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

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

brief paper output feedback controller synthesis for descriptor systems satisfying closed loop dissipativity this paper is concerned with synthesis of output feedback controllers for descriptor systems to attain dissipativity of the closed loop system a necessary and sufficient condition is provided in terms of lmis for the existence of a controller satisfying dissipativity and admissibility an internal stability of the closed loop system unlike previous results the condition does not depend on the choice of the descriptor realization the derived lmi condition with a rank constraint for synthesis is a generalization of those for lmi based h control of state space systems to descriptor systems

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

a stochastic multidimensional scaling vector threshold model for the spatial representation of pick any n data this paper presents a new stochastic multidimensional scaling vector threshold model designed to analyze pick any n choice data e g consumers rendering buy no buy decisions concerning a number of actual products a maximum likelihood procedure is formulated to estimate a joint space of both individuals represented as vectors and stimuli represented as points the relevant psychometric literature concerning the spatial treatment of such binary choice data is reviewed the nonlinear probit type model is described as well as the conjugate gradient procedure used to estimate parameters results of monte carlo analyses investigating the performance of this methodology with synthetic choice data sets are presented an application concerning consumer choices for eleven competitive brands of soft drinks is discussed finally directions for future research are presented in terms of further applications and generalizing the model to accommodate three way choice data

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

comprehensive admissibility for descriptor systems this paper presents a complete solution to the problem of comprehensive admissibility for descriptor systems with unstable and nonproper weights in such non standard circumstances it is hard to render the closed loop system admissible due to the uncontrollable and unobservable weights the necessary and sufficient condition is given and a specifically structured output feedback controller is conducted in terms of the dynamics of the weighs it is shown that determining suitable controllers for a given descriptor system with the presence of unstable and nonproper weights requires solving an admissibility problem for an augmented system explicitly constructed in this paper a numerical example is included to illustrate the current result

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

a near optimal solution to a two dimensional cutting stock problem we present an asymptotic fully polynomial approximation scheme for strip packing or packing rectangles into a rectangle of fixed width and minimum height a classicalnp hard cutting stock problem the algorithm based on a new linear programming relaxation finds a packing ofn rectangles whose total height is within a factor of 1 e of optimal up to an additive term and has running time polynomial both in n and in 1 e

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

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

online multiple strip packing we study an online multiple strip packing problem whose goal is to pack the given rectangles into m vertical strips of unit width such that the maximum height used among the strips is minimized rectangles arrive one by one the decision of delivering the rectangles to a strip as well as packing them into the strip must be done immediately and irrevocably without any information on the next rectangles both randomized and deterministic online algorithms are investigated all of which are guaranteed a constant competitive ratio

on state feedback h control for discrete time singular systems this technical note deals with the state feedback h control problem for linear time invariant discrete time singular systems relied on the use of auxiliary matrices and a positive scalar a novel necessary and sufficient condition for the bounded real lemma is derived for discrete time singular systems the characterization is reduced to a strict linear matrix inequality lmi when the scalar is fixed and the resulting lmi is non conservative as long as the scalar is chosen sufficiently large moreover the result is further expanded to h controller design and a numerically efficient and reliable design procedure is given since no particular restriction is imposed on the auxiliary matrices the proposed result outperforms the existing methods in the literature numerical examples are included to illustrate the effectiveness of the present result

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 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

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

two logit models for external analysis of preferences a logit vector model and a logit ideal point model are presented for external analysis of paired comparison preference judgments aggregated over a homogeneous group the logit vector model is hierarchically nested within the logit ideal point model so that statistical tests are available to distinguish between these two models generalized least squares estimation procedures are developed to account for heteroscedastic sampling error variances and specification error variances two numerical illustrations deal with judgments concerning employee compensation plans and preferences for salt and sugar in the brine of canned green beans

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

a new lower bound for online strip packing in this paper we consider the online strip packing problem in which a list of online rectangles has to be packed without overlap or rotation into a strip of width 1 and infinite length so as to minimize the required height of the packing we derive a new improved lower bound of 3 5 2 2 618 for the competitive ratio for this problem this result improves the best known lower bound of 2 589

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

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

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

unstable and nonproper weights in h control an h control problem is examined in which the controller can and need only stabilize a part of the generalized closed loop due to unstable weights the procedure is a simple extension of known results and is computationally the easiest method available

brief extended h control h control with unstable weights this paper presents a complete solution to an extended h control problem for a generalized plant comprising a physical system cascaded with weights containing poles in the closed right half plane necessary and sufficient conditions for a solution to exist are obtained which guarantee closed loop stability of the physical system and controller as well as achieving the h norm constraint on the closed loop of the transfer function matrix of the generalized plant and controller interconnection the set of all feasible controllers is characterized conditions for solvability are a minimal variation on those appearing in the standard h control problem

a strip packing algorithm with absolute performance bound 2 this paper proposes a new approximation algorithm m for packing rectangles into a strip with unit width and unbounded height so as to minimize the total height of the packing it is shown that for any list l of rectangles m l leq 2 cdot mbox opt l where m l is the strip height actually used by the algorithm m when applied to l and opt l is the minimum possible height within which the rectangles in l can be packed

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 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

shelf algorithms for two dimensional packing problems this paper studies two approximation algorithms for packing rectangles using the two dimensional packing model of baker coffman and rivest siam j comput 9 1980 pp 846 855 the algorithms studied are called next fit and first fit shelf algorithms respectively they differ from previous algorithms by packing the rectangles in the order given the previous algorithms required sorting the rectangles by decreasing height or width before packing them which is not possible in some applications the shelf algorithms are a modification of the next fit and first fit decreasing height level algorithms of coffman garey johnson and tarjan siam j comput 9 1980 pp 808 826 each shelf algorithm takes a parameter r it is shown that by choosing r appropriately the asymptotic worst case performance of the shelf algorithms can be made arbitrarily close to that of the next fit and first fit level algorithms without the restriction that items must be packed in order of decreasing height nonasymptoti

h2 output feedback control for descriptor systems this paper solves the h 2 output feedback control problem for continuous time descriptor systems an existence condition of the h 2 optimal controller is derived based on the standard model matching technique and a characterization of the optimal controller is given in terms of the solutions of two generalized algebraic riccati equations it turns out that the optimal controller has an observer based structure well known in the state space case so that the results in this paper are natural extensions of the state space results to the descriptor systems a numerical example is also included to show the applicability of the proposed results

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

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

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

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

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

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

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

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

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

optimal product positioning based on paired comparison data a new approach for analyzing paired comparison data is proposed which combines a probabilistic ideal point model with product positioning issues unlike traditional approaches based on paired comparison data the same formulation is used for estimating a joint space representation of consumer segments and products as well as for determining optimal new product positioning options in a relevant product market a monte carlo experiment is presented and real world coffee market data are used to show advantages of the new approach

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

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

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

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