comments on perturbation bounds for root clustering of linear systems in a specified second order subregion this paper comments on the results of the above mentioned paper by bakker luo johnson ibid vol 40 1995 we note that theorems 3 1 and 4 1 are incorrectly stated i e they are not valid for the non spl omega transformable regions the results cannot cover the ride quality region listed in table 1 since it is a non spl omega transformable region

root exclusion from complex polydomains and some of its applications abstract a solution to an open research problem related to testing root exclusion of a real n dimensional polynomial n 1 from a subspace of n defined as a cartesian product n times of c c is given in this paper the solution is presented in two theorems which have application to several research problems related to robust relative multidimensional stability among them are the testing of robust relative stability of linear differential systems the testing of robust relative stability of linear delay differential systems and a complementary test for a robust stabilization algorithm several examples are presented to illustrate some of these applications

remarks on the global sobolev inequalities in the minkowski space rn 1 on demontre des inegalites de sobolev globales sur l espace de minkowski r n 1 le theoreme principal est valable sur des tranches a temps fixe

pole assignment by output feedback using cylindrical algebraic decomposition recently a new polynomial method for pole assignment by static output feedback has been developed in this paper we show how this method can be generalized to partial pole clustering some poles are exactly assigned the others being clustered in a specified region of the complex plane a constructive and systematic algorithm for the numerical resolution of both problems the collins cylindrical algebraic decomposition algorithm is presented and applied to an illustrative example

necessary and sufficient conditions for existence of bound states in a central potential we obtain using the birman schwinger method a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics these conditions yield a monotonic series of lower limits on the critical value of the strength of the potential for which a first bound state appears which converges to the exact critical strength we also obtain a sufficient condition for the existence of bound states in a central monotonic potential which yield an upper limit on the critical strength of the potential

global existence of null form wave equations on small asymptotically euclidean manifolds abstract we prove the global existence of the small solutions to the cauchy problem for quasilinear wave equations satisfying the null condition on r 3 g where the metric g is a small perturbation of the flat metric and approaches the euclidean metric like 1 x 2 2 with 1 global and almost global existence for systems without the null condition are also discussed for certain small time dependent perturbations of the flat metric in appendix a

new results on the separation of matrix eigenvalues and the clustering of matrix elements the problem of separation of matrix eigenvalues is considered in this paper necessary and sufficient conditions are given for a matrix to have all eigenvalues contained in an open set defined on the complex plane by a separable polynomial spl gamma z sub 1 z sub 2 the problem of clustering of matrix elements is also considered in this case a set of matrices is identified having all eigenvalues in a given subset of the complex plane the presented results can be useful in both robust stability analysis and the design of control systems

linear matrix equations and root clustering abstract given a e n n and we search for a criterion assuring that the spectrum of a is clustered in a one approach to root clustering is the linear matrix equation whose half plane version dates back to lyapunov the existing literature deals with an algebraic region defined by a single polynomial in this paper we construct a novel linear matrix equation related to the intersection of algebraic regions this considerably enlarges the family of regions with root clustering criteria

linear quadratic optimal output feedback control for systems with poles in a specified region the problem of output feedback linear quadratic regulator synthesis with regional pole constraints is studied the synthesis algorithm is presented and its convergence is also proved the effectiveness of the algorithm is illustrated by an example

robustness of eigenvalue clustering in various regions of the complex plane for perturbed systems abstract sufficient conditions of robust eigenvalue clustering for perturbed systems are presented if all the eigenvalues of the nominal system are located in a specified region of the complex plane then the proposed sufficient conditions guarantee that all the eigenvalues of the perturbed system remain inside the same region the characteristics of a linear dynamical system are influenced by the eigenvalue locations therefore through the study of eigenvalue clustering more features about perturbed systems such as stability margin performance robustness and so on can be investigated it is emphasized that the proposed perturbation bounds for robust eigenvalue clustering in a specified region can be applied to both continuous and discrete time systems three illustrative examples are given to show the applicability of the proposed theorems

pole assignment of linear uncertain systems in a sector via a lyapunov type approach the problem of designing robust control laws in performance and in stability for uncertain linear systems is considered performances are taken into account using root clustering of the closed loop dynamic matrix in a sector of the complex plane a synthesis procedure based on a sufficient condition for quadratic stabilization and root clustering such as stabilizability is given using an auxiliary convex problem the results are illustrated by a significant example from the literature

root distribution for the ellipse it is shown that the number of characteristic roots of a given matrix or polynomial inside outside and on the boundary of a given ellipse can be determined by a common half plane test e g routh test the test should be performed on a polynomial which is received from the original characteristic polynomial by a simple transformation root exclusion and root clustering criteria are included as special cases

controller design with regional pole constraints a design procedure is developed that combines linear quadratic optimal control with regional pole placement specifically a static and dynamic output feedback control problem is addressed in which the poles of the closed loop system are constrained to lie in specified regions of the complex plane these regional pole constraints are embedded within the optimization process by replacing the covariance lyapunov equation by a modified lyapunov equation whose solution in certain cases leads to an upper bound on the quadratic cost functional the results include necessary and sufficient conditions for characterizing static output feedback controllers with bounded performance and regional pole constraints sufficient conditions are also presented for the fixed order i e full and reduced order dynamic output feedback problem with regional pole constraints circular elliptical vertical strip parabolic and section regions are considered

robust stability test of a class of linear time invariant interval fractional order system using lyapunov inequality this paper provides a new analytical robust stability checking method of fractional order linear time invariant interval uncertain system this paper continues the authors previous work yangquan chen hyo sung ahn i podlubny robust stability check of fractional order linear time invariant systems with interval uncertainties in proceedings of the ieee conference on mechatronics and automation niagara falls canada july 2005 pp 210 215 where matrix perturbation theory was used for the new robust stability checking lyapunov inequality is utilized for finding the maximum eigenvalue of a hermitian matrix through numerical examples the usefulness and the effectiveness of the newly proposed method are verified

stability analysis of systems with generalized frequency variables a class of large scale multi agent systems with decentralized information structures can be represented by a linear system with a generalized frequency variable in this paper we investigate fundamental properties of such systems stability and d stability exploiting the dynamical structure specifically we first show that such system is stable if and only if the eigenvalues of the connectivity matrix lie in a region of the complex plane specified by the generalized frequency variable the stability region is characterized in terms of polynomial inequalities leading to an algebraic stability condition we also show that the stability test can be reduced to a linear matrix inequality lmi feasibility problem involving generalized lyapunov inequalities and that the lmi result can be extended for robust stability analysis of systems subject to uncertainties in the interconnection matrix we then extend the result to d stability analysis to meet practical requirements and provide a unified treatment of d stability conditions for ease of implementation finally numerical examples illustrate utility of the stability conditions for the analysis of biological oscillators and for the design of cooperative stabilizers

complete root distribution with respect to parabolas and some results with respect to hyperbolas and sectors criteria are derived to determine the distribution of the characteristic roots of a byatem with respect to parabolas and hyperbolas in the complex plane which are related to certain physical properties of the system the criteria are given in terms of a classical half plane algorithm e g a routh array carried out on a transformed polynomial of double the degree of the original characteristic polynomial for parabolas left right or shifted the algorithm provides the complete root distribution including criteria for root clustering and root exclusion as bpecial cases for hyperbolas the algorithm provides in all cases criteria for root clustering inside the open or closed left or right branch of the hyperbola and for characteristic polynomials which are hurwitz the algorithm provides the complete root distribution with respect to the left branch of the hyperbola also by an additional classical test sturm the algorithm provides in all cases the exact number of roots on the left boundary of t

an algebraic algorithm for determining the desired gain of multivariable feedback systems in this paper an algebraic method is presented whereby one can obtain the relevant values of the gain k of a multivariable multi input multi output feedback system to be stable or relatively stable the basis of the method involves the algebraic solution of the two equations obtained from the real and imaginary parts of the characteristic equation of the system the proposed method offers an alternative procedure for determining stability relative stability to the graphical methods based on the generalized nyquist criterion and the multivariable root locus method this method is analogous to the analytical form of the root locus combined with the routh hurwitz criterion as compared to the nyquist or graphical root locus methods when applied to single input single output feedback systems several examples are presented illustrating the applications of the method and compared with the graphical methods

a sufficient condition for the existence of bound states for scalar spherically symmetric potentials we consider the class of three dimensional attractive finite range or similar potentials depending on a strength constant beyond a critical value the potential has at least one bound state for the s wave we propose simple bounds for obtained by formally solving the schrodinger equation for the zero energy bound state the various bounds are compared with the exact value for a set of usual potentials they are also compared with bounds derived in earlier works by glaser et al and by calogero we show that the case is solved by equations very similar to ones

loose eigenstructure assignment via rank one lmi approach with application to transient response shaping in h control this article proposes a new regional eigenstructure assignment via rank one lmi approach a gain parameter condition for the regional eigenvalue eigenstructure assignment is newly derived this assignment condition is easily combined with h design by means of enhanced lmi characterisation in the present approach the desired assignment of closed loop eigenvalues i e poles are not previously fixed but constrained into individual assignment regions to bring us more design freedom than classical exact assignment the regional assignment discussed in this article never falls into an ordinary lmi root clustering because the union of assignment regions is disjoint in general each closed loop eigenvector is also constrained into individual alignment cone to show the practical use of the extra design freedom brought by regional assignment a transient response shaping in h design is also discussed a useful design algorithm based on linearisation algorithm is proposed

on eigenvalue and canonical form assignments abstract we first present a constructive matrix procedure to assign an arbitrary nonderogatory matrix by state feedback specifically given a controllable pair m c t the procedure finds a vector f and a transforming matrix l such that the closed loop matrix m c t f t is similar to a preassigned arbitrary nonderogatory matrix such as the jordan companion schwarz or triangular the method is direct in the sense that it does not require knowledge of eigenvalues and eigenvectors of m or solution of any matrix equation or even computation of the characteristic polynomial we then propose an algorithm to assign an arbitrary normalized hessenberg matrix given a controllable pair m c t and a normalized upper hessenberg matrix b the algorithm computes an upper triangular matrix l l ij with l ij 1 and a vector f such that l m c t f l 1 b the algorithm seems to be computationally more effective than the former and in particular can be used to assign most of the important canonical forms above and a given set of eigenvalues as well

a generalization of the routh hurwitz stability criteria and an application to a problem in robust controller design the classical results of routh and hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions g of the complex plane by our method arbitrary conic sections can be handled the results are interpreted as criteria for g stability of linear systems a numerical algorithm to compute the criteria is given an application to a problem in robust controller design is outlined

necessary and sufficient lmi conditions for stability and performance analysis of 2 d mixed continuous discrete time systems this paper proposes necessary and sufficient conditions for stability and performance analysis of 2 d mixed continuous discrete time systems that can be checked with convex optimization in particular linear matrix inequalities lmis specifically the first contribution of the paper is a condition for exponential stability based on the introduction of a complex lyapunov function depending polynomially on a parameter and on the use of the gram matrix method it is shown that this condition is sufficient for any chosen degree of the complex lyapunov function and necessary for an a priori known degree the second contribution is a non lyapunov condition for exponential stability based on eigenvalue products this condition is necessary and sufficient and has the advantage of requiring a significantly smaller computational burden for achieving necessity lastly the third contribution is to show how upper bounds on the h norm of 2 d mixed continuous discrete time systems can be obtained through a semidefinite program based on complex lyapunov functions a necessary and sufficient condition is provided for establishing the tightness of the found upper bounds

robust root clustering for linear uncertain systems using generalized lyapunov theory in this paper the problem of matrix root clustering in sub regions of complex plane for linear state space models with real parameter uncertainty is considered the nominal matrix root clustering theory of gutman and jury 1981 ieee trans aut control ac 26 403 using generalized lyapunov equation is extended to the perturbed matrix case and bounds are derived on the perturbation to maintain root clustering inside a given region the theory allows us to get an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space the current literature available on perturbation bounds for robust stability becomes a special case of this unified theory

perturbation bounds for root clustering of linear systems in a specified second order subregion sufficient bounds for structured and unstructured uncertainties for root clustering in a specified second order subregion of the complex plane for both continuous time and discrete time systems are given using the generalized lyapunov theory furthermore for unstructured uncertainties a still less conservative result is obtained by shifting the center or focus of the subregion along the real axis to the origin and by applying root clustering to the shifted eigenvalue system matrix which is obtained by shifting the eigenvalues of the system matrix correspondingly

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

characterizing polynomials with roots in a semialgebraic set let p spl isin r x be a real valued polynomial and s spl sube c a set defined by polynomial inequalities g sub k z z spl ges 0 for some polynomials g sub k in c z z we provide a necessary and sufficient condition on the coefficients of p for all the zeros of p to be in s

linear and numerical linear algebra in control theory some research problems abstract this paper presents an informal survey of theoretical and computational aspects of three linear algebra problems arising in control theory namely the sylvester observer matrix equation the matrix eigenvalue assignment problem and the stability and stabilization of large second order systems difficulties are highlighted recent developments are mentioned some research problems in these areas which should be of interest to both linear algebraists and control theorists are described

upper and lower limits on the number of bound states in a central potential in a recent paper new upper and lower limits were given in the context of the schrodinger or klein gordon equations for the number n0 of s wave bound states possessed by a monotonically nondecreasing central potential vanishing at infinity in this paper these results are extended to the number nl of bound states for the lth partial wave and results are also obtained for potentials that are not monotonic and even somewhere positive new results are also obtained for the case treated previously including the remarkably neat lower limit nl 2l 1 1 2 with 2 max0 r r v r 1 2 valid in the schrodinger case for a class of potentials that includes the monotonically nondecreasing ones entailing the following lower limit for the total number n of bound states possessed by a monotonically nondecreasing central potential vanishing at infinity n 1 2 3 2 2 here the double braces denote the integer part

almost global existence to nonlinear wave equations in three space dimensions on considere l existence a t grand de solutions de petite amplitude pour des equations d onde d ordre 2 non lineaires a 4 dimensions d espace temps

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

interval stability and stabilization of linear stochastic systems this technical note applies the spectrum technique to deal with the interval stability and stabilization of linear stochastic time invariant systems first the notion of beta alpha stability of stochastic systems is defined and some relationships among the beta alpha stability the decay rate of system state response and the second order moment lyapunov exponent are revealed we then address the beta alpha stabilization problem and give a sufficient condition via a linear matrix inequality approach

critical strength of attractive central potentials we obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive purely negative central potentials these conditions yield several sequences of upper and lower limits on the critical value g of the coupling constant strength g of the potential v r gv r for which a first wave bound state appears which converges to the exact critical value

generalized pole placement via static output feedback a methodology based on projections this paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form given n subsets of the complex plane find a static output feedback that places in each of these subsets a pole of the closed loop system the algorithm presented is iterative in nature and is based on alternating projection ideas each iteration of the algorithm involves a schur matrix decomposition a standard least squares problem and a combinatorial least squares problem while the algorithm is not guaranteed to always find a solution computational results are presented demonstrating the effectiveness of the algorithm

d stability of continuous time delay systems subjected to a class of highly structured perturbations the d stability testing problem for continuous time delay systems subjected to a class of highly structured parametric perturbations is addressed in this note by means of the lyapunov stability theorem razumikhin type theorem gersgorin theorem concept of spectral radius and norm and matrix measure techniques the author has developed several new sufficient conditions for guaranteeing that all characteristic roots of the above systems are located inside a specified disk d spl alpha r with center at spl alpha j0 and radius r in the left half complex plane for the present results it is not necessary to solve any lyapunov equation which may be unsolvable though the lyapunov stability theorem is utilized

the lifespan of a class of smooth spherically symmetric solutions of the compressible euler equations with variable entropy in three space dimensions we consider smooth three dimensional spherically symmetric eulerian flows of ideal polytropic gases with variable entropy whose initial data are obtained by adding a small smooth perturbation with compact support to a constant state under a natural assumption we obtain precise information on the asymptotic behavior of their lifespan when the size of the initial perturbation tends to 0 this is achieved by the construction and estimate of a suitable approximate flow

root distribution of a polynomial in subregions of complex plane modified processes are proposed for directly treating singularities in the routh array and procedures are developed for determining the respective orders of simple and or repeated roots lying on the imaginary axis the extended sturm test is developed for determining the root distribution on some specified lines moreover to enhance the routh stability theorem the extended routh theorem for finding the numbers of roots of a polynomial lying within some specified regions is proposed

robust matrix root clustering analysis through extended kyp lemma this paper is dedicated to robust matrix eigenvalue clustering in a subregion mathcal d of the complex plane a norm bounded uncertainty is considered cd is any intersection and or union of half planes discs and outsides of discs this work aims at computing the associated complex cd stability radius this challenge was already tackled in a recent paper but the technique therein may fail or lead to conservative results when the subregions overlap the present paper proposes to circumvent those limits thanks to an extended version of the kalman yakubovich popov kyp lemma which is deduced from the so called generalized s procedure

on finding eigenvalue distribution of a matrix in several regions of the complex plane a direct method is proposed for determining eigenvalue distribution of a matrix with respect to several important regions of the complex plane these regions include half planes shifted half planes hyperbolas sectors quadrants imaginary axis region contained within two straight lines that pass through the orgin etc the method neither requires computation of the characteristic polynomial of the given matrix nor solution of any matrix equations the method seems to be more efficient than the eigenvalue and matrix equations methods

the matrix equation xa atx and an associated algorithm for solving the inertia and stability problems abstract we develop a constructive procedure for generating nonsingular solutions of the matrix equation xa a t x and establish an interesting relationship between a given solution x of the above equation and the associated matrix polynomial p a the latter is then used to develop an algorithm for computing the inertia of a matrix the algorithm is more efficient than the other common procedures

pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized h representation abstract the problem of pth moment asymptotic interval stability and stabilization for linear stochastic systems is investigated in this paper firstly we define the generalized h representation which is very helpful to transform stochastic systems into deterministic systems then the problems of pth moment interval stability the decay rate of state response and the estimation of pth moment lyapunov exponent are proposed with the help of the model transformation method furthermore the criteria for pth moment interval stabilization of the linear stochastic systems are addressed some necessary numerical examples are also provided to show the effectiveness of the addressed method

existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data on considere le probleme aux valeurs initiales pour certaines equations hyperboliques non lineaires d ordre 2

robust root clustering of a matrix in intersections or unions of regions this paper considers robust stability analysis for a matrix affected by unstructured complex uncertainty a method is proposed to compute a bound on the amount of uncertainty ensuring robust root clustering in a combination intersection and or union of several possibly nonsymmetric half planes discs and outsides of discs in some cases to be detailed this bound is not conservative the conditions are expressed in terms of linear matrix inequalities lmis and derived through lyapunov s second method as a distinctive feature of the approach the lyapunov matrices proving robust root clustering one per subregion are not necessarily positive definite but have prescribed inertias depending on the number of roots in the corresponding subregions as a special case when root clustering in a single half plane disc or outside of a disc is concerned the whole clustering region reduces to only one convex subregion and the corresponding unique lyapunov matrix has to be positive definite as usual

upper and lower limits for the number of s wave bound states in an attractive potential new upper and lower limits are given for the number of s wave bound states yielded by an attractive monotonic potential in the context of the schrodinger or klein gordon equation

generalized hankel matrices of markov parameters and their applications to control problems abstract the concept of hankel matrices of markov parameters associated with two polynomials is generalized for matrices the generalized hankel matrices of markov parameters are then used to develop methods for testing the relative primeness of two matrices a and b for determining stability and inertia of a matrix and for constructing a class of matrices c such that a c has a desired spectrum neither the method of construction of the generalized hankel matrices nor the methods developed using these matrices require explicit computation of the characteristic polynomial of a or of b

on the number of bound states for the one dimensional schrodinger equation the number of bound states of the one dimensional schrodinger equation is analyzed in terms of the number of bound states corresponding to fragments of the potential when the potential is integrable and has a finite first moment the sharp inequalities 1 p j 1p nj n j 1p nj are proved where p is the number of fragments n is the total number of bound states and nj is the number of bound states for the jth fragment when p 2 the question of whether n n1 n2 or n n1 n2 1 is investigated in detail an illustrative example is also provided

sufficient conditions for the existence of bound states in a central potential we show how a large class of sufficient conditions for the existence of bound states in non positive central potentials can be constructed these sufficient conditions yield upper limits on the critical value g l c of the coupling constant strength g and of the potential v r gv r for which a first l wave bound state appears these upper limits are significantly more stringent than hitherto known results

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

automated generation and comparison of takagi sugeno and polytopic quasi lpv models in the last decades gain scheduling control techniques have consolidated as an efficient answer to analysis and synthesis problems for non linear systems among the approaches proposed in the literature the linear parameter varying lpv and takagi sugeno ts paradigms have proved to be successful in dealing with the different trials that the analyzer or the designer of a gain scheduled control system has to face despite the strong similarities between the two paradigms research on lpv and ts systems has been performed in an independent way and some results that could be useful for both paradigms were obtained only for one of them however in recent works some clues that there is a very close connection between lpv and ts worlds have been presented the present paper openly addresses the presence of strong analogies between lpv and ts models in an attempt to establish a bridge between these two worlds so far considered different in particular this paper addresses the modeling problem presenting two methods for the automated generation of lpv and ts systems and introducing some measures in order to compare the obtained models a mathematical example is used to illustrate the proposed methods

relative stability gain in multivariable feedback systems the problem of finding the stability range of a scalar gain or parameter is a simple one for multivariable feedback systems we propose an algebraic procedure for the relative stability range using the so called critical constraint this method is simpler than the frequency domain approach and compared favourably with a recently proposed approach

common lyapunov function approach to matrix root clustering abstract this paper proposes an alternative route to the matrix root clustering problem which enables to use a result on the common lyapunov function for solving the problem efficiently a necessary and sufficient condition is obtained in terms of the existence of a common positive definite solution to a set of lyapunov inequalities for eigenvalues of a matrix to lie in a prescribed subregion of the complex plane applications to root clustering in sector regions are shown for illustration

location of matrix eigenvalues in the complex plane let s be a region which can be mapped into a standard region r of the complex plane unit circle or half plane by a rational transformation then the problem of locating the eigenvalues of a relative to s can be transformed into that for an appropriate block companion matrix relative to r

bound states in one and two spatial dimensions in this article we study the number of bound states for potentials in one and two spatial dimensions we first show that in addition to the well known fact that an arbitrarily weak attractive potential has a bound state it is easy to construct examples where weak potentials have an infinite number of bound states these examples have potentials which decrease at infinity faster than expected using somewhat stronger conditions we derive explicit bounds on the number of bound states in one dimension using known results for the three dimensional zero angular momentum a change of variables which allows us to go from the one dimensional case to that of two dimensions results in a bound for the zero angular momentum case finally we obtain a bound on the total number of bound states in two dimensions first for the radial case and then under stronger conditions for the noncentral case

eigenvalue clustering in subregions of the complex plane eigenvalue clustering in subregions of the complex plane is investigated for multivariable linear feedback systems critical constraints of all the eigenvalues of a perturbed system causing it to stay within a specified region of the nominal system arc discussed a design procedure is developed for the selection of a parametrized class of state feedback gains for eigenvalue clustering an illustration of the method for the case of a bounded frequency region is included

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

ellipsoidal sets for resilient and robust static output feedback the implementation of a controller if not exact may lead to the so called fragility problem i e the loss of expected closed loop properties in the present note this difficult problem is dealt with considering robust static output feedback sof control for uncertain linear time invariant systems by analogy with robust analysis theory based on quadratic separation a new formulation for the sof design is shown to be a valuable way to tackle fragility issues indeed the use of a quadratic separator for design purpose allows to define a whole resilient nonfragile set of sof control laws results are formulated as matrix inequalities one of which is nonlinear a numerical algorithm based on nonconvex optimization is provided ant its running is illustrated on classical examples from literature

equations d ondes quasilineaires et estimations de strichartz dans cet article notre but est de resoudre des equations d ondes quasilineaires pour des donnees initiales moins regulieres que ce qu imposent les methodes d energie ceci impose de demontrer des estimees de type strichartz pour des operateurs d ondes a coefficients seulement lipschitziens

on stabilization of 2d roesser models this note is devoted to the stabilization of 2d roesser models which are discrete continuous or mixed continuous discrete a recent linear matrix inequalities lmis necessary and sufficient condition for stability of such models is used to derive a quasi non conservative technique for state feedback stabilization

robust control of the characteristic values of systems with possible parameter variations an analytical method to control by multiparameter output feedback the characteristic values of a closed loop multi input multi output system inside or outside general aubregions of the complex plane is presented the method pertains to analogue as well as discrete systems the design method is robust in the sense that the characteristic values are designed to cluster inside the desired subregion even though any number of the specifying parameters are only known to within a given interval the interval may possibly be disjoint and possibly infinite completely unknown examples are provided which illustrate the broadness and effectiveness of the method

an lmi approach for designing sliding mode observers this paper presents a method to design sliding mode observers for a class of uncertain systems using linear matrix inequalities the objective is to exploit the degrees of freedom available in the design which have hitherto been ignored because of the lack of a tractable solution framework the relationship between the linear component of the sliding mode observer and a particular sub optimal observer arising from classical linear quadratic gaussian lqg theory is demonstrated this helps motivate how the design weighting matrices inherent in the method may be chosen in practice it will also be shown how the weighting matrices affect the dynamics of the sliding motion furthermore using pole placement and pole clustering methods the poles of the sliding motion can be forced to lie in a specified region in the complex plane so that the performance of the sliding motion can be tuned this paper will also present a more general solution where the eigenvalues of the linear part of the observer are forced

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

h control with regional stability constraints abstract the problem of static state feedback h control with various regional stability constraints for the closed loop system is considered a general framework for solving this problem is established using the lagrange multiplier method in conjunction with generalised lyapunov theory and riccati equation based h optimization characterization necessary conditions are given for the existence of the desired optimal feedback gains furthermore as the simplest regional stability case the stability degree problem is studied with two different approaches one an indirect overbounding method that extends the standard h problem formulation with an shift and another that uses the direct optimization of the h performance measure with stability degree as a constraint under the general framework the conservativeness of the former approach and the generality of the latter approach are clearly demonstrated finally the theory is illustrated with examples and the computational issues are discussed it is shown that the successive approximation technique of liu and of liu and yedavalli can be used to partially solve the problem

a new approach to optimal regional pole placement abstract the multi constraints optimal regional pole placement problem is studied the constrained region is represented by several algebraic inequalities necessary conditions for which the optimal solution must be satisfied are derived furthermore a solution algorithm is provided finally an analysis of robustness with rsepest to structured uncertainty for continuous system is discussed 1997 elsevier science ltd

stability and inertia abstract the purpose of this paper is to present a brief overview of matrix stability and inertia theory a few applications of inertia and stability theorems and a nonspectral implicit matrix equation method for determining stability and inertia of a nonhermitian matrix are also presented inter relationships between different theorems are explicitly stated whenever appropriate the paper concludes with some problems for future research in this area

on a sufficient condition of the existence of n particle bound states the authors use a birman schwinger type analysis to derive a sufficient condition for the existence of bound states in a certain class of n body systems this condition is given in terms of the underlying subsystem with the threshold energy sigma inf sigma ess h

roots of composite polynomials an application to root clustering abstract in 1900 stephanos showed that given a c n n with spectrum a i the eigenvalues of the composite matrix p q c pq a p a q are the n 2 values p q c pq p i q j this fact has been recently used in the theory of root clustering throug the characteristics polynomial of if a characteristic polynomial is given rather than a we can use the companion matrix to generate the characteristic coefficients of in this paper we develop a direct theory for composite polynomials

a root clustering theorem we consider the problem of root clustering of a real matrix in an algebraic region of the complex plane it is shown that a criterion previously obtained based on an n 2 times n 2 matrix reduces to a criterion based on an frac 1 2 n n 1 times frac 1 2 n n 1 matrix this is done for any transformable region and thus generalizes earlier results

stability of a matrix polynomial in continuous systems two sufficient conditions under which the roots of the determinant of a given m times m matrix polynomial of n th order lie in the open left half plane have been obtained the first condition is given in terms of the positive definiteness of an mn times mn symmetric matrix while the second condition is given in terms of the positive definiteness of an m times m matrix that is a function of s re s leq 0 these conditions are represented in terms of rational functions of the coefficient matrices of the given matrix polynomial therefore the explicit computation of the determinant polynomial is not required

generalization of the calogero cohn bound on the number of bound states it is shown that for the calogero cohn type upper bounds on the number of bound states of a negative spherically symmetric potential v r in each angular momentum state that is bounds containing only the integral 0 v r 1 2 dr the condition v r 0 is not necessary and can be replaced by the less stringent condition d dr r1 2p v 1 p 0 1 2 p 1 which allows oscillations in the potential the constants in the bounds are accordingly modified depend on p and l and tend to the standard value for p 1 2

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

determining dynamic output feedback of the least order for simo systems to locate poles in a specified region this paper presents a new theory for determining dynamic output feedback of the least order for a linear time invariant controllable and observable simo system such that poles of the closed loop system lie in a given region in the complex plane when some poles have prespecified stationary locations in the complex plane dynamic output feedback is obtained in the sense that the remaining poles lie in this theory applies to continuous time as well as discrete time systems here a design algorithm for complete system realization and an illustrative example are given