have uniform normal structure if c nj x 1 3 2 the garcia falset coefficient r x is estimated by the c nj x constant and the weak orthogonality coefficient introduced by b sims finally we present an affirmative answer to a conjecture by l maligranda concerning the relation between the james and c nj x constants for a banach space

a division algorithm for polynomial matrices a new algorithm is presented for directly determining both the quotient and the remainder associated with the division of one polynomial matrix by another the procedure requires that the denominator matrix be column proper with nonzero column degrees however unlike earlier algorithms only real matrix multiplications are employed i e there is no need for matrix inversions either explicit or implicit

model matching of discrete linear systems an analysis of the exact model matching problems of discrete time linear multivariable systems is presented the approach is based on input output polynomial models and all solutions to the problem are expressed in a parametric form compact necessary and sufficient conditions for the existence of causal and stable solutions are given a simple design procedure is proposed which provides a stable causal solution it consists essentially of solving a linear equation in polynomial matrices and yields the compensator in a form suitable for direct realisation

a generalized banach stone theorem for c0 k x spaces via the modulus of convexity of x abstract suppose that k and s are locally compact hausdorff spaces x is a banach space and is a real number satisfying 2 1 x 2 r where x denotes the modulus of convexity of the dual space x and r is the unique real root of the polynomial p x 2 x 3 x 2 8 x 20 we prove that if t is an isomorphism from c 0 k x onto c 0 s x with t t 1 then k is homeomorphic to s this improves an earlier generalization of the banach stone theorem via geometric properties of x due to jarosz the case where k and s are compact and r is exchanged by the smaller number 4 3 in the process of the proof we establish a connection between the moduli of convexity of x and x which has independent interest namely put c r 4 then c is approximately 0 41883 and for all banach space x and e 0 2 we have 1 c e x e 1 1 2 e x e

methods of solving a polynomial equation for an h sub infinity optimal control problem for a single input single output discrete time system a polynomial equation for the h sub infinity optimal control problem is reduced to a nonlinear algebraic equation two methods are proposed for solving the algebraic equation one method uses the singularity of a linear algebraic equation as the optimality index the other gives an approximate solution by solving an eigenvalue problem a numerical example is presented

computation of the singular values of toeplitz operators and the gap metric it is widely recognized that the computation of gap metric is equivalent to a certain two block h problem i e the gap is equal to the norm of a certain two block operator however it can also be characterized as the smallest singular value of a certain toeplitz operator this paper derives a simple computational method for finding such singular values and the gap between two plants by using a state space approach

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

minimax lq exact and inexact model matching problems abstract a mixed h 2 h optimal problem is presented for both disturbance attenuation and model mismatching minimization its solution is in the form of a two degrees of freedom controller whose feedback and feedforward paths can be independently designed if the conditions for exact model matching are not met an inexact model matching problem is addressed this solution provides an effective model matching design methodology for non minimum phase plants

paper uniformly optimal control of linear feedback systems the problem of uniformly optimal control is posed in the context of linear time varying discrete time systems the controller is optimal uniformly over a pre specified set of exogenous signals existence of an optimal controller is proved and a formula for the minimum cost is derived the time invariant case is treated in the frequency domain it is shown that for time invariant systems an optimal time varying controller is no better than an optimal time invariant controller

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

a hyperchaotic system from a chaotic system with one saddle and two stable node foci this paper presents a 4d new hyperchaotic system which is constructed by a linear controller to a 3d new chaotic system with one saddle and two stable node foci some complex dynamical behaviors such as ultimate boundedness chaos and hyperchaos of the simple 4d autonomous system are investigated and analyzed the corresponding bounded hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories lyapunove exponents bifurcation path analysis of power spectrum and poincare projections finally two complete mathematical characterizations for 4d hopf bifurcation are rigorous derived and studied

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

on computing the spectral radius of the hankel plus toeplitz operator the square root of the spectral radius of the hankel plus toeplitz operator has been shown to be the achievable performance of the mixed sensitivity h sup infinity design the computation of the spectral radius is the bottleneck in the synthesis of the h sup infinity controller in this paper the spectral properties of the hankel plus toeplitz operator are investigated a finite procedure for computing the spectral radius of the hankel plus toeplitz operator is proposed

a multivariable self tuning pid controller abstract a multivariable self tuning controller with a proportional plus integral plus derivative pid structure is derived the algorithm features a combination of the self tuning property in which the controller parameters are tuned automatically on line and also the structure of a multivariable pid controller making it more favourable to be used in industry a stability proof of the algorithm is also presented here comparison of the performance of the algorithm with a fixed tuned multivariable pid controller in the simulation examples demonstrates the effectiveness of the proposed algorithm

optimal extensions of the banach stone theorem abstract let c 0 k x denote the banach space of all x valued continuous functions defined on the locally compact hausdorff space k which vanish at infinity provided with the supremum norm we prove that if x is a real banach space and t is an isomorphism from c 0 k 1 x onto c 0 k 2 x satisfying j x t t 1 2 where j x is the james constant of x then k 1 is homeomorphic to k 2 in the complex case we provide a similar result for reflexive spaces x in other words we obtain a vector valued extension of the classical amir cambern theorem x r or x c which at the same time unifies and strengthens several generalizations of the classical banach stone theorem due to cambern 1976 and 1985 behrends cambern 1988 and jarosz 1989 in the case where x l p 2 p our results are optimal

triangles inscribed in a semicircle in minkowski planes and in normed spaces in this paper we mainly consider triangles inscribed in a semicircle of a normed space in two dimensional spaces their perimeter has connections with the perimeter of the sphere moreover by using the largest values the perimeter of such triangles can have we define two new simple parameters in real normed spaces one of these parameters is strictly connected with the modulus of convexity of the space while the study of the other one seems to be more complicated we calculate the value of our two parameters and we bring out a few connections among their values and the geometry of real normed spaces

polynomial lqg regulator design for general system configurations a polynomial equation approach to the linear quadratic gaussian lqg regulation problem for a general system configuration is presented the solution is given in terms of a left spectral factorization plus a pair of bilateral diophantine equations the resulting control design procedure is based on an innovations representation of the system this can be obtained from a physical description by solving via polynomial equations a minimum mean square error filtering problem the use in cascade of the above two procedures allows one to generalize previous polynomial design results to general system configurations

sensitivity minimization in an h norm parametrization of all suboptimal solutions a number of problems in the control of linear feedback systems can be reduced to the following we are given three stable rational matrix functions k of sizes p 1 x q 1 p 1 x q 2 and p 2 x q 1 respectively and seek a stable rational q 2 x p 2 matrix function s so as to minimize k s we assume that p 1 q 2 p 2 q 1 and that and have maximal rank q 2 and p 2 respectively on the j axis given a tolerance level sufficiently large we obtain a linear fractional map g f 0 11 g 0 12 0 13 0 21 g 0 22 0 23 1 such that f k s with s stable and f if and only if g is a stable q 2 x p 2 matrix function with g 1 the computation of 0 0 ij 1 i 2 1 j 3 reduces to solving a pair of symmetric wiener hopf factorization problems for the special case where i q2 0 t i p2 0 and k not necessarily stable to which the general case can be reduced we provide explicit state space formulae for 0 in terms of a state space realization of k and the

a stable state space realization in the formulation of h norm computation in the two block hinftyoptimization problem usually we are given the state space realizations of the proper rational matrices r 1 s and r 2 s whose poles are all the open right half plane two problems are studied in the note the first is the evaluation of phi s r 1 s at s s k k 1 2 n where phi s is an inner function whose zeros s k k 1 2 n are the poles of r 1 s this evaluation is essential if chang and pearson s method is used for computing the optimal hinftynorm the problem is solved in state space via the solutions of lyapunov equations neither polynomial matrix manipulations nor numerical pole zero cancellations are involved in the evaluation the second problem is to find a stable state space realization of s s u s r 2 s where u s is an inner matrix this problem arises in the spectral factorization of gamma 2 r 2 ast r 2 doyle and chu had a method for constructing stable s s based on a minimal realization of r 2 s an alternate method is proposed the alternate method does not require a minimal realization of r 2 s and only a lyapunov equation is involved

spectral theory of the linear quadratic and h problems abstract an overview of the spectral theory of the linear quadratic and h problems is presented originally the spectral theory of the linear quadratic problem emerged out of the problem of characterizing the finite time escape of the riccati differential equation as a condition on the spectrum of a toeplitz plus hankel operator later and following an independent line of thought the spectral theory of the h problem emerged as a toeplitz plus hankel operator characterization of the smallest achievable tolerance in feedback design this common toeplitz plus hankel operator structure shared by the linear quadratic and h problems is elucidated by mapping the usual h frequency response specification into the time domain leading to an inequality bound on a quadratic functional precisely induced by the toeplitz plus hankel operator with this deep linear quadratic h connection at hand we derive a linear quadratic solution to the h problem and show that such issues as the adamjan arov krein problem pole zero cancellation in optimal h compensation etc can be fruitfully attacked using simple linear quadratic arguments

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

on the optimal and suboptimal solutions of the mixed sensitivity problem abstract in this note using elementary operator theoretic methods we give a method for the explicit computation of the suboptimal and optimal solutions to the mixed sensitivity problem for stable single input single output distributed systems

isometries between function spaces surjective isometries between some classical function spaces are investigated we give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding hausdorff compact spaces in particular the answer is positive for the c x ac 0 1 lip0 x and lip0 x spaces provided with various natural norms

operator theoretic approach to the optimal two disk problem the nonstandard two disk problem plays a fundamental role in robust feedback optimization here it is shown via banach space duality theory that its solutions satisfy an extremal identity and may be viewed as a dual extremal kernel of a particular l sup 1 optimization problem a novel operator theoretic framework to characterize explicitly its solutions is developed in particular the two disk optimization is shown to be equal to the induced norm of a specific operator defined on a projective tensor product space involving a non hilbert version of a vector valued h sup 2 space moreover this operator is shown to be a combination of multiplication and toeplitz operators under certain conditions existence of maximal vectors is established leading to an explicit formula for the optimal controller an infinite matrix representation with respect to a canonical basis is derived together with an algorithm to compute it the norm of the relevant operator is approximated by special finite dimensional optimizations whose solutions lead to solving semi definite programming problems involving the computation of a matrix projective tensor norm

a multivariable self tuning controller with integral action abstract in this paper a novel stochastic self tuning control algorithm for multivariable linear systems described by controlled autoregressive integrating moving average carima models is proposed in particular the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant the leading assumption is made that the system interactor matrix is known a priori the algorithm is derived by resorting to the generalized minimum variance approach two simulation examples illustrate the main features of the method

reverse discrete time riccati equation and extended nehari s problem abstract necessary and sufficient conditions for the existence of the anticausal stabilizing solution to the so called reverse discrete time riccati equation are derived under very relaxed conditions imposed on the initial data further a suboptimal solution of prescribed tolerance to the extended nehari s problem is constructed

on the global dynamics of the rabinovich system in this paper by using the poincare compactification in we make a global analysis of the rabinovich system with and we give the complete description of its dynamics on the sphere at infinity for ten sets of the parameter values the system has either first integrals or invariants for these ten sets we provide the global phase portrait of the rabinovich system in the poincare ball i e in the compactification of with the sphere of the infinity we prove that for convenient values of the parameters the system has two families of singularly degenerate heteroclinic cycles then changing slightly the parameters we numerically found a four wings butterfly shaped strange attractor

deterministic lq preview tracking design in this note the discrete time linear quadratic tracking problem with previewed feedforward action is considered it is assumed that the initial plant state is arbitrary and the whole reference sequence on 0 spl infin is known in advance the controller solving the problem is in a two degrees of freedom form whose feedback part equals the solution to the standard lq pure regulation problem whereas the feedforward part consists of an anticipative dynamic action whose calculation does not require a dynamic reference model an example is presented to show the use of the theory

minimax frequency domain performance and robustness optimization of linear feedback systems it is shown that feedback system design objectives such as disturbance attenuation and rejection power and bandwidth limitation and robustness may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis this leads to a minimax frequency domain optimization problem whose solution is reduced to the solution of a polynomial equation

reduced order adaptive pole placement for multivariable systems a method is suggested for adaptively assigning the closed loop poles of a continuous time linear multivariable system the resulting design significantly reduces the complexity in comparison to any other known multivariable scheme for implementation one needs to know the order of the system and an upper bound on the observability index

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam