unified treatment of robust stability conditions for discrete time systems through an infinite matrix framework abstract this paper is motivated by the study on clarifying further relationship between the conventional lifting free causal linear time invariant lti scaling and lifting based noncausal linear periodically time varying lptv scaling approaches to robust stability analysis to facilitate such a study this paper gives the infinite matrix representation counterparts of the robust stability conditions in the separator type robust stability theorems for these approaches these counterparts lead to the idea of infinite dimensional separators and provide us with a unified framework for studying the mutual relationship between these two approaches this paper takes causal lti and noncausal lptv separators characterized by finite impulse response which are respectively defined in the lifting free and lifting based frameworks and compares them with respect to conservativeness of robust stability analysis by means of the unified framework through such a discussion it is demonstrated that the unified framework can lead to a very comprehensible and intuitive study on the mutual relationship between causal lti and noncausal lptv scaling approaches

well posedness of feedback systems insights into exact robustness analysis and approximate computations this paper establishes a framework for robust stability analysis of linear time invariant uncertain systems the uncertainty is assumed to belong to an arbitrary subset of complex matrices the concept used here is well posedness of feedback systems leading to necessary and sufficient conditions for robust stability based on this concept some insights into exact robust stability conditions are given in particular frequency domain and state space conditions for well posedness are provided in terms of hermitian form inequalities it is shown that these inequalities can be interpreted as small gain conditions with a generalized class of scalings given by linear fractional transformations lft using the lft scaled small gain condition in the state space setting the duality is established between the h sub spl infin norm condition with frequency dependent scalings and the parameter dependent lyapunov condition connections to the existing results including the structured singular value and the integral quadratic constraints are also discussed finally we show that our well posedness conditions can be used to give a less conservative yet computable bound on the real structured singular value this result is illustrated by numerical examples

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

sobriety and spatiality in varieties of algebras the paper considers a generalization of the classical papert papert isbell adjunction between the categories of topological spaces and locales to an arbitrary variety of algebras and illustrates the obtained results by the category of algebras over a given unital commutative quantale

properties of discrete time noncausal linear periodically time varying scaling and their relationship with shift invariance in lifting timing this article is concerned with the technique called discrete time noncausal linear periodically time varying lptv scaling for robust stability analysis noncausal lptv scaling has already been shown to be effective for reducing the conservativeness of robustness analysis in theoretical and numerical ways however there still remain some issues to be resolved for further understanding and exploiting noncausal lptv scaling e g its relationship with the conventional analysis approach of causal linear time invariant scaling in this article by introducing the key idea of shift invariance in lifting timing we discuss the difference and corresponding relationship between the conventional approach and noncausal lptv scaling

from quantale algebroids to topological spaces fixed and variable basis approaches using the category of quantale algebroids the paper considers a generalization of the classical papert papert isbell adjunction between the categories of topological spaces and locales to partial algebraic structures it also provides a single framework in which to treat the concepts of quasi standard and stratified fuzzy topology

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

residuated frames with applications to decidability residuated frames provide relational semantics for substructural logics and are a natural generalization of kripke frames in intuitionistic and modal logic and of phase spaces in linear logic we explore the connection between gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut elimination the finite model property and the finite embeddability property we use our results to prove the decidability of the equational and or universal theory of several varieties of residuated lattice ordered groupoids including the variety of involutive

dynamical surface structures in multiparticle correlated surface growths we investigate the scaling properties of the interface fluctuation width for the q mer and q particle correlated deposition evaporation models these models are constrained with a global conservation law that the particle number at each height is conserved modulo q in equilibrium the stationary roughness is anomalous but universal with the roughness exponent alpha 1 3 while the early time evolution shows nonuniversal behavior with the growth exponent beta varying with models and q nonequilibrium surfaces display diverse growing and stationary behaviors the q mer model shows a faceted structure while the q particle correlated model shows a macroscopically grooved structure

robust stability analysis with cycling based lptv scaling part i fundamental results on its relationship with lifting based lptv scaling abstractthis paper is concerned with robust stability analysis of discrete time linear periodically time varying lptv systems using the cycling based lptv scaling approach to study the properties of this approach in comparison with the lifting based lptv scaling approach we consider exploiting the framework of representing the associated robust stability conditions with infinite matrices since it serves as a common framework for comparing the two different lptv scaling approaches it provides us with new insights into the relationship between the cycling based and lifting based scaling approaches in particular we derive fundamental results that enable us to reduce the comparison with respect to conservativeness in robust stability analysis of the two scaling approaches with restricted and tractable classes of separators to a modified comparison of the associated classes of what we call infinite dimensional separators arising in the above infinite matrix framework

fuzzy sets and sheaves part ii sheaf theoretic foundations of fuzzy set theory with applications to algebra and topology this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

survey invariant representations of discrete time periodic systems the correspondence between periodic and time invariant systems can take a variety of forms the purpose of this survey paper is to present a complete and clear picture on time invariant representations for discrete time periodic systems the core of the treatment evolves around the concept of periodic transfer function

critical behavior of roughening transitions in parity conserving growth processes we investigate a class of parity conserving solid on solid models that describes the growth of an interface by the deposition and evaporation of dimers as a key feature of the models evaporation of dimers takes place only at the edges of terraces leading to a roughening transition between a smooth and a rough phase we consider several variants of growth models in order to identify universal and nonuniversal properties moreover a parity conserving polynuclear growth model is proposed all variants display the same type of universal critical behavior at the roughening transition because of parity conservation the critical behavior at the first few layers can be explained in terms of unidirectionally coupled branching annihilating random walks with an even number of offspring

brief paper noncausal linear periodically time varying scaling for robust stability analysis of discrete time systems frequency dependent scaling induced by static separators this article is concerned with robust stability analysis of discrete time systems and introduces a novel and powerful technique that we call noncausal linear periodically time varying lptv scaling based on the discrete time lifting together with the conventional but general scaling approach we are led to the notion of noncausal lptv scaling for lptv systems and its effectiveness is demonstrated with a numerical example to separate the effect of noncausal and lptv characteristics of noncausal lptv scaling to see which is a more important source leading to the effectiveness we then consider the case of lti systems as a special case then we show that even static noncausal lptv scaling has an ability of inducing frequency dependent scaling when viewed in the context of the conventional lti scaling while causal lptv scaling fails to do so it is further discussed that the effectiveness of noncausal characteristics leading to the frequency domain interpretation can be exploited even for lptv systems by considering the nn lifted transfer matrices of n periodic systems

category theoretic aspects of chain valued frames part i categorical and presheaf theoretic foundations this paper is part i of a two part series dealing with category theoretic aspects of chain valued frames a new categorical motivation for lattice valued frames is given from presheaves and then under the assumption that l be a complete chain it is established that standard category theoretic properties completeness cocompleteness factorization structures hold for l frm the category of l frames and l frame morphisms properties which are a platform for the upper free functor l and lower free functor r used in part ii to give a broad range of applications of chain valued frames to lattice valued topology

etale groupoids and their quantales abstract we establish close and previously unknown relations between quantales and groupoids in particular to each etale groupoid either localic or topological there is associated a unital involutive quantale we obtain a bijective correspondence between localic etale groupoids and their quantales which are given a rather simple characterization and here are called inverse quantal frames we show that the category of inverse quantal frames is equivalent to the category of complete and infinitely distributive inverse monoids and as a consequence we obtain a non functorial correspondence between these and localic etale groupoids that generalizes more classical results concerning inverse semigroups and topological etale groupoids this generalization is entirely algebraic and it is valid in an arbitrary topos as a consequence of these results we see that a localic groupoid is etale if and only if its sublocale of units is open and its multiplication map is semiopen and an analogue of this holds for topological groupoids in practice we are provided with new tools for constructing localic and topological etale groupoids as well as inverse semigroups for instance via presentations of quantales by generators and relations the characterization of inverse quantal frames is to a large extent based on a new quantale operation here called a support whose properties are thoroughly investigated and which may be of independent interest

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

on the injective hulls of quantum b algebras abstract quantum b algebras as implicational subreducts of quantales were introduced by rump and yang which cover the majority of implicational algebras and provide a unified semantics for non commutative algebraic logic due to the adjunction between multiplication and its residuals they can be regarded as the implicational counterpart of partially ordered semigroups by means of the injective hulls envelopes of quantum b algebras rump gave the injective hulls of partially ordered semigroups in this paper one part of our work is to give new examples of quantum b algebras where the lower sets do not form a quantale another part of our work is to consider the inverse problem of rump s way that is we can also give the injective hulls of quantum b algebras in terms of the injective hulls of partially ordered semigroups

the completions of multi posets and quantum b algebras abstract multi posets as the generalization of quantum b algebras and partially ordered semigroups etc were firstly introduced and studied by rump in this paper we shall continue his work and investigate the completions of multi posets and quantum b algebras firstly we introduce the notions of the precoherent completions of a multi poset m and the algebraic consistent quantic nuclei on the power set p m f of the free semigroup of m and prove that the precoherent completions of a multi poset m is completely determined by the algebraic consistent quantic nuclei on p m f up to isomorphism moreover we give the concrete forms of the least and the largest standard precoherent completions and obtain the free quantale over a multi poset in the category of multi posets finally when the completions and consistent quantic nuclei of multi posets are applied to the cases of quantum b algebras and partially ordered semigroups several analogous results can also be obtained

periodic memory state feedback controller new formulation analysis and design results this paper proposes a unified setup for robust stability and performance analysis and synthesis for periodic polytopic discrete time systems relying on a general formulation for state feedback periodic memory controllers and a new time lifting new sufficient lmi conditions for the existence of robust stability certificates and h2 guaranteed cost control laws are derived comparisons of the efficiency of different controller structures illustrate these developments on a numerical example

nonuniversal dynamics of dimer growing interfaces a finite temperature version of body centered solid on solid growth models involving attachment and detachment of dimers is discussed in 1 1 dimensions the dynamic exponent of the growing interface is studied numerically via the spectrum gap of the underlying evolution operator the finite size scaling of the latter is found to be affected by a standard surface tension term on which the growth rates depend this nonuniversal aspect is also corroborated by the growth behavior observed in large scale simulations by contrast the roughening exponent remains robust over wide temperature ranges