two conditions concerning common quadratic lyapunov functions for linear systems concerning a pair of linear systems some triangle conditions for the existence of a common quadratic lyapunov function are presented in this paper these conditions are derived from a criterion for judging the semipositiveness of a linear map defined on symmetric matrices

finitely many delta interactions with supports on concentric spheres using the theory of self adjoint extensions of symmetric operators the precise mathematical definition of the quantum hamiltonian describing a finite number of interactions with supports on concentric spheres is given its resolvent is also derived its spectral properties are described and it is shown how this hamiltonian can be obtained as a norm resolvent limit of a family of local scaled short range hamiltonians

singularity conditions for the non existence of a common quadratic lyapunov function for pairs of third order linear time invariant dynamic systems abstract the condition that a finite collection of stable matrices a 1 a m has no common quadratic lyapunov function cqlf is formulated as a hierarchy of singularity conditions for block matrices involving a number of unknown parameters these conditions are applied to the case of two stable 3 3 matrices where they are used to derive necessary and sufficient conditions for the non existence of a cqlf

level shift under the influence of relativistic point interaction potentials the level shift of dirac particles under the influence of point interaction potentials has been determined a green function method is used to obtain closed expressions for the level shift and perturbed wavefunctions provided that the corresponding eigenvalue problem without point interaction potentials can be solved exactly several applications are discussed in detail

on pseudo spectral factorization over the complex numbers and quaternions abstract this paper is a continuation of the research of our previous work 5 and considers quaternionic generalized caratheodory functions and the related family of generalized positive functions it is addressed to a wide audience which includes researchers in complex and hypercomplex analysis in the theory of linear systems but also electric engineers for this reason it includes some results on generalized caratheodory functions and their factorization in the classic complex case which might be of independent interest an important new result is a pseudo spectral factorization and we also discuss some interpolation problems in the class of quaternionic generalized positive functions

real perturbation values and real quadratic forms in a complex vector space abstract a sequence of real numbers connected to a complex matrix is introduced it is shown how these real perturbation values can be computed and that they have several properties similar to the singular values the so called real pseudospectra and real stability radii can be computed using the real perturbation values the main result concerns the signature of real quadratic forms in complex vector spaces

phase semantics for light linear logic light linear logic girard inform comput 14 1998 175 204 is a refinement of the propositions as types paradigm to polynomial time computation a semantic setting for the underlying logical system is introduced here in terms of fibred phase spaces strong completeness is established with a purely semantic proof of cut elimination as a consequence a number of mathematical examples of fibred phase spaces are presented that illustrate subtleties of light linear logic

when are the complex and the real stability radii equal characterization of those real stable matrices for which the unstructured complex and real stability radii are equal is presented special cases of this equality are discussed as application of this result it is shown that for 2 2 matrices with nonreal eigenvalues neither the case of equality nor the case of strict inequality is generic

a necessary and sufficient criterion for the stability of a convex set of matrices a hurwitz stability criterion for the convex hull of two matrices due to c r johnson 1976 is generalized to the case of any compact convex set of matrices it is shown that the same criterion is not available in the case of schur stability

on the decision problem for mell in this short paper i will exhibit several mistakes in the recent attempt by bimbo to prove the decidability of the multiplicative exponential fragment of linear logic mell in fact the main mistake is so serious that there is no obvious fix and therefore the decidability of mell remains to be an open problem as a side effect this paper contains a complete syntactic proof of the decidability of the relevant version of mell called rmell in this paper that is the logic obtained from mell by replacing the linear logic contraction rule by a general unrestricted version of the contraction rule this proof can also be found with a small error in bimbo s work and a semantic proof has been given by okada and terui

two dimensional dirac operators with singular interactions supported on closed curves abstract we study the two dimensional dirac operator with a class of interface conditions along a smooth closed curve which model the so called electrostatic and lorentz scalar interactions of constant strengths and we provide a rigorous description of their self adjoint realizations and their qualitative spectral properties we are able to cover in a uniform way all so called critical combinations of coupling constants for which there is a loss of regularity in the operator domain for the case of a non zero mass term this results in an additional point in the essential spectrum which reflects the creation of an infinite number of eigenvalues in the central gap and the position of this point can be made arbitrary by a suitable choice of the parameters the analysis is based on a combination of the extension theory of symmetric operators with a detailed study of boundary integral operators viewed as periodic pseudodifferential operators

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

linear concurrent constraint programming in this paper we give a logical semantics for the class cc of concurrent constraint programming languages and for its extension lcc based on linear constraint systems besides the characterization in intuitionistic logic of the stores of cc computations we show that both the stores and the successes of lcc computations can be characterized in intuitionistic linear logic we illustrate the usefulness of these results by showing with examples how the phase semantics of linear logic can be used to give simple semantical proofs of safety properties of lcc programs

on the 45 region and the uniform asymptotic stability of classes of second order parameter varying and switched systems in this paper we present sufficient conditions for the stability of a number of classes of time varying systems these results are of interest for two reasons firstly the conditions presented take the form of matrix pencil eigenvalue criteria and are therefore co ordinate independent and easily verifiable secondly we show a direct relationship between the form of our criteria and the choice of lyapunov function used to demonstrate stability quadratic or unic these results indicate the importance of the region of the complex plane known as the 45 region

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

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

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

a formula for computation of the real stability radius this paper presents a readily computable formula for the real stability radius with respect to an arbitrary stability region in the complex plane

exponential stability of triangular differential inclusion systems abstract we consider a differential inclusion system of the form dot x a x where a is a collection of upper triangular matrices conditions for exponential stability of all the possible solutions are given

strong stability of discrete time systems the paper introduces a new notion of stability for internal state space autonomous system descriptions in discrete time referred to as strong stability which extends a parallel notion introduced in the continuous time case this is a stronger notion of stability compared to alternative definitions asymptotic lyapunov which prohibits systems described by natural coordinates to have overshooting responses for arbitrary initial conditions in state space three finer notions of strong stability are introduced and necessary and sufficient conditions are established for each one of them the class of discrete time systems for which strong and asymptotic stability coincide is characterized and links between the skewness of the eigen frame and the violation of strong stability property are obtained connections between the notions of strong stability in the continuous and discrete domains are briefly discussed finally strong stabilization problems under state and output feedback are studied the results of the paper are illustrated with a numerical example

convex cones of generalized positive rational functions and the nevanlinna pick interpolation abstract scalar rational functions with a non negative real part on the right half plane called positive are classical in the study of electrical networks dissipative systems nevanlinna pick interpolation and other areas we here study generalized positive functions i e with a non negative real part on the imaginary axis these functions form a convex invertible cone cic in short and we explore two partitionings of this set i into infinitely many non invertible convex cones of functions with prescribed poles and zeroes in the right half plane and ii each generalized positive function can be written as a sum of even and odd parts the sets of even generalized positive and odd functions form sub cic s it is well known that the nevanlinna pick interpolation problem is not always solvable by positive functions unfortunately there is no computationally simple procedure to carry out this interpolation in the framework of generalized positive functions through examples it is illustrated how the two above partitionings of generalized positive functions can be exploited to introduce simple ways to carry out the nevanlinna pick interpolation finally we show that only some of these properties are carried over to rational generalized bounded functions mapping the imaginary axis to the unit disk

design of controller for a class of pendulum like system guaranteeing dichotomy in this paper the problems of controller design for a class of nonlinear pendulum like control system with multiple equilibria guaranteeing dichotomy and gradient like property of the closed loop systems are investigated by applying kyp lemma and some results of positive real control the method of controller design based on linear matrix inequality is proposed

a unifying framework for the siso circle criterion and other quadratic stability criteria we present a result on the existence of a common quadratic lyapunov function for a pair of stable linear time invariant systems we show that this result characterizes generalizes and provides new perspectives on several well known stability results

common lyapunov solutions for two matrices whose difference has rank one abstract real stable matrices a and b with rank of a b equal to one have a common lyapunov solution if and only if their product ab has no real negative eigenvalue this was proved by shorten and narendra r n shorten k s narendra on common quadratic lyapunov functions for pairs of stable lti systems whose system matrices are in companion form ieee trans automat control 48 4 2003 618 621 whose proof is based on the fundamental results of kalman on lure s problem in this paper we give an alternative proof of this result and its generalization to the general regular inertia case and to the case when the matrices a and b are complex

on the spectral theory of gesztesy seba realizations of 1 d dirac operators with point interactions on a discrete set abstract we investigate spectral properties of gesztesy seba realizations d x and d x of the 1 d dirac differential expression d with point interactions on a discrete set x x n n 1 r here n n 1 and n n 1 r the gesztesy seba realizations d x and d x are the relativistic counterparts of the corresponding schrodinger operators h x and h x with and interactions respectively we define the minimal operator d x as the direct sum of the minimal dirac operators on the intervals x n 1 x n then using the regularization procedure for direct sum of boundary triplets we construct an appropriate boundary triplet for the maximal operator d x in the case d x inf x i x j i j 0 it turns out that the boundary operators b x and b x parameterizing the realizations d x and d x are jacobi matrices these matrices substantially differ from the ones appearing in spectral theory of schrodinger operators with point interactions we show that certain spectral properties of the operators d x and d x correlate with the corresponding spectral properties of the jacobi matrices b x and b x respectively using this connection we investigate spectral properties self adjointness discreteness absolutely continuous and singular spectra of gesztesy seba realizations moreover we investigate the non relativistic limit as the velocity of light c most of our results are new even in the case d x 0

on cones and stability abstract lyapunov while studying the asymptotic stability of solutions of differential systems proved a theorem which yields a necessary and sufficient condition for stability of a matrix lyapunov s theorem was a breakthrough in the research of stability among others it links cones and stability in various directions in this survey we review some of the links between convexity and matrix stability mainly such links that are derived from lyapunov s theorem the article does not cover the wide variety of all such links but rather gives some of the flavor of this rich theory

the lyapunov order for real matrices abstract the real lyapunov order in the set of real n n matrices is a relation defined as follows a b if for every real symmetric matrix s sb b t s is positive semidefinite whenever sa a t s is positive semidefinite we describe the main properties of the lyapunov order in terms of linear systems theory nevenlinna pick interpolation and convexity

the distance to strong stability the notion of strong stability has been introduced in a recent paper 12 this notion is relevant for state space models described by physical variables and prohibits overshooting trajectories in the state space transient response for arbitrary initial conditions thus strong stability is a stronger notion compared to alternative definitions e g stability in the sense of lyapunov or asymptotic stability this paper defines two distance measures to strong stability under absolute additive and relative multiplicative matrix perturbations formulated in terms of the spectral and the frobenius norm both symmetric and non symmetric perturbations are considered closed form or algorithmic solutions to these distance problems are derived and interesting connections are established with various areas in matrix theory such as the field of values of a matrix the cone of positive semi definite matrices and the lyapunov cone of hurwitz matrices the results of the paper are illustrated by numerous computational examples

common solution to the lyapunov equation for 2 2 complex matrices abstract in this work we solve the problem of a common solution to the lyapunov equation for 2 2 complex matrices we show that necessary and sufficient conditions for the existence of a common solution to the lyapunov equation for 2 2 complex matrices a and b is that matrices a i i b i i and a i i 1 b i i have no negative real eigenvalues for all r we show how these results relate to a special class of 4 4 real matrices

inverse closed ray nonsingular cones of matrices abstract a description is given of those ray patterns which will be called inverse closed ray nonsingular of complex matrices that contain invertible matrices only and are closed under inversion here two n n matrices are said to belong to the same ray pattern if in each position either the entries of both matrices are zeros or both entries are nonzero and their quotient is positive possible jordan forms of matrices in the inverse closed ray nonsingular ray patterns are characterized

the bounded real lemma for internally positive systems and h infinity structured static state feedback we consider the bounded real lemma for internally positive linear time invariant systems we show that the h norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function taking advantage of this fact the problem of designing a structured static state feedback controller achieving internal stability contractiveness and internal positivity in closed loop becomes convex and tractable

a uniform semantic proof for cut elimination and completeness of various first and higher order logics we present a natural generalization of girard s first order phase semantics of linear logic theoret comput sci 50 1987 to intuitionistic and higher order phase semantics then we show that this semantic framework allows us to derive a uniform semantic proof of the first order and higher order cut elimination theorem as well as a first order and higher order phase semantic completeness theorem for various different logical systems at the same time our semantic proof works for various different logical systems uniformly in a strong sense without any change of the argument of proof it works for both first order and higher order versions and for linear substructural and standard logics uniformly and for both their intuitionistic and classical versions uniformly

a pair of matrices sharing common lyapunov solutions a closer look abstract let a b be a pair of matrices with regular inertia if ha a h and hb b h are both positive definite for some hermitian matrix h then all matrices in conv a a 1 b b 1 have identical regular inertia this in turn implies that both conv a b and conv a b 1 consist of non singular matrices in general neither of the converse implications holds in this paper we seek situations where they do hold in particular when a and b are real 2 2 matrices several aspects of the above statements for n n matrices are discussed a connection to the characterization of the convex hull of matrices with regular inertia is introduced differences between the real and the complex case are indicated

the relativistic spherical δ shell interaction in r 3 spectrum and approximation this note revolves on the free dirac operator in r 3 and its shell interaction with electrostatic potentials supported on a sphere on one hand we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle on the other hand we prove that the domains given by dittrich et al j math phys 30 12 2875 2882 1989 and by arrizabalaga et al j math pures appl 102 4 617 639 2014 for the realization of an electrostatic spherical shell interaction coincide finally we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support improving previous results in the spherical case

finitely many sphere interactions in quantum mechanics nonseparated boundary conditions let h be the closure of the restriction of the three dimensional laplacian on the domain c 0 r3 where nj 1 k 0 rj and k 0 rj is a closed ball of radius rj centered at the origin in r3 it is well known that h is a closed symmetric operator with deficiency indices in this paper all self adjoint s a extensions of h are constructed these extensions contain as particular cases the quantum hamiltonian describing concentric and sphere interactions it is also shown that the s a extensions of h may be obtained as norm resolvent limits of momentum cutoff and scaled separable potentials

convex invertible cones of matrices a unified framework for the equations of sylvester lyapunov and riccati abstract convex cones of matrices which are closed under matrix inversion were defined and various connections with the algebraic lyapunov equation of general inertia were studied in n cohen i lewkowicz linear algebra and its appl 250 1997 105 131 here in the price of doubling the size of the matrices involved we introduce a unified framework for the equations of sylvester lyapunov and riccati this enables one to extend the convex invertible cone structure to all these three equations and explore related properties in particular the use of the matrix sign function for solving these equations is examined

on the kalman yacubovich popov lemma and common lyapunov solutions for matrices with regular inertia in this paper we extend the classical lefschetz version of the kalman yacubovich popov kyp lemma to the case of matrices with general regular inertia we then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common lyapunov solution cls extending a recent result on cls existence for pairs of hurwitz matrices

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

on common quadratic lyapunov functions for pairs of stable lti systems whose system matrices are in companion form in this note the problem of determining necessary and sufficient conditions for the existence of a common quadratic lyapunov function for a pair of stable linear time invariant systems whose system matrices a sub 1 and a sub 2 are in companion form is considered it is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product a sub 1 a sub 2 does not have an eigenvalue that is real and negative examples are presented to illustrate the result

an easy to compute factorization of rational generalized positive functions we give a simple constructive proof of a factorization theorem for scalar rational functions with a non negative real part on the imaginary axis a mathematica program performing this factorization is provided

a result on common quadratic lyapunov functions in this note we define strong and weak common quadratic lyapunov functions cqlfs for sets of linear time invariant lti systems we show that the simultaneous existence of a weak cqlf of a special form and the nonexistence of a strong cqlf for a pair of lti systems is characterized by easily verifiable algebraic conditions these conditions are found to play an important role in proving the existence of strong cqlfs for general lti systems

a characterization of convex cones of matrices with constant regular inertia abstract let a be a convex cone of n n matrices in this paper we present a necessary and sufficient condition for a to contain matrices with a constant regular inertia based on a version of the lyapunov equation the condition involves only the normalized extreme points of a this extends a previous paper by the authors where a robust stability criterion for a was obtained

on lti output strictly negative imaginary systems abstract this paper deals with the notion of output strictly negative imaginary systems a definition is given for the class of output strictly negative imaginary systems and a lemma is proposed to test the necessary and sufficient conditions required to satisfy output strictly negative imaginary system properties a set theoretic relationship is established between the existing class of strictly negative imaginary systems and the newly defined output strictly negative imaginary systems class a stability analysis result for interconnected systems with positive feedback is presented while one of the systems is negative imaginary and the other one is output strictly negative imaginary contrary to the existing results where at least one of the systems in the interconnection belongs to the strictly negative imaginary class several numerical examples have been studied to demonstrate the proposed results

on the spectrum of convex sets of matrices let k be an arbitrary compact convex set of square matrices this paper presents necessary and sufficient conditions for the spectrum of k to have no eigenvalues in a prespecified closed convex subset of the complex plane the obtained result implies different criteria for analysis of the spectral set of k in particular we have formulated criteria for nonsingularity inertia and hurwitz stability of k which can be used in the robustness analysis of linear control systems with uncertain parameters

on the uniqueness of the lyapunov scaling factors sufficient conditions are given for a lyapunov diagonally semistable matrix a to have a unique up to scalar multiplication lyapunov scaling factor suppose d is a lyapunov scaling factor of a a necessary and sufficient condition is given for the uniqueness of d the results extend work of hershkowitz and schneider

scattering theory for finitely many sphere interactions supported by concentric spheres we study stationary scattering theory for finitely many sphere interactions formally given by the hamiltonian h j 1n j x rj and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions in a previous publication j math phys 29 660 664 1988 it was shown that the self adjoint hamiltonian h l r corresponding to h may be defined as a limit in norm resolvent convergence of a family he of local scaled short range hamiltonians in this paper we also study scattering theory corresponding to he and show that the scattering quantities associated with he converge to those of h l r as e 0

dirac operators with a spherically symmetric δ shell interaction dirac operators with a contact interaction supported by a sphere are studied restricting attention to the operators that are rotationally and space reflection symmetric the partial wave operators are constructed using the self adjoint extension theory a particular attention being paid to those among them that can be interpreted as function shells of scalar and vector nature the class of interactions for which the sphere becomes impenetrable is specified and spectral properties of the obtained hamiltonians are discussed

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

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

convex invertible cones and the lyapunov equation abstract convex cones of matrices which are closed under matrix inversion are defined and their structure is studied various connections with the algebraic lyapunov equation of general inertia are explored

ltv model reduction with upper error bounds a new approach for computing upper error bounds for reduced order models of linear time varying systems is presented it is based on a transformation technique of the hankel singular values using positive real odd incremented functions by applying such time varying functions the singular values to be removed can be forced to become equal and constant so that they can be reduced two variations of this method are proposed one for finite time horizons and the other for infinite time problems including periodic systems

lmi approach to linear positive system analysis and synthesis abstract this paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities lmis we first show that the celebrated perron frobenius theorem can be proved concisely by a duality based argument again by duality we next clarify a necessary and sufficient condition under which a hurwitz stable metzler matrix admits a diagonal lyapunov matrix with some identical diagonal entries as the solution of the lyapunov inequality this new result leads to an alternative proof of the recent result by tanaka and langbort on the existence of a diagonal lyapunov matrix for the lmi characterizing the h performance of continuous time positive systems in addition we further derive a new lmi for the h performance analysis where the variable corresponding to the lyapunov matrix is allowed to be non symmetric we readily extend these results to discrete time positive systems and derive new lmis for the h performance analysis and synthesis we finally illustrate their effectiveness by numerical examples on robust state feedback h controller synthesis for discrete time positive systems affected by parametric uncertainties

the positive real lemma and construction of all realizations of generalized positive rational functions we here extend the well known positive real lemma also known as the kalman yakubovich popov lemma to complex matrix valued general ized positive rational function when non minimal realizations are considered we then exploit this result to provide an easy construction procedure of all not necessarily minimal state space realizations of generalized positive func tions as a by product we partition all state space realizations into subsets each is identified with a set of matrices satisfying the same lyapunov inclusion and thus form a convex invertible cone cic in short moreover this approach enables us to characterize systems which may be brought to be generalized positive through static output feedback the formulation through lyapunov inclusions suggests the introduction of an equivalence class of rational functions of various dimensions associated with the same system matrix

block diagonal semistability factors and lyapunov semistability of block triangular matrices abstract the concept of lyapunov diagonal semi stability is generalized to the block diagonal case unifying the theory of lyapunov diagonal stability and lyapunov stability the corresponding generalizations of the concepts of maximal lyapunov scaling factors are applied to study the lyapunov semistability of block triangular matrices

input design via lmis admitting frequency wise model specifications in confidence regions a framework for reformulating input design problems in prediction error identification as convex optimization problems is presented for linear time invariant single input single output systems this framework unifies and extends existing results on open loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided a wide range of model quality constraints can be handled in particular different frequency by frequency constraints can be used this opens up new applications of input design in areas such as robust control furthermore quality specifications can be imposed on all models in a confidence region thus allowing for statements such as with at least 99 probability the model quality specifications will be satisfied

convex invertible cones and positive real analytic functions in this paper we study classical spaces of analytic functions which are convex cones and closed under the involution f 1 f these include the spaces of positive real positive real odd and strictly positive real functions these spaces are associated in the engineering literature with energy dissipation in the sense of lyapunov we discuss the geometric aspects of these spaces in analogy with similar spaces in matrix theory which are also related to the matrix lyapunov equation stability and in view of a general theory of convex invertible cones

on the stability of a convex set of matrices in this paper we give an alternative proof of the constant inertia theorem for convex compact sets of complex matrices it is shown that the companion matrix whose non trivial column is negative satisfies the directional lyapunov condition inclusion for real multiplier vectors an example of a real matrix polytope that satisfies the directional lyapunov condition for real multiplier vectors and which has nonconstant inertia is given a new stability criterion for convex compact sets of real z matrices is given this criterion uses only real vectors and positive definite diagonal matrices

on kalman yakubovich popov lemma for stabilizable systems the kalman yakubovich popov kyp lemma has been a cornerstone in system theory and network analysis and synthesis it relates an analytic property of a square transfer matrix in the frequency domain to a set of algebraic equations involving parameters of a minimal realization in time domain this note proves that the kyp lemma is also valid for realizations which are stabilizable and observable

necessary and sufficient conditions for the hurwitz and schur stability of interval matrices establishes a set of new sufficient conditions for the hurwitz and schur stability of interval matrices the authors use these results to establish necessary and sufficient conditions for the hurwitz and schur stability of interval matrices the authors relate the above results to the existence of quadratic lyapunov functions for linear time invariant systems with interval valued coefficient matrices using the above results the authors develop an algorithm to determine the hurwitz and the schur stability properties of interval matrices the authors demonstrate the applicability of their results by means of two specific examples

convex invertible sets and matrix sign function it is proved that in two dimensional unital real algebras a step by step construction of minimal convex invertible sets terminates in two steps an analogous construction of minimal convex conditionally invertible sets of the complex field also terminates in two steps and the complex field is the only finite dimensional complex algebra with this property connections are made with the matrix sign function the matrix sign function of a matrix belongs to the convex invertible set generated by the matrix an example is given to show that the matrix sign function cannot always be obtained in two steps by following the step by step construction

some results on quadratic stability of switched systems with interval uncertainty in this paper we present some results on the quadratic stability of switched systems with uncertain parameters we show that the quadratic stability of a class of switched uncertain systems may be readily verified using simple algebraic conditions

a less conservative lmi condition for stability of discrete time systems with slope restricted nonlinearities many conditions have been found for the absolute stability of discrete time lur e systems in the literature it is advantageous to find convex searches via lmis where possible in this technical note we construct two less conservative lmi conditions for discrete time systems with slope restricted nonlinearities the first condition is derived via lyapunov theory while the second is derived via the theory of integral quadratic constraints iqcs and noncausal zames falb multipliers both conditions are related to the jury lee criterion most appropriate for systems with such nonlinearities and the second generalizes it numerical examples demonstrate a significant reduction in conservatism over competing approaches

the undecidability of second order multiplicative linear logic the multiplicative fragment of second order propositional linear logic is shown to be undecidable

semidefinite programming duality and linear time invariant systems several important problems in control theory can be reformulated as semidefinite programming problems i e minimization of a linear objective subject to linear matrix inequality lmi constraints from convex optimization duality theory conditions for infeasibility of the lmis as well as dual optimization problems can be formulated these can in turn be reinterpreted in control or system theoretic terms often yielding new results or new proofs for existing results from control theory we explore such connections for a few problems associated with linear time invariant systems

distinguished self adjoint extensions of dirac operators via hardy dirac inequalities we prove some hardy dirac inequalities with two different weights including measure valued and coulombic ones those inequalities are used to construct distinguished self adjoint extensions of dirac operators for a class of diagonal potentials related to the weights in the mentioned inequalities

strong stability of internal system descriptions this article introduces a new notion of stability for internal autonomous system descriptions that is referred to as strong stability and characterises the case of avoiding overshoots for all initial conditions within a given sphere this is a stronger notion of stability compared with alternative definitions asymptotic lyapunov which allows the analysis and design of control systems described by natural coordinates to have no overshooting response for arbitrary initial conditions for the case of linear time invariant systems necessary and sufficient conditions for strong stability are established in terms of the negative definiteness of the symmetric part of the state matrix the invariance of strong stability under orthogonal transformations is established and this enables the characterisation of the property in terms of the invariants of the schur form of the state matrix some interesting relations between strong stability and special forms of coordinate frames are examined and links between th