fuzzy least squares linear regression analysis using shape preserving operations abstract in this paper we introduce a new class of fuzzy linear regression model with fuzzy input fuzzy output data using shape preserving arithmetic operations on l r fuzzy numbers for least squares fitting a mixed nonlinear programming approach is used to derive the satisfying solution this answers one of diamond s questions inform sci 46 1988 141

the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

explicit characterization of decentralized coprime factors this paper is concerned with parametrization of all decentralized stabilizing controllers the auxiliary diagonal system which is defined by the diagonal elements of bezout factors plays an important role in the parametrization of decentralized controllers this paper gives an explicit characterization of the auxiliary system

t norm based addition of fuzzy intervals abstract the aim of this paper is to provide new results regarding the effective practical computation of t norm based additions of lr fuzzy intervals

quadratic stabilizability of switched linear systems with polytopic uncertainties in this paper we consider quadratic stabilizability via state feedback for both continuous time and discrete time switched linear systems that are composed of polytopic uncertain subsystems by state feedback we mean that the switchings among subsystems are dependent on system states for continuous time switched linear systems we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices then the switched system is quadratically stabilizable via state feedback for discrete time switched linear systems we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non negative scalars and a common positive definite matrix for both continuous time and discrete time switched systems we propose the switching rules by using the obtained common positive definite matrix

shape preserving additions of fuzzy intervals abstract triangular norm based additions preserving the lr shape of lr fuzzy intervals are studied the connection between t norm based additions preserving the linearity of fuzzy intervals and additions preserving lr shape for invertible shapes l and r is given a possibility of controlling the growth of the spread during the calculations with lr fuzzy intervals is shown

on the compositional rule of inference under triangular norms abstract the aim of this paper is to provide a close upper bound of the membership function for the compositional rule of inference under archimedean t norm where both the observation and the relation parts are given by hellendoorn s function 1980 in particular if the left and right spreads of the observation part is the same as those of the relation part then this upper bound is the exact membership function which generalizes the earlier result by fuller and zimmermann 1982 in that assumption of twice differentiability is deleted

t sum of sigmoid shaped fuzzy intervals the usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of zadeh s extension principle based on a t norm t a t norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class it is important to know which t norms are consistent with particular types of fuzzy intervals recently dombi and gyorbiro j dombi n gyorbiro additions of sigmoid shaped fuzzy intervals using the dombi operator and infinite sum theorems fuzzy sets and systems 157 2006 952 963 proved that addition is closed if the dombi t norm is used with sigmoid shaped fuzzy intervals in this paper we define a broader class of sigmoid shaped fuzzy intervals then we study t norms that are consistent with these particular types of fuzzy intervals dombi and gyorbiro s results are special cases of the results described in this paper

a heuristic approach to solving a class of bilinear matrix inequality problems abstract many canonical and modern control problems can be recast into the problem of a group of matrix inequalities some of them are in the form of linear matrix inequalities lmis which can be solved very efficiently by the powerful lmi toolbox in matlab but some others are in the form of bilinear matrix inequalities the characteristic of this latter class of problems is that when the so called communicating variables are fixed the overall problem will be reduced to the problem in lmis thus how to find the communicating variables is the key to solve the whole problem in this paper an optimal estimate for the communicating variables is presented we will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems numerical examples are provided to show the effectiveness of the proposed method

parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences we show that a linear partial differential operator with constant coefficients p d is surjective on the space of e valued ultra distributions over an arbitrary convex set if e is a nuclear frechet space with property dn in particular this holds if e is isomorphic to the space of tempered distributions s or to the space of germs of holomorphic functions over a one point set h 0 this result has an interpretation in terms of solving the scalar equation p d u f such that the solution u depends on parameter whenever the right hand side f also depends on the parameter in the same way a suitable analogue for surjective convolution operators over rd is obtained as well to get the above results we develop a splitting theory for short exact sequences of the form 0 x y z 0 where z is a frechet schwartz space and x y are pls spaces like the spaces of distributions or real analytic functions or their subspaces in particular an extension of the dn splitting theorem of vogt and wagner is obtained

fuzzy least absolutes regression using shape preserving operations the purpose of this study is to introduce a new fuzzy regression model based on the least absolutes method the fuzzy simple and fuzzy multivariate regression models with fuzzy input fuzzy output are considered in which the coefficients of the models are themselves fuzzy the proposed method is based on a new metric on the space of lr fuzzy numbers fuzzy arithmetic operations are based on the weakest triangular norm t w which is the unique triangular norm that preserves the shape of fuzzy numbers during multiplication the results of comparative studies and numerical examples indicate that using the similarity measure criterion as well as a predictive ability index the proposed method has a better performance than the least squares method especially when the data set includes some outlier data point s

robust controller synthesis via non linear matrix inequalities over thelastseveralyears fixed structure multiplier versions of mixed structured singular value mssv theory have been developed and have led to the development of linear matrix inequalities lmis for the analysis of robust stability and performance these lmis have in turn led to the development of bilinear matrix inequalities bmis for the synthesis of robust controllers the bmi formulation in practice requires the multiplier to lie in the span of a stable basis potentially introducing significant conservatism this paper uses the lmi approach to mssv analysis to develop an approach to robust controller synthesis that is based on the stable factors of the multipliers and does not require the multipliers to be restricted to a basis it is shown that this approach requires the solution of non linear matrix inequalities nmis a continuation algorithm is presented for the solution of nmis this algorithm may be used to solve nmis in general and its usefulness is not limited to the robust controller synt

brief paper unification of independent and sequential procedures for decentralized controller design this paper is concerned with decentralized control problems there are two typical procedures to design decentralized controllers independent and sequential design procedures as the concepts and the techniques in these two approaches are too different from each other there have been no attempts to unify these approaches this paper proposes an iterative independent design procedure for decentralized control systems which is a unified approach to these conventional approaches

shape preserving multiplications of fuzzy numbers abstract in this note we show that t w the weakest t norm is the only t norm t which induces a shape preserving multiplications of lr fuzzy numbers

design of nonlinear interconnections guaranteeing the absence of periodic solutions abstract in this paper a novel methodology for scheming interconnection structure for a class of nonlinearly interconnected systems is proposed to guarantee the absence of a specific kind of periodic solutions those types of systems can be viewed as an interconnection of single input single output isolated subsystems with the interconnection structure specified by a square matrix frequency domain inequalities conditions as well as linear matrix inequalities lmis conditions for nonexistence of limit cycles of the second kind in the entire interconnected system are established the main results also define the frequency range on which cycles of the second kind of the system cannot exist based on this lmi approach an estimate of the largest bound of the frequency of cycles of the second kind can be explicitly computed by solving a generalized eigenvalue minimization problem numerical results show the effect of the nonlinear interaction on system behavior and the applicability and validity of the proposed method

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

t sum of l r fuzzy numbers abstract the sum of l r fuzzy numbers based on a given archimedian continuous t norm t is studied a series of improving sufficient conditions of several authors ensuring an analytical form of the output sum is completed by a sufficient and necessary condition i e the best sufficient condition some applications are indicated

a parametrization approach to optimal h 2 and h decentralized control problems the paper proposes a two stage design approach to optimal h2 and h decentralized control problems in the first stage an optimal centralized controller is computed then in the second stage based on the optimization results for centralized controllers the parameter that decentralizes the controller is optimized the design approach is applied to an observer based decentralized controller optimality conditions are derived and examples are given to illustrate the design

special decentralized control problems in discrete time interconnected systems composed of two subsystems in this paper some special decentralized control problems are addressed for discrete time interconnected systems first it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases then a special kind of decentralized control problem is studied this kind of problem can be viewed as harmonic control among independent subsystems research results show that two unstable systems can generate a stable system through some effective cooperations in addition a decentralized controller design method based on linear matrix inequality is also given by using parameter dependent lyapunov function method developed for the study of robust stability a special linear star coupled dynamical network is also considered the central subsystem must be unstable to stabilize the whole network under a special coupling several examples are given to illustrate the results

brief decentralized h controller design a matrix inequality approach using a homotopy method this paper considers a decentralized h control problem for multi channel linear time invariant systems our interest is focused on dynamic output feedback the control problem is reduced to a feasibility problem of a bilinear matrix inequality bmi the objective of this paper is to propose an algorithm for solving the bmi by using the idea of the homotopy method where the controller s coefficient matrices are deformed from full matrices defined by a centralized h controller to block diagonal matrices of specified dimensions which describe a decentralized h controller when a feasible decentralized h control problem is considered it can be expected that there always exists a centralized h controller for which the algorithm converges and presents a desired solution to find such a suitable centralized h controller random search in a parametrized set of h controllers with a proper dimension is suggested the efficiency of the proposed algorithm is demonstrated by an example

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

fuzzy measures for a correlation coefficient of fuzzy numbers under tw the weakest t norm based fuzzy arithmetic operations recently the sup min convolution based on zadeh s extension principle has been used by liu and kao fuzzy measures for correlation coefficient of fuzzy numbers fuzzy sets and systems 128 2002 267 275 to calculate a fuzzy correlation coefficient they used a mathematical programming approach to derive fuzzy measures based on the classical definition of the correlation coefficient it is well known that t w the weakest t norm based addition and multiplication preserve the shape of l r fuzzy numbers in this paper we consider the computational aspect of the t w based extension principle when the principle is applied to a correlation coefficient of l r fuzzy numbers we give the exact solution of a fuzzy correlation coefficient without programming or the aid of computer resources

a note to the sum of fuzzy variables abstract we generalize the results of rao and rashed 1981 285 292 and the results of nahmias 1978 97 110 for the membership function of a finite sum of mutually unrelated fuzzy variables the main result is to give a necessary and sufficient condition to the following problem if x1 x2 xn are mutually unrelated fuzzy variables with common membership function and 1 2 n are real numbers satisfying i 0 for every i and i 1n i when does z ni 1 ixi have the same membership function

decentralized h_ 2 control for multi channel stochastic systems this technical note investigates a decentralized h 2 control problem for multi channel linear time invariant stochastic systems governed by ito s differential equation after using a stochastic algebraic riccati equation sare to establish the necessary conditions for the existence of the optimal strategy set that minimizes an h 2 norm we show that the necessary conditions can also be expressed using a linear matrix inequality lmi the equivalence between the solvability of the sare and the feasibility of the lmi is proved for the first time using a karush kuhn tucker kkt condition furthermore the static output feedback solution was also studied a numerical example is given to demonstrate the usefulness of the obtained features

correspondence analysis with fuzzy data the fuzzy eigenvalue problem this paper constitutes a first step towards an extension of correspondence analysis with fuzzy data fca at this stage our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis a two step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one we consider a fuzzy matrix as the set of its cuts each such cut is an interval valued matrix viewed as a line segment in the matrix space in this way line segments of cut matrices are transformed into intervals of eigenvalues therefore the two step method is essentially a reduction of the fuzzy eigenvalue problem to an ordinary one we illustrate the fca fuzzy eigenvalue problem with a simple numerical example we hope upon the completion of this project in near future to be able to supply the necessary tools for the end user of the correspondence analysis with fuzzy data

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

static output feedback stabilisation with h performance for a class of plants in this paper the problem of static output feedback control of a linear system is considered the existence of a static output feedback control law is given in terms of the solvability of two coupled lyapunov inequalities which result in a non linear optimisation problem however using state coordinate and congruence transformations and by imposing a block diagonal structure on the lyapunov matrix we will see that the determination of a static output feedback gain reduces for a specific class of plants to finding the solution of a system of linear matrix inequalities the class of plants considered is those which are minimum phase with a full row rank markov parameter the method is extended to incorporate h performance objectives this results in a sub optimal static h control law found by non iterative means the simplicity of the method is demonstrated by a numerical example

a t sum bound of lr fuzzy numbers abstract in this paper we provide an upper bound and a lower bound of t sum of lr fuzzy numbers with different spreads where t is archimedean t norm and also show in three examples how close they are to actual membership functions furthermore we study when the membership function of t sum achieves the upper bound

on computation of the compositional rule of inference under triangular norms abstract this paper is devoted to the derivation of exact calculation formulas for the compositional rule of inference under archimedean t norms when both the observation and the relation parts are given by hellendoorn s function 6

fuzzy system reliability analysis by the use of t ω the weakest t norm on fuzzy number arithmetic operations abstract in general the sup min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability where the reliability of each system component is represented by fuzzy numbers it is well known that t based addition preserves the shape of l r type fuzzy numbers in this paper we show t based multiplication also preserves the shape of l r type fuzzy numbers we then apply t based arithmetic operations to fuzzy system reliability analysis in fact we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for l r type fuzzy system reliability while others singer fuzzy sets syst 34 1990 145 cheng and mon fuzzy sets syst 56 1993 29 chen fuzzy sets syst 64 1994 31 have got the approximate solutions using sup min convolution for evaluating fuzzy system reliability

a note on t norm based addition of fuzzy intervals we generalize a result of fuller and keresztfalvi 1992 regarding the computation of t norm based additions of lr fuzzy intervals the proof of which is new and simple

positivity and stability analysis for linear implicit difference delay equations abstract this paper deals with positivity and stability of linear implicit difference delay equations being different from the lyapunov function approach commonly used in stability analysis the method employed in this paper gives a way to solve the exponential stability of linear implicit difference equations with time varying delay by decomposition state space and mathematical induction method new necessary and sufficient conditions for positivity and stability of such systems are derived numerical examples are given to illustrate the proposed results

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

some results on surjectivity of augmented differential operators abstract considering a problem of bonet and domanski 2006 1 problem 9 1 we prove that for a polynomial p on r 2 surjectivity of the differential operator p d on d x implies surjectivity of the augmented operator p d on d x r where p x 1 x 2 x 3 p x 1 x 2 moreover we give a sufficient geometrical condition on an open subset x of r d such that an analogous implication is true for arbitrary dimension d in case of p being homogeneous semi elliptic or of principal type

a homotopy method for eigenvalue assignment using decentralized state feedback this paper addresses the following problem given an interconnected system m composed of n subsystems of the form a i b i k i i 1 n a i b i a controllable pair and where the off diagonal blocks of m lie in the image of the appropriate b i then is it possible to arbitrarily assign the characteristic polynomial of m by a suitable selection of the characteristic polynomials of a i b i k i moreover is it possible to compute the appropriate characteristic polynomials of the a i b i k i or equivalently construct the k i needed to do so the first question is answered by constructing a mapping f r n rightarrow r n which maps a prescribed set of n of the feedback gains elements of k i i 1 n to the n coefficients of the characteristic polynomial of m the question then becomes given a p in r n does f x p have a solution the answer is found by constructing a homotopy h r n x o 1 rightarrow r n where h x 1 f x and h x 0 is some trivial function degree theory is then applied to guarantee that there exists an x t such that h x t t p for all t in 0 1 the parameterized sard s theorem is then utilized to prove that with probability 1 x t is a smooth curve and hence can be followed numerically from x 0 to x 1 by the solution of a differential equation davidenko s method

t sum of bell shaped fuzzy intervals the usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of zadeh s extension principle based on a t norm t a t norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class it is important to know which t norms are consistent with a particular type of fuzzy intervals recently dombi and gyorbiro proved that addition is closed if the dombi t norm is used with two bell shaped fuzzy intervals a result proved by mesiar on a strict t norm based shape preserving additions of lr fuzzy intervals with unbounded support is recalled as applications we define a broader class of bell shaped fuzzy intervals then we study t norms which are consistent with these particular types of fuzzy intervals dombi and gyorbiro s results are special cases of the results described in this paper

a j spectral factorization approach to control necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with mathcal h infty control j control are derived using j spectral factorization theory the existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled j spectral factorization problems with the second factor providing a parametrization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of nonnegative definite stabilizing solutions to two indefinite algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given a virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework and no additional auxiliary riccati equations are required

global low rank enhancement of decentralized control for large scale systems this note proposes a new control strategy which is computationally attractive for systems of large dimensions the main idea is to supplement decentralized feedback with a global additive term which is computed as a product of two low rank matrices this feature is of critical importance for systems that cannot be adequately stabilized using standard decentralized control the low rank matrices can be efficiently obtained using linear matrix inequalities and the resulting control is suitable for implementation in a multiprocessor environment simulations on a platoon of vehicles demonstrate that such a control can significantly improve the robustness of the closed loop system with respect to uncertain nonlinearities

some applications of small gain theorem to interconnected systems based on small gain theorem decentralized control of interconnected systems is studied linear matrix inequality conditions are given for stabilizability of interconnected systems interconnections can be used to improve system robustness in the sense of small gain theorem an example is given to illustrate the results finally interconnected systems composed of symmetric subsystems are studied

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

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

h control for fuzzy singularly perturbed systems in this paper both the state feedback and static output feedback h controllers for fuzzy singularly perturbed systems are investigated we give sufficient conditions for the existence of h controller such that the closed loop fuzzy control system is globally stable and achieves a prescribed level of disturbance attenuation for sufficiently small perturbation parameters the linear matrix inequality lmi approach is proposed to obtain the state feedback gains and a homotopy based iterative lmi algorithm is developed to get the static output feedback gains simulation results for two examples are included to demonstrate the effectiveness of the proposed approaches

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

a note to the t sum of l r fuzzy numbers abstract we generalize the results of hong and hwang 1994 for the membership function of finite infinite sum of l r fuzzy numbers where the sum is based on some continuous archimedean t norm t

a note to the addition of fuzzy numbers based on a continuous archimedean t norm abstract a simple method of computing the t sum of special types of fuzzy numbers is introduced for the lukasiewicz t norm tl the proposed method can be applied to the addition of fuzzy numbers with convex membership functions the classes of fuzzy numbers leading to t idempotents are studied for continuous t norms

brief decentralized h controller design in this paper a decentralized h controller design problem for two channel systems is considered a parametrization of all decentralized stable factors is proposed with the parametrization of all decentralized stable factors the class of decentralized compensators is parametrized the decentralized h controller design procedure is built upon the j spectral factorization approach to h control a class of decentralized suboptimal controllers satisfying the h norm bound is parametrized a design procedure for decentralized suboptimal h controllers is suggested

fuzzy linear regression using rank transform method in regression analysis the rank transform rt method is known to be neither dependent on the shape of the error distribution nor sensitive to outliers in this paper we construct a so called level fuzzy regression model based on the resolution identity theorem and apply rt method to this model fuzzy regression models with crisp input fuzzy output and fuzzy input fuzzy output are investigated to show the effectiveness of the proposed method to compare its effectiveness with existing methods we introduce a new performance measure in addition we propose a method to obtain a predicted output with respect to a specific target value and show that our model is more robust compared with other methods when the data contain some outliers

memoryless h controller design for switched non linear systems with mixed time varying delays this article deals with the h control problem for a class of switched non linear systems with mixed time varying delays the novel features here are that the system in consideration is non linear perturbation with discrete and distributed delays the time varying delay is also involved in the observation output and the controllers to be designed satisfy some exponential stability constraints on the closed loop poles by using lyapunov razumikhin functional approach new sufficient conditions for the h control with exponential stability constraint are derived in terms of the solution of riccati type equations the approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution

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

a new decentralised controller design method for a class of strongly interconnected systems abstractin this paper two interconnected structures are first discussed under which some closed loop subsystems must be unstable to make the whole interconnected system stable which can be viewed as a kind of strongly interconnected systems then comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown a new approach for the design of decentralised controllers is presented by determining the lyapunov function structure previously which allows the existence of unstable subsystems by fully utilising the orthogonal space information of input matrix some new understandings are presented for the construction of lyapunov matrix this new method can deal with decentralised state feedback static output feedback and dynamic output feedback controllers in a unified framework furthermore in order to reduce the design conservativeness and deal with robustness a new robust decentralised controller design method is given by combining with the parameter depend

on the game riccati equations arising in h_ infty control problems in the state space approach to h infty optimal control feasible closed loop gains gamma are characterized via a pair of game riccati equations depending on gamma this paper is concerned with the properties of these equations as gamma varies the most general problem is considered d 11 neq 0 and the variations of the riccati solutions are thoroughly analyzed insight is gained into the behavior near the optimum and into the dependence on gamma of the suboptimality conditions in addition concavity is established for a criterion that synthesizes the three conditions x geq 0 y geq 0 and rho xy gamma 2 this suggests a numerically reliable newton scheme for the computation of the optimal gamma most results presented here are extensions of earlier contributions the main concern is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically sound algorithms

some results on surjectivity of augmented semi elliptic differential operators we show that for a semi elliptic polynomial p on mathbb r 2 surjectivity of p d on fancyscript d omega implies surjectivity of the augmented operator p d on fancyscript d omega times mathbb r where p x1 x2 x3 p x1 x2 for arbitrary dimension n we give a sufficient geometrical condition on omega subset mathbb r n such that an analogous implication is true for semi elliptic p moreover we give an alternative proof of a result due to vogt which says that for elliptic p the operator p d is surjective if this is true for p d

decentralized control through parameter space optimization the decentralized control problem for linear dynamic systems is revisited using a parameter space approach which enables the definition of the decentralized feedbacks from the existence of non empty parameter convex sets the convexity property enables the derivation of efficient numerical algorithms based on standard approaches in convex programming the continuous time and discrete time cases are investigated and the decentralized control design is also treated to meet other important assignments such as optimal h2 performance index absolute stability h prescribed attenuation and robustness against actuator failures some numerical experiments illustrate the potential of this new control design

integrated design of structural and control systems with a homotopy like iterative method we consider an integrated design problem of structural and control systems it is well known that even the simplest formulation of this problem results in a kind of a bmi problem in this paper homotopy like iterative design method based on lmis is proposed to obtain an optimal plant and a controller simultaneously for a full order output feedback problem we can deal with a multiobjective problem e g control problem etc in the proposed design method we can also optimize structural design parameters appearing non linearly in the coefficient matrices of the plant state space form using the first order approximation of the non linear dependence in the proposed algorithm several design examples show that the proposed algorithm works quite effectively for various integrated design problems

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

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

on shape preserving additions of fuzzy intervals abstract we prove an open problem suggested by mesiar 1997 fuzzy sets and systems86 73 78 concerning continuous t norm based additions preserving the lr fuzzy intervals

continuation methods theory and applications this paper surveys in a tutorial fashion theoretical and applications aspects of the confirmation method for the solution of large scale system engineering problems the continuation method is motivated and defined the existence of the method is formulated in terms of degree theory a la algebraic topology examples are given throughout the paper and applications to engineering and economic problems are cited and described

every p convex subset of mathbb r 2 is already strongly p convex a classical result of malgrange says that for a polynomial p and an open subset of mathbb r d the differential operator p d is surjective on c if and only if is p convex hormander showed that p d is surjective as an operator on fancyscript d omega if and only if is strongly p convex it is well known that the natural question whether these two notions coincide has to be answered in the negative in general however treves conjectured that in the case of d 2 p convexity and strong p convexity are equivalent a proof of this conjecture is given in this note

decentralized control of symmetric systems abstract this paper is concerned with the stabilizability problem of symmetric systems by means of decentralized controllers it is shown that the set of decentralized fixed modes of a symmetric system is equal to the set of uncontrollable and unobservable modes of the system and implies that the stabilizability of a state space symmetric system by means of a decentralized controller is equivalent to the stabilizability for the system by means of a centralized controller

simplifying the h theory via loop shifting matrix pencil and descriptor concepts the 2 riccati h controller formulae and derivations are simplified via various loop shifting transformations that are naturally expressed in terms of a degree one polynomial system matrix psm closely related to the luenberger descriptor form of a system the technique enables one without loss of generality to restrict attention to the simple case in which d 11 0 d 22 0 d t 12 0 l d 21 0 l d l 12 c1 0 and b 1 d t 21 0 matrix fraction descriptions mfds for the algebraic riccati equation solutions afford another change of variables which brings the 2 riccati h controller formulae into a cleaner more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the riccati solutions pi and q blow up and in cases where l qp is nearly singular numerical difficulties previously associated with verifying the existence conditions p 0 q 0 and maxlpar qp 1 are largely eliminated by e

a double homotopy method for decentralised control design an iterative algorithm that is based on the idea of two homotopy paths is proposed for output feedback decentralised control design the approach follows a bilinear matrix inequality bmi formulation of the decentralised control problem along one homotopy path the bmi problem which is non convex is locally linearised and solved along the second homotopy path the controller is deformed at each step so that in the end it attains a decentralised structure the proposed computational algorithm can also be applied to obtain reduced order decentralised controllers numerical examples are used to demonstrate the efficacy of the proposed algorithm

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

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

computational complexity of a problem arising in fixed order output feedback design this paper is concerned with a matrix inequality problem which arises in fixed order output feedback control design this problem involves finding two symmetric and positive definitive matrices x and y such that each satisfies a linear matrix inequality and that xy i it is well known that many control problems such as fixed order output feedback stabilization h control guaranteed h2 control and mixed h2 h control can all be converted into the matrix inequality problem above including static output feedback problems as a special case we show however that this matrix inequality problem is np hard

stabilization and h control of symmetric systems an explicit solution abstract in this paper we address the h control analysis the output feedback stabilization and the output feedback h control synthesis problems for state space symmetric systems using a particular solution of the bounded real lemma for an open loop symmetric system we obtain an explicit expression to compute the h norm of the system for the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state space symmetric systems for the h control synthesis problem we derive an explicit expression for the optimally achievable closed loop h norm and the optimal control gains extension to robust and positive real control of such systems are also examined these results are obtained from the linear matrix inequality formulations of the stabilization and the h control synthesis problems using simple matrix algebraic tools

robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback the objective of this note is to propose a dynamic output control scheme within the lmi framework for robust decentralized stabilization of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints the procedure utilizes the general linear dynamic feedback structure and consists of two steps the first giving a block diagonal lyapunov matrix together with the robustness degree and the second the controller parameters a numerical example illustrates the applicability of the method

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

the convergence of t product of fuzzy numbers abstract this paper is to provide new results regarding the effective practical computation of t norm based products of r type fuzzy numbers and their limits