minimal simple closed 18 surfaces and a topological preservation of 3d surfaces the aim of this paper is to investigate a map which preserves digital topological properties of a digital 3d surface such as the topological number digital k contractibility and so on furthermore the two types of minimal simple closed 18 surfaces mss 1 8 and mss 1 8 are established in z 3 in relation with 18 contractibility which are shown to be different from each other up to digital 18 homotopy moreover it is proved that mss 1 8 is the minimal simple closed 18 surface without 18 contractibility and mss 1 8 is the minimal malgouyres simple closed 18 surface with 18 contractibility finally we show that a digital k 0 k 1 homeomorphism preserves a simple k 0 surface to a simple k 1 surface and vice versa

a less conservative lmi condition for the robust stability of discrete time uncertain systems abstract in this paper a less conservative condition for the robust stability of uncertain discrete time linear systems is proposed the uncertain parameters assumed to be time invariant are supposed to belong to convex bounded domains polytope type uncertainty the stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain a simple and numerically efficient feasibility test provides a set of lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain examples illustrate the results

new approach to robust cal d stability analysis of linear time invariant systems with polytope bounded uncertainty this note presents a new approach to robust d stability analysis of linear time invariant systems with polytope bounded uncertainty the proposed approach combines sufficient conditions for robust d stability in terms of feasibility problems with linear matrix inequalities lmi constraints and a new polytope partition technique if the initial polytope does not attain the robust d stability sufficient condition the polytope is successively subdivided until all subpolytopes attain the sufficient condition in the case of robustly d stable uncertain system or it is found a subpolytope vertex that does not attain the regional pole placement constraints in the case of an uncertain system that is not robustly d stable it is presented a new general format polytope partition technique that allows the implementation of the proposed approach the efficiency of the proposed approach is verified by means of illustrative examples and three different lmi based analysis formulations

on the structure of generalized rough sets in this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1 any reflexive binary relation determines a topology 2 if q is a reflexive and symmetric relation on a set x then o email protected x q a a is a topology such that a is open if and only if it is closed 3 conversely for every topological space x o satisfying the condition that a is open if and only if it is closed there exists a reflexive and symmetric relation r such that o email protected x r a a 4 let q be an equivalence relation on x for any pseudo w closed subset a of x q a is an w closed set if and only if w x x x email protected a for any email protected x moreover we consider properties of generalized rough sets

extensions and intentions in the rough set theory abstract the approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension it is different from the well known approaches in the literature in that the upper approximations and the lower approximations of unknown sets are considered as certain families of known sets this approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets which are analogous to classical operations on sets the basic results presented in this paper based on certain ideas of the second author were formulated by the first author in his doctoral dissertation prepared under the supervision of the third author

rough ideals in semigroups abstract we shall introduce the notion of a rough left right two sided bi ideal in a semigroup which is an extended notion of a left right two sided bi ideal in a semigroup and give some properties of such ideals

a boundary value problem for the poisson equation with multi scale oscillating boundary the paper is concerned with the homogenization problem for the poisson equation in a domain a part of whose boundary is rapidly oscillating according to several scales such a problem arises in the processing of devices with very small features such as semiconductors we construct homogenized boundary layers and use them to establish effective approximation to the solution

uniform resolvent convergence for strip with fast oscillating boundary abstract in a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small on the oscillating boundary we impose dirichlet neumann or robin boundary condition in all cases we describe the homogenized operator establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one and prove the estimates for the rate of convergence these results are obtained as the order of the amplitude of the oscillations is less equal or greater than that of the period it is shown that under the homogenization the type of the boundary condition can change

relationship between generalized rough sets based on binary relation and covering rough set theory is a powerful tool for dealing with uncertainty granularity and incompleteness of knowledge in information systems this paper systematically studies a type of generalized rough sets based on covering and the relationship between this type of covering based rough sets and the generalized rough sets based on binary relation firstly we present basic concepts and properties of this kind of rough sets then we investigate the relationships between this type of generalized rough sets and other five types of covering based rough sets the major contribution in this paper is that we establish the equivalency between this type of covering based rough sets and a type of binary relation based rough sets through existing results in binary relation based rough sets we present axiomatic systems for this type of covering based lower and upper approximation operations in addition we explore the relationships among several important concepts such as minimal description reduction representative covering exact covering and unary covering in covering based rough sets investigation of this type of covering based will benefit to our understanding of other types of rough sets based on covering and binary relation

technical communique time invariant uncertain systems a necessary and sufficient condition for stability and instability via homogeneous parameter dependent quadratic lyapunov functions this paper investigates linear systems with polynomial dependence on time invariant uncertainties constrained in the simplex via homogeneous parameter dependent quadratic lyapunov functions hpd qlfs it is shown that a sufficient condition for establishing whether the system is either stable or unstable can be obtained by solving a generalized eigenvalue problem moreover this condition is also necessary by using a sufficiently large degree of the hpd qlf

an lmi condition for the robust stability of uncertain continuous time linear systems a new sufficient condition for the robust stability of continuous time uncertain linear systems with convex bounded uncertainties is proposed in this note the results are based on linear matrix inequalities lmis formulated at the vertices of the uncertainty polytope which provide a parameter dependent lyapunov function that assures the stability of any matrix inside the uncertainty domain with the aid of numerical procedures based on unidimensional search and the lmis feasibility tests a simple and constructive way to compute robust stability domains can be established

equivalent k0 k1 covering and generalized digital lifting this paper studies various properties of k 0 k 1 continuity in relation to uniform k 0 k 1 continuity and a pasting theorem which can be used in image synthesis image segmentation and image weaving furthermore we establish an equivalent k 0 k 1 covering and provide some condition to construct the generalized digital lifting of an equivalent k 0 k 1 covering map which is used to calculate the digital fundamental group of a digital image and to classify digital images by a discrete deck s transformation group to be specific let p e e 0 b b 0 be a pointed k 0 k 1 covering map and let f x x 0 b b 0 be a pointed k 2 k 1 continuous map then we can provide a condition to have a concerning pointed k 2 k 0 continuous map email protected x x 0 e e 0 such that email protected email protected f

relational interpretations of neighborhood operators and rough set approximation operators this paper presents a framework for the formulation interpretation and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations a special class of neighborhood systems called 1 neighborhood systems is introduced three extensions of pawlak approximation operators are analyzed properties of neighborhood and approximation operators are studied and their connections are examined

rough set theory for the interval valued fuzzy information systems the notion of a rough set was originally proposed by pawlak z pawlak rough sets international journal of computer and information sciences 11 5 1982 341 356 later on dubois and prade d dubois h prade rough fuzzy sets and fuzzy rough sets international journal of general system 17 2 3 1990 191 209 introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets this paper deals with an interval valued fuzzy information system by means of integrating the classical pawlak rough set theory with the interval valued fuzzy set theory and discusses the basic rough set theory for the interval valued fuzzy information systems in this paper we firstly define the rough approximation of an interval valued fuzzy set on the universe u in the classical pawlak approximation space and the generalized approximation space respectively i e the space on which the interval valued rough fuzzy set model is built secondly several interesting properties of the approximation operators are examined and the interrelationships of the interval valued rough fuzzy set models in the classical pawlak approximation space and the generalized approximation space are investigated thirdly we discuss the attribute reduction of the interval valued fuzzy information systems finally the methods of the knowledge discovery for the interval valued fuzzy information systems are presented with an example

on the topological properties of fuzzy rough sets this paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe the tc axiom for fuzzy topology is proposed it is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies tc axiom and conversely a fuzzy topology which obey tc axiom is just the set of all lower approximation sets under a reflexive and transitive fuzzy relation that is to say there exists a one to one correspondence between the set of all reflexive and transitive fuzzy relations and the set of all fuzzy topologies which satisfy tc axiom

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

a non stationary multi scale oscillating free boundary for the laplace and heat equations the paper is concerned with the homogenization problem for the poisson equation in a domain a part of whose boundary varies in time and is rapidly oscillating in space at each time such a problem arises in growing semiconductor film taking into account the fact that the surface of the film is changing in time by chemical vapor deposition or by etching we prove existence and uniqueness of the solution and establish its homogenizated approximation we obtain an l estimate on the error between the free boundary and the homogenized boundary

on the topological properties of generalized rough sets in this paper we consider some topological properties of generalized rough sets induced by binary relations and show that1 any serial binary relation can induce a topology 2 let r be a binary relation on a universe u t r and e r denote the transitive closure and the equivalence closure of r respectively if r is a reflexive relation on u then r and t r induce the same topology i e t r t t r the interior and closure operators of the topology t r induced by r are the lower and upper approximation operators t r and t r respectively moreover r t r t r where r t r is the relation induced by the topology t r 3 when r is a reflexive and symmetric relation r and e r induce the same topology i e t r t e r the interior and closure operators of the topology t r induced by r are the lower and upper approximation operators e r and e r respectively moreover r t r e r 4 based on the above conclusions the notion of topological reduction of incomplete information systems is proposed and characterizations of reduction of consistent incomplete decision tables are obtained

rough sets and intelligent data analysis rough set based data analysis starts from a data table called an information system the information system contains data about objects of interest characterized in terms of some attributes often we distinguish in the information system condition and decision attributes such information system is called a decision table the decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table with every decision table a set of decision rules called a decision algorithm can be associated it is shown that every decision algorithm reveals some well known probabilistic properties in particular it satisfies the total probability theorem and the bayes theorem these properties give a new method of drawing conclusions from data without referring to prior and posterior probabilities inherently associated with bayesian reasoning

topological characterizations of covering for special covering based upper approximation operators the relationships among properties of covering approximation operators and their corresponding coverings have attracted intensive research in recent years in particular those among topological properties have drawn special attention because of their important applications in rough set theory in this paper we give topological characterizations of covering c for covering based upper approximation operators fh sh th and rh to be closure operators we also give intuitive characterizations of covering c and describe covering based approximation space u c as certain types of information exchange systems when sh or rh is a closure operator by applying our new characterizations we give inequalities about the relationship between the number of members in c and the number of elements in u and discuss relationships among conditions for different covering based upper approximation operators to be closure operators to the best of our knowledge it is the first time that such characterizations descriptions inequalities and discussions are systematically considered in the literature of rough set theory furthermore in this paper we also give several characterizations of unary coverings an important type of coverings in studying relationships among basic concepts in covering based rough sets by the relationships among different types of covering base approximation operators

generalized rough sets based on reflexive and transitive relations in this paper we investigate the relationship between generalized rough sets induced by reflexive and transitive relations and the topologies on the universe which is not restricted to be finite it is proved that there exists a one to one correspondence between the set of all reflexive and transitive relations and the set of all topologies which satisfy a certain kind of compactness condition

neighborhood operators for covering based rough sets covering based rough sets are important generalizations of the classical rough sets of pawlak a common way to shape lower and upper approximations within this framework is by means of a neighborhood operator in this article we study 24 such neighborhood operators that can be derived from a single covering we verify equalities between them reducing the original collection to 13 different neighborhood operators for the latter we establish a partial order showing which operators yield smaller or greater neighborhoods than others six of the considered neighborhood operators result in new covering based rough set approximation operators we study how these new approximation operators relate to existing ones in terms of partial order relations i e whether the generated approximations are in general greater smaller or incomparable finally we discuss the connection between the covering based approximation operators and relation based approximation operators another prominent generalization of pawlak s rough sets

technical communique stabilization for takagi sugeno fuzzy systems based on partitioning the range of fuzzy weights in this note the state feedback stabilization for continuous time takagi sugeno t s fuzzy systems is addressed where the fuzzy weighting functions are assumed to be differentiable and their ranges of variation are possibly bounded by some parameters by utilizing the matrix elimination lemma and introducing a polyhedral partition to the range of the fuzzy weights the quadratically parameterized condition is transformed to being piecewise linear in both the fuzzy weights and their derivatives then a switching control based on the partition is considered by utilizing the extreme points in each partition to address the constraints of the fuzzy weights and their derivatives the simulation shows that finer subdivision in the partition leads to better stability and stabilization margins

stability analysis of linear time varying systems improving conditions by adding more information about parameter variation abstract in this paper a new lyapunov function is proposed for stability analysis of linear time varying systems this new function carries more information regarding parameter variation leading to less conservative conditions using finsler s lemma and a suitable form to describe the high order time derivatives of the parameters finite sets of lmis are obtained which are progressively less conservative as a pair of parameters grow previous results can be seen as a special case and numerical examples are carried out for the sake of illustration

pontryagin maximum principle for semilinear and quasilinearparabolic equations with pointwise state constraints this paper studies the first order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial differential equations with pointwise state constraints a pontryagin type maximum principle is obtained

simplicial grid refinement on freudenthal s algorithm and the optimal number of congruence classes in the present paper we investigate freudenthal s simplex refinement algorithm which can be considered to be the canonical generalization of bank s well known red refinement strategy for triangles freudenthal s algorithm subdivides any given n simplex into 2 n subsimplices in such a way that recursive application results in a stable hierarchy of consistent triangulations our investigations concentrate in particular on the number of congruence classes generated by recursive refinements after presentation of the method and the basic ideas behind it we will show that freudenthal s algorithm produces at most n 2 congruence classes for any initial n simplex no matter how many subsequent refinements are performed moreover we will show that this number is optimal in the sense that recursive application of any affine invariant refinement strategy with 2 n sons per element results in at least n 2 congruence classes for almost all n simplices

robust model reduction of uncertain systems maintaining uncertainty structure this article presents a new approach for or robust model reduction for uncertain systems based on an optimisation algorithm applied directly in the space of reduced order model parameters the proposed approach can be applied to both polytopic or affine parameter dependent models as well as for continuous or discrete time systems the developed procedure is capable of computing both fixed reduced order model as well as uncertain reduced order model keeping the original uncertainty structure the resulting reduced order model is guaranteed to be robust stable

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

covering rough set structures for a locally finite covering approximation space abstract the purpose of this paper is to introduce the notion of locally finite covering approximation lfc for brevity space u c which is a generalization of a finite covering approximation space furthermore for a subset x of the universe u we develop two kinds of neighborhood systems derived from the covering c specifically k1 x and k2 x which are not comparable with each other next the paper establishes two topologies on u alexandroff and quasi discrete topologies generated by systems k1 x and k2 x as bases respectively after suggesting many examples explaining the above notions and systems we develop two new types of rough set structures an h rough set operator h h and a khalimsky k for short topological rough set operator d k d k the present paper investigates various properties of these operators and refers to certain advantages of them which can be used in applied science including digital geometry information geometry computer vision pattern recognition image processing and so on in order to accomplish this we use some tools such as granulations neighborhood systems typical pawlak s tools related topologies rough set structures associated with the k topology and so on furthermore through this work we can obtain strong connections between covering rough set theory and applied geometry in the present paper all sets u c and x u need not be finite

constructive and algebraic methods of the theory of rough sets this paper reviews and compares constructive and algebraic approaches in the study of rough sets in the constructive approach one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation different classes of rough set algebras are obtained from different types of binary relations in the algebraic approach one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators various classes of rough set algebras are characterized by different sets of axioms axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators

technical communique lmi conditions for time varying uncertain systems can be non conservative establishing robust asymptotic stability of uncertain systems affected by time varying uncertainty is a key problem lmi sufficient conditions have been proposed in the literature for addressing this problem based on homogeneous polynomial lyapunov functions unfortunately till now it has been unclear whether these conditions are also necessary this paper proposes a proof in order to show that one of these conditions is not only sufficient but also necessary for a sufficiently large degree of the lyapunov function

topological approaches to covering rough sets rough sets a tool for data mining deal with the vagueness and granularity in information systems this paper studies covering based rough sets from the topological view we explore the topological properties of this type of rough sets study the interdependency between the lower and the upper approximation operations and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation lastly axiomatic systems for the lower approximation operation and the upper approximation operation are constructed

robust h performance using lifted polynomial parameter dependent lyapunov functions this paper investigates the robust h performance of time invariant linear uncertain systems where the uncertainty is in polytopic domains robust h is checked by constructing a quadratic parameter dependent lyapunov function the matrix associated with this quadratic lyapunov function is a polynomial function of the uncertain parameters expressed as a particular polynomial matrix involving powers of the dynamic matrix of the system and one symmetric matrix to be determined the degree of this polynomial matrix function is arbitrary finsler s lemma is used to lift the obtained stability conditions into a larger space in which sufficient stability tests can be developed in the form of linear matrix inequalities as increases less conservative h evaluations are obtained both continuous and discrete time systems are investigated numerical examples illustrate the method and compare the present results with similar works in the literature

local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations we consider solutions and subsolutions and supersolutions of the boundary value problem au x u du diju u x u du 0 in 2 s x diu y x u g x on3fi for a lipschitz domain s a positive definite matrix valued function u j and a vector field s which points uniformly into q without making any continuity assumptions on the known functions we prove harnack and holder estimates for u near 3i2 in addition we bound the l norm of u near 3i2 in terms of an appropriate lp norm and the known functions our approach is based on that for the corresponding interior estimates of trudinger this paper is concerned with analogs for solutions of oblique boundary value problems of the results in 10 our results will extend previous work of lieberman and trudinger 5 and of nadirashvili 9 specifically we consider second order differential operators q of the form

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

fuzzy rough set theory for the interval valued fuzzy information systems the concept of the rough set was originally proposed by pawlak as a formal tool for modelling and processing incomplete information in information systems then in 1990 dubois and prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets the aim of this paper is to present a new extension of the rough set theory by means of integrating the classical pawlak rough set theory with the interval valued fuzzy set theory i e the interval valued fuzzy rough set model is presented based on the interval valued fuzzy information systems which is defined in this paper by a binary interval valued fuzzy relations r f i uxu on the universe u several properties of the rough set model are given and the relationships of this model and the others rough set models are also examined furthermore we also discuss the knowledge reduction of the classical pawlak information systems and the interval valued fuzzy information systems respectively finally the knowledge reduction theorems of the interval valued fuzzy information systems are built

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

relationship among basic concepts in covering based rough sets uncertainty and incompleteness of knowledge are widespread phenomena in information systems rough set theory is a tool for dealing with granularity and vagueness in data analysis rough set method has already been applied to various fields such as process control economics medical diagnosis biochemistry environmental science biology chemistry psychology and conflict analysis covering based rough set theory is an extension to classical rough sets in covering based rough sets there exist several basic concepts such as reducible elements of a covering minimal descriptions unary coverings and the property that the intersection of any two elements is the union of finite elements in this covering these concepts appeared in the literature of covering based rough sets separately in this paper we study the relationships between them in particular we establish the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering we also investigate the relationship between the covering lower approximation operation and the interior operator a characterization of the interior operator by the covering lower approximation operation is presented in this paper correspondingly we study the relationship between the covering upper approximation operation and the closure operator in addition we explore the conditions under which the covering upper approximation operation is monotone the study of the relationships between these concepts will help us have a better understanding of covering based rough sets

an lpd approach to robust h sub 2 and h sub spl infin static output feedback design a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with uncertain parameters that achieves a minimum bound on either the h sub 2 or h sub spl infin performance level is introduced assuming that the uncertain parameters reside in a given polytope a parameter dependent lyapunov function is described which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope

covering based rough set approximations we propose a framework for the study of covering based rough set approximations three equivalent formulations of the classical rough sets are examined by using equivalence relations partitions and s algebras respectively they suggest the element based the granule based and the subsystem based definitions of approximation operators covering based rough sets are systematically investigated by generalizing these formulations and definitions a covering of universe of objects is used to generate different neighborhood operators neighborhood systems coverings and subsystems of the power set of the universe they are in turn used to define different types of generalized approximation operators within the proposed framework we review and discuss covering based approximation operators according to the element granule and subsystem based definitions

design of mixed h2 h control systems using algorithms inspired by the immune system we utilize optimization algorithms inspired by the immune system for treating the mixed h 2 h control problem both precisely known systems and uncertain systems with polytopic uncertainties are investigated for the latter a novel methodology is proposed to compute the worst case norms within the polytope of matrices this methodology consists in defining the worst case norm computation as an implicit optimization problem with a special structure we exploit this structure of the problem for its solution the paper presents both mono and multiobjective optimization algorithms developed from the clonal selection principle the former is the real coded clonal selection algorithm rcsa and the latter is the multiobjective clonal selection algorithm mocsa the complete design process involves the combination of synthesis and analysis the rcsa is used for analysis through the worst case norm computation for a given provided controller the mocsa is used for synthesis working on a population of candidate controllers until providing an estimate of the pareto set for the mixed h 2 h control problem the numerical examples illustrate the power and the validity of the proposed approach for robust control design moreover our approach for worst case norm evaluation is compared with other approaches available in literature

a new method for robust schur stability analysis this article is concerned with robust stability of uncertain discrete time linear systems the matrix defining the linear system system matrix is assumed to depend affinely on a set of time invariant unknown parameters lying on a known polytope robust stability is investigated by checking whether a certain integer power of the uncertain system matrix has spectral norm less than one this peculiar stability test is shown to be equivalent to the positivity analysis of a homogeneous symmetric matrix polynomial with precisely known coefficients and degree indexed by a unique feature is that no extra variables need to be added to the problems being solved numerical experiments reveal that the value of needed to test robust stability is mostly independent of the system dimension but grows sharply as the eigenvalues of the uncertain system approach the unit circle by identifying the proposed stability test with a particular choice of a parameter dependent lyapunov function extra variables can be int