on robust hurwitz polynomials in this note kharitonov s theorem on robust hurwitz polynomials is simplified for low order polynomials specifically for n 3 4 and 5 the number of polynomials required to check robust stability is one two and three respectively instead of four furthermore it is shown that for n geq 6 the number of polynomials for robust stability checking is necessarily four thus further simplification is not possible the same simplifications arise in robust schur polynomials by using the bilinear transformation applications of these simplifications to two dimensional polynomials as well as to robustness for single parameters are indicated

stability of polynomials under coefficient perturbation let the real polynomial a 0 x n a 1 x n 1 a n 1 x a n be stable and let the real numbers b k c k geq 0 0 leq k leq n be given we present a simple determinant criterion for finding the largest t 0 geq 0 such that the polynomial alpha 0 x n alpha 1 x n 1 alpha n 1 x alpha n is stable for all alpha k in a k b k t 0 a k c k t 0 cup a k 0 leq k leq n several further observations allow us to reduce the computational cost considerably

robust stabilization of interval plants using lead or lag compensators abstract a lead or lag compensator robustly stabilizes a family of interval plants if and only if it simultaneously stabilizes the vertex plants

extreme points in triangular uhf algebras we examine the strongly extreme point structure of the unit balls of triangular uhf algebras the semisimple triangular uhf algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal in contrast to this for the class of full nest algebras we prove a krein milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points results concerning the geometry of the unit ball have a long history both in banach space theory and in the theory of operator algebras this geometry can be affiliated with structural and algebraic properties moreover differences in geometric properties can prove useful in classification problems two fundamental results are the russo dye theorem and kadison s theorem on isometries more recently there has been interest in the unit balls of nonselfadjoint operator algebras especially nest algebras 1 2 3 4 15 16 this paper concerns the unit balls of triangular uhf algebras these and the larger class of triangular af algebras are nonselfadjoint analogues of the uhf and af c algebras studied by glimm and bratteli their theory has grown rapidly cf 8 9 18 19 20 we focus on the extreme point structure and our results have a different flavor than those for nest algebras specifically we study the strongly extreme points those boundary points whose stable character with respect to approximations makes them behave well under direct limits triangular uhf algebras are direct limits of full upper triangular matrix algebras unit balls embed into unit balls in the direct limit scheme and some types of embeddings respect the extreme point structure while others do not this leads to structural differences in the limit algebras the geometric structures of the unit balls of different triangular uhf algebras can be very dissimilar the convex hull of the strongly extreme points even without closure always contains the unit ball of the diagonal theorem 7 shows that the two coincide if and only if the algebra is semisimple this is a characterization of a purely geometric property in terms of a purely algebraic one in contrast to received by the editors january 11 1996 and in revised form march 28 1996 1991 mathematics subject classification primary 47d25 46k50 46b20

bisimulation on speed a unified approach two process algebraic approaches have been developed for comparing two bisimulation equivalent processes with respect to speed the one of moller tofts equips actions with lower time bounds while the other by luttgen vogler considers upper time bounds instead this article sheds new light on both approaches by testifying to their close relationship we introduce a general intuitive concept of faster than which is formalised by a notion of amortised faster than preorder when closing this preorder under all contexts exactly the two faster than preorders investigated by moller tofts and luttgen vogler arise for processes incorporating both lower and upper time bounds we also show that the largest precongruence contained in the amortised faster than preorder is not a proper preorder but a timed bisimulation in the light of this result we systematically investigate under which circumstances the amortised faster than preorder degrades to an equivalence

bisimulation on speed worst case efficiency this paper introduces a novel bi simulation based faster than preorder which relates asynchronous processes where the relative speeds of system components are indeterminate with respect to their worst case timing behavior the study is conducted for a conservative extension of the process algebra ccs called tacs which permits the specification of upper time bounds on action occurrences tacs complements work in plain process algebras which compares asynchronous processes with respect to their functional reactive behavior only and in timed process algebras which focus on analyzing synchronous processes the most unusual contribution is in showing that the proposed faster than preorder coincides with several other preorders two of which consider the absolute times at which actions occur in system runs the paper also develops the semantic theory of tacs by studying congruence properties equational laws and abstractions from internal actions two examples one dealing with mail delivery and one relating two implementations of a simple storage system testify to the practical utility of the new theory

on guarded recursion abstract we introduce a logical notion of well guardedness for recursive terms on arbitrary signatures defined in plotkin s framework of structural operational specifications restricted by se simone s realizability requirements we then suggest a simpler form for the logical rule that gives the behaviour of a recursively defined expression in terms of the behaviour of its unfoldings for well guarded terms the simplified rule is logically equivalent to the general rule but it does not have the drawback of asking for premises more complex than consequences

isometric isomorphisms of cartan bimodule algebras abstract this paper is dedicated to proving a single result that isometric isomorphisms of cartan bimodule algebras can be extended to isomorphisms of the generated von neumann algebras if m is a von neumann algebra with cartan subalgebra a then a cartan bimodule algebra is simple a weakly closed subalgebra s of m which contains a s generates m if there is no proper von neumann subalgebra of m containing s the key idea is that a theorem of muhly saito and solel concerning isomorphisms of maximal subdiagonal algebras can be extended to this much wider class of algebras if we restrict our attention to isometric isomorphisms although the algebras are not assumed to be hyperfinite a finite dimensional result of davidson and power lies at the leart of the proof what makes the use of finite dimensional techniques possible is the existence of sufficiently many finite subequivalence relations of an arbitrary countable measurable equivalence relation

robust controller synthesis using kharitonov s theorem the authors present a method based upon kharitonov s theorem for synthesizing robustly stabilizing feedback controllers the approach is based upon a multiple plant model formulation with a quadratic cost functional sufficient conditions are obtained for characterizing robustly stabilizing static output feedback proportional controllers for mimo multiple input multiple output plants with denominator polynomial uncertainty

a class of stability regions for which a kharitonov like theorem holds families of complex polynomials whose coefficients lie within given intervals are discussed in particular the problem of determining if all polynomials in a family have the property that all of their roots lie within a given region is discussed towards this end a notion of a kharitonov region is defined roughly speaking a kharitonov region is a region in the complex plane with the following property given any suitable family of polynomials in order to determine if all polynomials in the family have all of their roots in the region it suffices to check only the vertex polynomials of the family the main result is a sufficient condition for a given region to be a kharitonov region

isometries of the toeplitz matrix algebra abstract we study the structure of isometries defined on the algebra a of upper triangular toeplitz matrices our first result is that a continuous multiplicative norm preserving map a m n c must be of the form either a u a u or a u a u where a is the complex conjugation and u is a unitary matrix in our second result we use a range of ideas in operator theory and linear algebra to show that every linear isometry a m n c is of the form a u a v where u and v are two unitary matrices this implies in particular that every such an isometry is a complete isometry and that a unital linear isometry a m n c is necessarily an algebra homomorphism

isomorphisms of certain csl algebras abstract we show that an isomorphism between two reflexive operator algebras on hilbert space with commutative subspace lattices csl is automatically continuous and induces an isomorphism between the lattices for such algebras with completely distributive subspace lattices cdc algebras the quasi spatially implemented isomorphisms are shown to be exactly those that preserve the rank of all finite rank operators we present some examples of nonspatial isomorphisms and discuss some sufficient conditions on the lattices that ensure that all isomorphisms be spatially implemented the relationship between isomorphisms and derivations of csl algebras is also investigated

an algorithm for simultaneous stabilization using decentralized constant gain output feedback an algorithm which solves numerically the simultaneous stabilization problem using a constant gain decentralized control law is presented the algorithm is determined from the necessary conditions for minimizing an optimal control problem the optimal control problem consists of n plant models each with its own cost function the costs are summed to create an average cost function and equality constraints are added to yield the decentralized control structure the algorithm can start with any stabilizing full state feedback gain for each model and will converge to the optimal constant feedback gain for all models assuming a solution exists examples of the algorithm are given for kharitonov synthesis and optimal gain scheduled control law synthesis using output feedback

lie isomorphisms of reflexive algebras a lie isomorphism between algebras is called trivial if where is an algebraic isomorphism or a negative of an algebraic anti isomorphism and is a linear map with image in the center vanishing on each commutator in this paper we investigate the conditions for the triviality of lie isomorphisms from reflexive algebras with completely distributive and commutative lattices cdcsl in particular we prove that a lie isomorphism between irreducible cdcsl algebras is trivial if and only if it preserves i idempotent operators the sum of an idempotent and a scalar multiple of the identity in both directions we also prove the triviality of each lie isomorphism from a cdcsl algebra onto a csl algebra which has a comparable invariant projection with rank and corank not one some examples of lie isomorphisms are presented to show the sharpness of the conditions

gsos and finite labelled transition systems recently there has been considerable interest in studying formats of plotkin style inference rules which ensure that the induced labelled transition system semantics have certain properties in this note i shall give a contribution to this line of research by giving a restricted version of bloom istrail and meyer s gsos format bloom et al 1988 bloom 1989 which induces finite labelled transition systems

semisimple triangular af algebras abstract we give several necessary and sufficient conditions for a triangular af algebra to be semisimple in particular a triangular af algebra which can be written using the standard embedding infinitely often is semisimple we also give a semisimple triangular af algebra which does not have a presentation of this form if two triangular af algebras have the same peters poon wagner diagonal invariant then either both are semisimple or both are not however we give two algebras with the same diagonal invariant where one has the jacobson radical equal to the strong radical and the other does not semisimplicity can be characterized in terms of power s fundamental relation we give generalizations of these results to triangular subalgebras of groupoid c algebras it is shown that there is a unique maximal bimodule over the diagonal which does not intersect the radical using this we show that the wedderburn principal theorem does not hold for all triangular af algebras a necessary condition for the theorem to hold is that the above mentioned unique bimodule is a subalgebra

an approach to simultaneous system design part 11 nonswitching gain and dynamic feedback compensation by algebraic geometric methods this paper studies structured uncertainty problems in feedback system design considers a compact parameterization of the space of linear dynamical systems and introduces base points and critical points as two algebraic geometric objects that have significance in sensitivity and robustness studies respectively using the nevanlinna pick interpolation theory the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one parameter family of plants a recent result due to kharitonov on the simultaneous stability of a parameterized family of polynomials leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants furthermore the author considers simultaneous pole placement of an r tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system the concept of nondegenerate and twisted r tuples of plants is introduced as the pole placement problem is studie

isometries for unitarily invariant norms a survey of linear isometries for unitarily invariant norms on real or complex rectangular matrices is given which includes some latest development on the topic a result on isometries for unitarily invariant norms without the linearity assumption is presented related results and problems are discussed

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

a generalization of kharitonov s theorem robust stability of interval plants the robust stability problem is considered for interval plants in the case of single input multioutput or single output multi input systems a necessary and sufficient condition for the robust stabilization of such plants is developed using a generalization of v l kharitonov s theorem 1978 the generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta s q sub 1 s p sub 1 s q sub m s p sub m s where the q sub i are fixed and the p sub i are interval polynomials the coefficients of which are regarded as a point in parameter space which varies within a prescribed box this generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments it is shown that for special classes of polynomials q sub i s the set of line segments collapses to a set of points and this version of the box theorem in turn reduces to kharitonov s original theorem

the lattice of ideals of a triangular af algebra we study triangular af taf algebras in terms of their lattices of closed two sided ideals not isometrically isomorphic taf algebras can have isomorphic lattices of ideals indeed there is an uncountable family of pairwise non isomorphic algebras all with isomorphic lattices of ideals in the positive direction if a and b are strongly maximal taf algebras with isomorphic lattices of ideals then there is a bijective isometry between the subalgebras of a and b generated by their order preserving normalizers this bijective isometry is the sum of an algebra isomorphism and an anti isomorphism using this we show that if the taf algebras are generated by their order preserving normalizers and are triangular subalgebras of primitive c algebras then the lattices of ideals are isomorphic if and only if the algebras are either isometrically isomorphic or anti isomorphic finally we use complete distributivity to show that there are taf algebras whose 0 lattices of ideals can not arise from taf algebras generated by their order preserving 8 normalizers our techniques rely on constructing a topological binary relation based on the lattice of ideals this relation is closely connected to the spectrum or fundamental relation also a topological binary relation of the taf algebra

a non selfadjoint russo dye theorem one of the well known results in the theory of c algebras is the russo dye theorem 19 given a c algebra r the closed convex hull of the unitary elements in r equals the closed unit ball of r this result was later refined by gardner and reached its final form by kadison and pedersen today it is known that every operator in a c algebra r whose norm is less than 1 is the average of unitaries from a the russo dye theorem initiated the theory of unitary rank in selfadjoint operator algebras if r is an operator algebra the unitary rank of an element a e r is defined as the smallest number for which there is a convex combination of unitaries from r of length u a and equaling a if no such decomposition exists in particular if liaii 1 we define u a oo the literature on unitary rank is vast the earliest result is due to murray and yon neumann who proved that any selfadjoint operator of norm i or less is the mean of two unitary operators 12 p 239 1937 the first systematic study was given by r kadison and g pedersen 8 in 1984 previous work in the field included contributions by popa 15 robertson 17 gardner 6 and others in 1986 c olsen and g pedersen 14 characterized all elements in a factor von neumarm algebra with finite unitary rank in the general case of a c algebra a characterization was obtained by rordam in his important paper 18 for more details and further information on the theory of unitary rank we refer to the excellent articles of u haagerup 7 and m rordam 18 in the first section of the present paper we prove a russo dye type theorem for infinite multiplicity nest algebras the techniques employed in the proof of our result are different from that of gardner and kadison pedersen to our knowledge this is the first result of this type for non selfadjoint operator algebras and clearly initiates the unitary rank theory for such algebras

triangular matrix representations in this paper we develop the theory of generalized triangular matrix representation in an abstract setting this is accomplished by introducing the concept of a set of left triangulating idempotents these idempotents determine a generalized triangular matrix representation for an algebra the existence of a set of left triangulating idempotents does not depend on any specific conditions on the algebras however if the algebra satisfies a mild finiteness condition then such a set can be refined to a complete set of left triangulating idempotents in which each diagonal subalgebra has no nontrivial generalized triangular matrix representation we then apply our theory to obtain new results on generalized triangular matrix representations including extensions of several well known results

isometries of certain reflexive operator algebras abstract we consider linear surjective isometries acting on reflexive operator algebras with commutative completely distributive subspace lattices such isometries come in two types those implemented by unitary operators and conjugations acting on the hilbert space and those implemented by unitaries alone it is shown that every isometry is a direct sum of these types

a generalization of kharitonov s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations kharitonov s four polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions to this end a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis the present work is motivated by two fundamental limitations of kharitonov s theorem namely 1 the theorem only applies to polynomials with independent coefficient perturbations and 2 it only applies to zeros in the left hand plane

robust analysis and design of control systems using interval arithmetic abstract several robustness problems such as stability and performance robustness analysis of feedback systems and robust design of control systems in the presence of mixed nonlinear parametric and nonparametric perturbations can be solved by means of algorithms based on interval arithmetic computation some of the main algorithms available in the literature are presented and their efficiency is tested on some examples of robustness analysis and design of control systems 1997 elsevier science ltd

isometries of non self adjoint operator algebras abstract we study isometries of certain non self adjoint operator algebras by means of the structure of the complete holomorphic vector fields on their unit balls and the associated partial jordan triple products we show that isometries of nest sub algebras of b h are of the form t utw or t ujt jw where u w are suitable unitary operators and j a fixed involution of h

strongly extreme points in orlicz function spaces abstract for any orlicz function and any finite atomless measure a criterion for x from the unit sphere of the orlicz space l equipped with the luxemburg norm to be strongly extreme is given further orlicz spaces l which are isometric to l are characterized

some new results on the simultaneous stabilizability of a family of single input single output systems abstract in this paper we obtain sufficiency conditions on the problem of simultaneous stabilization of a parameterized family of single input single output plants by a non switching compensator the sufficiency conditions include simultaneous stabilization and simultaneous pole assignment of a finite number of plants

on isometries of operator algebras we study the banach space isometries of triangular subalgebras of c algebras that contain diagonals in the sense of kumjian under a mild technical assumption we prove that every isometry between two such algebras decomposes as a direct sum of a unitary multiple of an isometric algebra isomorphism and a unitary multiple of an isometric algebra anti isomorphism moreover each isometric algebraic isomorphism anti isomorphism between two algebras of the type considered here extends to a c isomorphism c anti isomorphism between the enveloping c algebras our hypotheses enable us to coordinatize the algebras under consideration and the structure of the isometries between the algebras is expressed in terms of the coordinates

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

controller synthesis via the 4 k polynomial approach abstract in some recent work it was shown that to stabilize systems with real parameter uncertainty it suffices to find a controller that simultaneously stabilizes a finite number of polynomials these polynomials include those generated from the vertex plants as well as some generated by some fictitious vertex plants that involve the controller this paper deals with the issues of existence of such a controller controller synthesis and conservativeness of the design it is shown how this approach can enhance the stability robustness of an h design

multiple models multiplicative noise and linear quadratic control algorithmic aspects numerical solution of certain linear quadratic lq control problems for robust design is addressed an iterative method is suggested and analysed for solving a minimax multiple model lq control problem a convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants furthermore a convergent iterative method is proposed for solving the maximum entropy parametric lq control problem with multiplicative noise