the discrete time h control problem with measurement feedback this paper is concerned with the discrete time h infty control problem with measurement feedback it follows that as in the continuous time case the existence of an internally stabilizing controller that makes the h infty norm strictly less than 1 is related to the existence of stabilizing solutions to two algebraic riccati equations however in the discrete time case the solutions of these algebraic riccati equations must satisfy extra conditions

solution to nonsingular h 2 optimal control problem with unstable weights abstract in this paper we propose an approach that treats the synthesis of servo systems as well as the estimation of unstable plants as h 2 control problems with unstable weights this approach is based on the notion of comprehensive stability and the parameterization of comprehensively stabilizing controllers the complete result for the nonsingular case is obtained this provides an h 2 optimal synthesis method for general linear servo problems and estimation problems of unstable plants

a high order iterative formula for simultaneous determination of zeros of a polynomial abstract we propose a hybrid method to determine all the zeros of a polynomial simultaneously by combining the single root method and the simultaneous one the present method has a high convergence order even for multiple roots by using the pade approximation

the robust h sub 2 control problem a worst case design the worst case effect of a disturbance system on the h sub 2 norm of the system is analyzed an explicit expression is given for the worst case h sub 2 norm when the disturbance system is allowed to vary over all nonlinear time varying and possibly noncausal systems with bounded l sub 2 induced operator norm an upper bound for this measure which is equal to the worst case h sub 2 norm if the exogeneous input is scalar is defined some further analysis of this upper bound is done and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given the latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature

h sub spl infin control of systems under norm bounded uncertainties in all system matrices this paper concerns h sub spl infin control of systems under norm bounded uncertainties in all the system matrices this is an extension of the work by xie et al 1992 where only the a matrix is allowed to be uncertain it is found that the problem shares the same formulation with the h sub spl infin control problem for systems without uncertainties it can also be viewed as reducing the problem of dealing with systems with both structured uncertainties and unstructured uncertainties to one with unstructured uncertainties only

the mean field scaling function of the universality class of absorbing phase transitions with a conserved field we consider two mean field like models which belong to the universality class of absorbing phase transitions with a conserved field in both cases we analytically derive the order parameter as a function of the control parameter and of an external field conjugated to the order parameter this allows us to calculate the universal scaling function of the mean field behaviour the obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models showing that four is the upper critical dimension of this particular universality class

brief further results on almost disturbance decoupling with global asymptotic stability for nonlinear systems as a complement to some new breakthroughs on global almost disturbance decoupling problem with stability for nonlinear systems in a recent note we identified a class of unstable zero dynamics that are allowed to be affected by disturbances the class of the unstable zero dynamics identified in that note is linear and have all the poles at the origin in this paper we enlarge such a class of zero dynamics to include any linear system with all its poles in the closed left half plane the condition on the way the disturbance affects this part of zero dynamics is also identified this enlargement is due to a new scaling technique that views each pair of jw axis zeros as a generalized integrator and transforms the zero dynamics into a number of chains of generalized integrators

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

novel all pass factorization all solutions to rational matrix equation and control application for an arbitrary rational matrix rm a new descriptor realization of its all pass factorization is presented the coefficients of the factors are expressed explicitly in the solution of a linear matrix inequality which is well known in control theory using the all pass factorization necessary and sufficient conditions for existence of a solution of an equation with rms where the unknown rm has its poles in the left closed complex half plane and it can be improper are presented as well as all solutions as an application of the latter result the notion of almost disturbance decoupling i e when the infimum of the mathscr h infty norm of the transfer matrix from the disturbance input to the controlled output over the stabilizing controllers is zero is generalized the generalization is such that instead of the whole frequency axis the frequency axis with excluded intervals of small lengths is considered the controller consists of output feedback plus disturbance feedforward designed independently a necessary and sufficient solvability condition is presented which is expressed in terms of the given data the three main results are illustrated by an example

the robust regulation problem with robust stability a subspace valued function approach among the most common purposes are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties the related design problem is called the robust regulation problem here we investigate the tradeoff between the robust regulation constraint and the requirement of robust stability with respect to perturbations in the normalized coprime factors of the plant we use an approach in terms of subspace valued functions associated to plant and controller in this way necessary and sufficient conditions for robust regulation with robust stability can be related to a simple geometric property

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

multiplicity estimating algorithm for zeros of a complex polynomial and its applications abstract miyakoda t multiplicity estimating algorithm for zeros of a complex polynomial and its applications journal of computational and applied mathematics 46 1993 357 368 this paper presents a method for estimating the multiplicity of zeros of a complex polynomial when the durand kerner method is applied to solve it the method is based on previous this journal 1989 1992 work of the author numerical examples are given which show the efficiency of our algorithm compared with another method and we propose further applications for accelerating convergence and improving the accuracy of approximations for multiple zeros

on some simultaneous methods based on weierstrass correction abstract the purpose of the paper is to present some procedures for the construction of simultaneous methods for finding all zeros of a polynomial f using weierstrass corrections w i z f z k i z z k in this manner some well known methods as well as new methods are obtained the proposed iterative algorithms are realized in ordinary complex arithmetic and circular interval arithmetic the convergence analysis of the presented methods and numerical examples are given

on an application of symbolic computation and computer graphics to root finders the contemporary powerful mathematical software enables a new approach to handling and manipulating complex mathematical expressions and other mathematical objects particularly the use of symbolic computation leads to new contribution to constructing and analyzing numerical algorithms for solving very difficult problems in applied mathematics and other scientific disciplines in this paper we are concerned with the problem of determining multiple zeros when the multiplicity is not known in advance a task that is seldom considered in literature by the use of computer algebra system mathematica we employ symbolic computation through several programs to construct and investigate algorithms which both determine a sought zero and its multiplicity applying a recurrent formula for generating iterative methods of higher order for solving nonlinear equations we construct iterative methods that serve i for approximating a multiple zero of a given function f when the order of multiplicity is unknown and simultaneously ii for finding exact order of multiplicity in particular we state useful cubically convergent iterative sequences that find the exact multiplicity in a few iteration steps such approach combined with a rapidly convergent method for multiple zeros provides the construction of efficient composite algorithms for finding multiple zeros of very high accuracy the properties of the proposed algorithms are illustrated by several numerical examples and basins of attraction

the generalized tp model transformation for t s fuzzy model manipulation and generalized stability verification this paper integrates various ideas about the tensor product tp model transformation into one conceptual framework and formulates it in terms of the takagi sugeno t s fuzzy model manipulation and control design framework several new extensions of the tp model transformation are proposed such as the quasi and full compact and rank reduced higher order singular value decomposition based canonical form of t s fuzzy models and the bilinear multi pseudo convex partial tp model transformations all of these extensions together form the generalized tp model transformation which provides an effective tool to freely and readily manipulate the antecedent sets and rules of t s fuzzy models and also provides main fuzzy rule component analysis as well as a means for complexity and accuracy tradeoffs it is demonstrated in this paper that the proposed manipulation forms a new effective and necessary optimization step of t s fuzzy or polytopic models and linear matrix inequality based control design and can also decrease conservativeness identification techniques are typically constructed according to the available data and measurement set as well as the type of system to be identified as a result they may not always provide good representations for control design frameworks this paper demonstrates that the proposed tp model transformation is unique in that it bridges between various soft computing based identification techniques and t s fuzzy model based approaches finally this paper proposes the multi tp model transformation which is a tractable and nonheuristic framework to verify the stability of the result of fuzzy or various soft computing based control designs the multi tp model transformation could provide an answer to the frequently emerging criticisms regarding the lack of mathematical stability verification techniques in the soft computing based control design control examples are provided in this paper

global convergence of the durand kerner method applied to the equation z 3 0 abstract it is proved that the durand kerner polynomial root finding method is globally convergent when it is applied to the equation z3 0 the behavior of orbits with real initial values is chaotic in contrast to the balanced convergence with complex initial values

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

computer methodologies for comparison of computational efficiency of simultaneous methods for finding polynomial zeros abstract the study and analysis of iterative methods for the determination of zeros of algebraic polynomials the subject of this paper is one of the most actual tasks in the theory and practice our main goal is to examine and compare the quality of most frequently used methods for simultaneously finding all zeros of a polynomial by combining numerical experiments theoretical models and empirical cpu time methodology special attention is devoted to empirical average case model assuming that average cpu times are calculated performing the experiment i on several different computers ii running each method through many loops for a fixed example iii testing reasonably large number of polynomials of different structure body and iv the use of almost arbitrary initial approximations the empirical model ranks the tested methods on the base of the consumed cpu times needed for the fulfillment of the required accuracy of approximations under the same initial conditions our aim is to select a group of the most powerful simultaneous methods with globally convergent performance convergence behavior of two most powerful methods is illustrated by trajectories in the complex plane that consist of the point approximations starting with initial points and going towards the endpoints where the iterative process stops due to the termination criterion

a family of simultaneous zero finding methods abstract applying hansen patrick s formula for solving the single equation f z 0 to a suitable function appearing in the classical weierstrass method two one parameter families of interation functions for the simultaneous approximation of all simple and multiple zeros of a polynomial are derived it is shown that all the methods of these families have fourth order of convergence some computational aspects of the proposed methods and numerical examples are given

robust regulation with h 2 performance abstract we consider the problem of minimizing the h 2 norm of a feedback system subject to the constraint that the controller robustly regulate against constants and sinusoids we show that for any 0 there exists a controller that both achieves robust regulation and renders the closed loop h 2 norm within of the optimal norm the norm achievable without the robust regulation constraint we also provide conditions that are both necessary and sufficient for there to exist a robustly regulating controller that achieves the optimal h 2 norm all proofs are constructive

h suboptimal control problem with boundary constraints abstract a necessary and sufficient condition is derived for the existence of a stabilizing controller such that i a specified closed loop transfer function g er s has h norm less than one and ii g er s satisfies generalized boundary constraints on the j axis

existence of an upper critical dimension in the majority voter model we study the critical properties of the majority voter model on d dimensional hypercubic lattices in two dimensions the majority voter model belongs to the same universality class as that of the ising model however the critical behaviors of the majority voter model on four dimensions do not exhibit mean field behavior using the monte carlo simulation on d dimensional hypercubic lattices we obtain the critical exponents up to d 7 and find that the upper critical dimension is 6 for the majority voter model we also confirm our results using mean field calculation

iterative methods for multiple zeros of a polynomial by clustering abstract for the numerical determination of zeros of a complex polynomial by simultaneous iterative methods we show theorems on the fact that the approximations for a multiple zero gather around the exact zero when they become close approximations application of our theorems makes it possible to estimate the multiplicity of zeros dynamically as well as to improve the convergence to multiple zeros for the known methods e g durand kerner s or tanabe s methods

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

robust performance of linear parametrically varying systems using parametrically dependent linear feedback abstract in this paper a parameter dependent control problem for linear parametrically varying lpv systems is presented sufficient conditions are given that guarantee an lpv system is exponentially stable and achieves an induced l 2 norm performance objective from the disturbance to error signals the usefulness of parameter dependent controllers is motivated from a gain scheduling viewpoint the resulting synthesis problem is reformulated into a convex optimization problem which can be solved using efficient new algorithms

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

h sub spl infin observer design for lipschitz nonlinear systems the problem of observer design for lipschitz nonlinear systems is considered a new dynamic framework which is a generalization of previously used lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented the equivalence between this condition and an h sub spl infin optimal control problem which satisfies the standard regularity assumptions in h sub spl infin optimization theory is shown and a parameterization of all possible observers is also presented a design procedure which is less restrictive than the existing design approaches is proposed and a simulation example is given to illustrate the observer design

almost disturbance decoupling with global asymptotic stability for nonlinear systems with disturbance affected unstable zero dynamics the problem of global almost disturbance decoupling problem with stability for nonlinear system is revisited and is shown to be solvable for a class of nonlinear systems whose zero dynamics contains a chain of integrators affected by disturbance this result complements some recent work on the topic where unstable zero dynamics is not allowed to be affected by the disturbances

basins of attraction for several methods to find simple roots of nonlinear equations there are many methods for solving a nonlinear algebraic equation the methods are classified by the order informational efficiency and efficiency index here we consider other criteria namely the basin of attraction of the method and its dependence on the order we discuss several third and fourth order methods to find simple zeros the relationship between the basins of attraction and the corresponding conjugacy maps will be discussed in numerical experiments the effect of the extraneous roots on the basins is also discussed

j factorizations of a general discrete time system abstract the problems of extending the j lossless conjugation the j j spectral factorization and the j j lossless factorization to a completely general discrete time system are considered existence conditions together with a numerically sound prototype algorithm for computing the factors are provided for a system having any type of singularity including arbitrary normal rank poles and zeros at infinity at zero or on the unit circle

j lossless and extended j lossless factorizations approach for domain h control the paper addresses problems of numerical conditioning of the discrete time h x control design based on j lossless factorizations of the chain scattering representation of a plant it is demonstrated that for a sufficiently small sampling period forward shift operator techniques may become ill conditioned and numerical robustness and reliability of design procedures can be significantly improved by utilizing a so called i operator form of the source problem state space models of all i domain controllers are given the solutions are obtained by considering two coupled i domain algebraic riccati equations that can be solved by applying a generalized eigenproblem formulation numerical conditioning of these solutions can effectively be evaluated by using a suitable relative condition number an extended j lossless factorization for generalized plants with zeros on the stability boundary circle is also given a so called zero compensator technique adapted to the i domain models is utilized to cancel suc

brief paper parameterization of all stabilizing h static state feedback gains application to output feedback design this paper presents a simplified parameterization of all h static state feedback controllers in terms of a single algebraic riccati equation and a free parameter matrix as a special case necessary and sufficient conditions for the existence of an static output feedback gain are given an efficient computational algorithm is given and its correctness proven no initial stabilizing output feedback gain is needed the technique is used to design an h lateral directional command augmentation system for the f 16 aircraft

a parallel algorithm for simple roots for polynomials abstract a method for finding simple roots of arbitrary polynomials based on divided differences is discussed theoretical background is presented for the case of simple roots numerical results are presented which show the algorithm finds simple and multiple zeros to an accuracy usually limited by the accuracy of polynomial evaluation the method is designed for a simd parallel computer the algorithm is compared to two other frequently used polynomial root finders the jenkins traub algorithm and laguerre s method

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

an lmi approach to h synthesis subject to almost asymptotic regulation constraints a multi objective controller synthesis problem is considered in which an output is to be regulated approximately by assuring a bound on the steady state peak amplification in response to an infinite energy disturbance while also guaranteeing a desired level of performance measured in terms of the worst case energy gain from a finite energy input to a performance output relying on a characterization of the controllers with which almost asymptotic regulation is accomplished the problem of guaranteeing the desired level of performance is reduced to solving a system of linear matrix inequalities subject to a set of linear equality constraints based on the solution of this system a procedure is outlined for the construction of a suitable controller whose order is equal to the order of the plant plus the order of the exogenous system

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

brief paper algebraic and topological aspects of the regulator problem for lumped linear systems the regulator problem with robustness is solved for systems modelled by rational transfer matrices a topology for possibly unstable plants is presented a necessary and sufficient condition is derived for the existence of a proper controller which provides internal stability and output regulation throughout an open neighbourhood of the plant a characterization of all such controllers is determined

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

performance with regulation constraints we study the problem where we have a regulation asymptotic tracking requirement together with a performance requirement for continuous time systems typically we measure performance by the h 2 or h norm of a chosen transfer function matrix although any other norm such as the l 1 norm could be used in the case when the performance is measured by the h 2 norm there is no loss in performance due to the regulation constraint on the other hand when the performance is measured by the h norm there exists in general certain loss of performance due to the regulation constraint and we explicitly characterize such a loss determining suitable controllers for a given system with both regulation and performance constraints requires solving only an unconstrained optimization problem for an auxiliary system which is explicitly constructed here

robust regulation in the presence of norm bounded uncertainty we consider robust regulation against steps and sinusoids in the presence of unstructured uncertainty the unstructured uncertainty is norm bounded by a constant that is given a priori this problem is equivalent to a certain multiobjective problem where one objective is robust regulation and the other is the standard objective of h sub spl infin suboptimal control it is shown that a solution to this problem exists if and only if the standard h sub spl infin problem admits a solution and certain matrix inequalities are satisfied these solvability conditions are readily computable controller synthesis is also addressed

sensitivity reduction by strongly stabilizing controllers for mimo distributed parameter systems this note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time invariant multi input multioutput distributed parameter system the plant we consider has finitely many unstable zeros which are simple and blocking but can possess infinitely many unstable poles we obtain a necessary condition and a sufficient condition for the solvability of the problem using the matrix nevanlinna pick interpolation with boundary conditions we also develop a necessary and sufficient condition for the solvability of the interpolation problem and show an algorithm to obtain the solutions our method to solve the interpolation problem is based on the schur nevanlinna algorithm

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

robust output regulation for a class of linear multivariable systems in the design of robust regulators the solution of anh norm optimization problem of the formmin q r h t11 t12qt21 is needed to get an optimal controller a difficulty in doing this is that t12 j will be singular at the poles of the external signals in 11 a lower bound for this norm has been found in this paper it will be shown that for stable plants this bound is an infimum and can be approximated as near as possible thus a necessary and sufficient condition for robust regulation is found for a class for a class of linear mimo systems moreover if the external signals are step functions an h optimal controller can be obtained

reduced order controllers for the h control problem with unstable invariant zeros this paper addresses the existence and design methods of reduced order controllers for the h control problem with unstable invariant zeros in the state space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output where the realization is induced from a stabilizable and detectable realization of the generalized plant this paper presents a new controller degree bound for the h control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region when the unstable invariant zero exists this paper shows that reduced order controllers with orders strictly less than that of the generalized plant exist if the h control problem is solvable moreover this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality based design methods algorithms for constructing the reduced order controllers the results developed in this paper are valid both for the continuous and discrete time h control problems

general optimal attenuation of harmonic disturbance with unknown frequencies we present algorithms for optimal harmonic disturbance attenuation in standard discrete time control structure based on a parametrisation of marginally stabilising controllers the frobenius norm and the spectral norm of the closed loop transfer matrix at the disturbance frequencies are minimised if there is only one frequency of the disturbance the controller has an observer based form which we obtain by solving a static output feedback sof stabilisation control problem although the sof stabilisation problem is hard the generical case of nonsquare matrix g 22 is solved by linear algebra methods numerical simulation results are presented as a corollary we transform the control problem with unit circle invariant zeros into a control problem without such zeros the elimination of the unit circle invariant zeros is based on the fact that matrix y zi a bf 1 is stable where y f with y 0 is a solution of a discrete time algebraic riccati system

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

technical communique h control with unstable and nonproper weights for descriptor systems this paper is concerned with a nonstandard h output feedback control problem for continuous time descriptor systems where unstable and nonproper weighting functions are used based on two generalized sylvester equations and two generalized algebraic riccati equations gares together with a spectral radius condition an explicit parametrization of all desirable controllers is deduced a numerical example is included to illustrate the validity of the proposed result

scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension we analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field phys rev lett 85 1803 2000 we determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in d 2 3 4 5 dimensions a comparison of our results and those obtained from a mean field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four

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

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

relationships between discrete time and continuous time algebraic riccati inequalities abstract the bilinear transformation is used to establish a direct relationship between a discrete time algebraic riccati inequality dari and an associated continuous time algebraic riccati inequality cari it is shown that under mild conditions the dari is solvable if and only if the corresponding cari is solvable the relationship between the dari and the cari is then used to translate the general solvability conditions for a cari given by scherer into analogous conditions for the dari it is shown how such conditions can be applied to determine the solvability of a discrete time h control problem whose solution set is characterized by two daris

on sigma lossless transfer functions and related questions abstract this paper is concerned with a systematic approach to the properties of lossless rational transfer functions in the discrete as well as in the continuous time case as a result a unifying framework is revealed where several known results fit naturally special attention is given to the embedding problem of the lyapunov equation in view of its direct application to generalized levinson algorithms

computational efficiency of some combined methods for polynomial equations abstract the iterative methods for the simultaneous determination of all simple complex zeros of algebraic polynomials based on the fixed point relation of ehrlich s type are considered using the iterative correction appearing in the jarratt method of the fourth order it is proved that the convergence rate of the modified ehrlich method is increased from 3 to 6 this acceleration of the convergence is obtained with few additional numerical operations which means that the proposed combined method possesses very high computational efficiency moreover the convergence rate can be further accelerated using the gauss siedel approach single step or serial mode a great part of the paper is devoted to the computational aspects of the discussed methods including numerical examples a comparison procedure shows that the new iterative method is more efficient than existing methods in the considered class

the singular minimum entropy h control problem abstract in this paper we search for controllers which minimize an entropy function of the closed loop transfer matrix under the constraint of internal stability and under the constraint that the closed loop transfer matrix has h norm less than some a priori given bound we find an explicit expression for the infimum moreover we give a characterization when the infimum is attained contrary to the regular case for the singular minimum entropy h control problem the infimum is not always attained

balanced convergence of iterative methods to a multiple zero of a complex polynomial abstract we deal with the durand kerner iterative method for a complex polynomial equation having multiple zeros we will give the detailed proofs that the durand kerner approximations to a multiple zero locate equidistant points on a sufficiently small circle when they are close to the exact zeros and furthermore that the durand kerner mapping whose definition is given in the present paper is contractive this fact supports the balanced convergence of iteration observed in the author s preceding paper this journal 1989

solutions to general h almost disturbance decoupling problem with measurement feedback and internal stability for discrete time systems in this paper we construct feedback controllers explicitly parameterized in a single parameter e that solve the well known h almost disturbance decoupling problem with measurement feedback and with internal stability h addpms for discrete time linear systems in particular we explicitly construct parameterized solutions for the following three cases the full state feedback the full information feedback and the general measurement output feedback the rst two cases have static solutions while the last one has only dynamic solutions both the full order and the reduced order measurement feedback controllers are presented for the latter case the problem considered in this paper is general and complete 2000 elsevier science ltd all rights reserved

reduced order controllers for continuous and discrete time singular h control problems based on lmi this paper describes a method for constructing a petri net controller for a discrete event system modeled by a petri net the controller consists only of places and arcs and is computed based on the concept of petri net place invariants the size of the controller is proportional to the number of constraints that must be satisfied this method is computationally efficient and can accommodate constraints written as boolean logic formulas in the conjunctive normal form or algebraic inequalities that contain elements of the marking and or the firing vectors

h optimization without assumptions on finite or infinite zeros explicit algebraic conditions are presented for the suboptimality of some parameter in the h infty optimization problem by output measurement control apart from two strict properness conditions no artificial assumptions restrict the underlying system in particular the plant may have zeros on the imaginary axis or at infinity these suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability

brief paper generalized asymptotic regulation with guaranteed h2 performance an lmi solution a multi objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix the generalized regulation constraints are expressed as bounds on the state steady peak in response to disturbances generated by an anti stable autonomous exogenous system with nonzero initial states the controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices which are subject to convex constraints and an accompanying controller with which the feedback loop is to be stabilized formulating the design of the accompanying controller in a way to guarantee the additional performance objective the overall design is rendered tractable over a set of free variables in terms of which the synthesis of a suitable controller is also outlined the order of the controller is equal to the order of the plant plus the order of the exogenous system by an adaptation of the developed techniques a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response

a complete and simple parametrization of controllers for a nonstandard h control problem abstract a complete and simple parametrization of all h controllers is derived for a class of nonstandard h control problems with d 12 and d 21 being of full row and column ranks respectively by making use of the youla parametrization and standard h control theory

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

further results on the robust tracking problem in two degree of freedom control systems the robust tracking problem in two degree of freedom control systems is formulated in a general setting which includes the case where the controlled output is not available directly a complete solution of the problem which is an extension of previous results is derived in a considerably simplified and transparent manner furthermore we show what kind of information about the output is needed to achieve robust tracking

the state feedback h problem at optimality abstract we discuss the infinite horizon h control problem by state feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure we provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict riccati inequality and propose possibilities for verifying these criteria if the optimum is not achieved we give a complete test for the need of high gain feedback in order to approach the optimal value

h control by state feedback for plants with zeros on the imaginary axis algebraic tests are derived for the suboptimality of some parameter in the h infty optimization problem by state feedback where the finite zero structure of the plant is not restricted as an application of these characterizations a quadratically convergent algorithm for the computation of the optimal value is presented the suboptimality tests are based on new solvability criteria for general algebraic riccati inequalities that are of independent interest

application of facial reduction to h state feedback control problem one often encounters numerical difficulties in solving linear matrix inequality lmi problems obtained from h control problems for semidefinite programming sdp relaxations for combinatorial p

synthesis of dissipative systems using quadratic differential forms part ii the problem discussed is that of designing a controller for a linear system that renders a quadratic functional nonnegative our formulation and solution of this problem is completely representation free the system dynamics are specified by a differential behavior and the performance is specified through a quadratic differential form we view control as interconnection a controller constrains a distinguished set of system variables the control variables the resulting behavior of the to be controlled variables is called the controlled behavior the constraint that the controller acts through the control variables only can be succinctly expressed by requiring that the controlled behavior should be wedged in between the hidden behavior obtained by setting the control variables equal to zero and the plant behavior obtained by leaving the control variables unconstrained the main result is a set of necessary and sufficient conditions for the existence of a controlled behavior that meets the performance specifications the essential requirement is a coupling condition an inequality that combines the storage functions of the hidden behavior and the orthogonal complement of the plant behavior

extended rm h _ 2 controller synthesis for continuous descriptor systems this technical note presents a complete solution to the nonstandard h2 output feedback control problem for continuous descriptor systems where unstable and nonproper weighting functions are used in such a problem the desired controller has to satisfy two conditions simultaneously i the closed loop is admissible and has a minimum h2 norm ii only the internal stability of a part of the closed loop is sought the condition of the existence of such a controller is deduced an explicit characterization of the optimal solution is also formulated based on two generalized algebraic riccati equations gares and two generalized sylvester equations a numerical example is included to illustrate the validity of the proposed results

basin attractors for various methods abstract there are many methods for the solution of a nonlinear algebraic equation the methods are classified by the order informational efficiency and efficiency index here we consider other criteria namely the basin of attraction of the method and its dependence on the order we discuss several methods of various orders and present the basin of attraction for several examples it can be seen that not all higher order methods were created equal newton s halley s murakami s and neta johnson s methods are consistently better than the others in two of the examples neta s 16th order scheme was also as good

the discrete time h sub spl infin control problem with strictly proper measurement feedback this paper is concerned with the discrete time h sub spl infin control problem with strictly proper measurement feedback we derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given h sub spl infin norm bound note that contrary to the continuous time in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator finally we give an explicit formula for one controller which achieves this bound

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

on halley like algorithms for simultaneous approximation of polynomial complex zeros let p z be a polynomial of degree n with n distinct zeros iterative methods for the simultaneous inclusion of k leqq n simple or multiple zeros are given the iterative formulas presented can be regarded as an interval version of halley s iterative formula for multiple zeros realized in circular arithmetic the convergence analysis is done in the presence of multiplicity the convergence order is three for k n and four if k n applying the gauss seidel approach to the basic iterative formula the single step method with accelerated convergence is stated and the lower bound of the r order of convergence of this method is obtained the dependence of convergence rate of the basic methods on the rounding errors is also studied some numerical examples illustrate the theoretical results

scaling exponents and transition behavior of the generalized conserved lattice gas model at zero temperature we study a generalized conserved lattice gas model in two dimensions by introducing an effective temperature to the conserved lattice gas model where the number of particles is conserved during the dynamical process we apply monte carlo simulation with the metropolis transition rate at zero temperature we find two transition behaviors one between the localized active states and absorbing states and the other between the localized active states and active states with a different definition of the order parameter for the second transition behavior we obtain the critical exponents at the transition point