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

the kharitonov theorem with degree drop the purpose of this paper is to present a proof of the kharitonov theorem based on bezoutians an interesting consequence of this proof is that it shows the validity of kharitonov s result in the presence of a degree drop

robust stability of a class of polynomials with coefficients depending multilinearly on perturbations necessary and sufficient conditions are given for robust stability of a family of polynomials each polynomial is obtained by a multilinearity perturbation structure restrictions on the multilinearity are involved but in contrast to existing literature these restrictions are derived from physical considerations stemming from analysis of a closed loop interval feedback system the main result indicates that all polynomials in the family of polynomials have their zeros in the strict left half plane if and only if two requirements are satisfied at each frequency the first requirement is the zero exclusion condition involving four kharitonov rectangles the second requirement is that a specially constructed theta 0 parameterized set of 16 intervals must cover the positive reals for each theta epsilon 0 2 pi

kharitonov s theorem and the second method of lyapunov in this paper kharitonov s theorem for the robust stability of interval polynomials is proved using the second method of lyapunov the hermite matrix is taken as the matrix of the quadratic form which is used as a lyapunov function to prove hurwitz stability it is shown that if the four hermite matrices corresponding to the four kharitonov extreme polynomials are positive definite the hermite matrix of any polynomial of the polynomial family remains positive definite

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

a sufficient condition for the stability of interval matrix polynomials the root location of sets of scalar polynomials whose coefficients are confined to intervals and the associated extension to eigenvalues of sets of constant matrices whose coefficients are contained in intervals are reviewed a central result for complex scalar interval polynomials is a theorem developed by v l kharatonov 1978 which states that each member of a set of such polynomials is stable if and only if eight special polynomials from the set are stable the case of interval matrix polynomials is examined and a kharitonov like result for their strong stability is provided this in turn yields a sufficient condition for stability of a set of interval matrix polynomials

robust stability of control systems extreme point results for the stability of edges for the investigation of the robust stability of control systems with structured uncertainties many results have been presented recently that lead to stability tests of the edges of a polytope in this paper some results are discussed where the stability of an edge is guaranteed by the stability of the vertices of the edge given the characteristic polynomial of a closed loop system with structured uncertainties in the parameters for special types of uncertainties the family of polynomials is defined by a polytope in the space of parameters in the frequency domain the corresponding value set of the family for s jw fixed is a polygon whose edges are formed by the so called exposed edges of the polytope for the investigation of the stability of the polynomial family these exposed edges must be tested kraus and truol 1991 a this test can be simplified if an edge has the vertex property i e if the stability of the edge is guaranteed by the stability of the two vertices

nontrivial solitary waves to the generalized kadomtsev petviashvili equations abstract in this note we study the existence of nontrivial solitary waves for the generalized kadomtsev petviashvili equation in multi dimensional spaces our main tool is a recent linking theorem stated in a paper by szulkin and zou a szulkin w zou homoclinic orbit for asymptotically linear hamiltonian systems j funct anal 187 2001 25 41

a simple proof of kharitonov s theorem an alternative proof of kharitonov s theorem on the stability of linear time invariant continuous systems under parameter variations is presented

robust strict positive realness new results for interval plant controller families a frequency domain approach is used to derive several robust strict positive realness results for interval plants and interval plant plus controller families of transfer functions based on simple frequency domain properties of transfer functions the approach provides a framework for obtaining new results and constructing easy proofs of several important existing results on robust strict positive realness the main new result states that the minimum of the real part of the transfer functions belonging to an interval plant controller family is achieved on one of the 32 kharitonov segments of the interval plant the argument used in the proof is of wider interest and suggests easy ways of proving that robustness of other different frequency properties of interval plant plus controller families of transfer functions such as robust stability of h sub infinity norm computation can be deduced from a fixed number of segments of transfer functions of the family

modified mikhailov plots for robust absolute stability with non parametric perturbations and uncertain nonlinearity this paper generalizes the classical mikhailov stability result for testing robust absolute stability of linear systems with both non parametric perturbations and uncertain nonlinearity three types of non parametric perturbations are considered additive multiplicative and stable factor perturbations modified mikhailov plots are developed for simultaneously testing the stability of the nominal system and computing the maximum robust absolute stability margin

on the robust popov criterion for interval lur e system the classical popov criterion is generalized to include problems with parametric uncertainty as well as nonlinear sector bounded perturbations the parametric dependence is modeled by an interval plant description a robust popov criterion is obtained for a plant controller configuration stronger external results are obtained for a special class of controllers an example illustrating the numerical implementation of these results is presented

application of kharitonov s theorem to mechanical systems kharitonov s theorem is used to derive a robust stability condition for proportional integral derivative pid controlled multi degree of freedom mechanical systems the characteristic equation of such a system is given as a determinant of a third order polynomial with matrix coefficients from which a scalar interval polynomial is obtained a simple procedure for designing pid controllers for these mechanical systems is described and a new kharitonov like result which states roughly that a controller designed for an upper bounding inertia matrix results in stable set point regulation for all other inertias is proved

criteria for robust absolute stability of time varying nonlinear continuous time systems the present paper establishes results for the robust absolute stability of a class of nonlinear continuous time systems with time varying matrix uncertainties of polyhedral type and multiple time varying sector nonlinearities by using the variational method and the lyapunov second method criteria for robust absolute stability are obtained in different forms for the given class of systems specifically the parametric classes of lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability the piecewise linear lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases two examples are presented as applications of the present results to a particular second order system and to a specific class of systems with time varying interval matrices in the linear part

solitary waves for a class of generalized kadomtsev petviashvili equation in rn with positive and zero mass abstract in this paper we use variational methods to establish existence of solitary waves for a class of generalized kadomtsev petviashvili g k p equation in r n the positive and zero mass cases are considered the main argument is to find a palais smale sequence satisfying a property related to pohozaev identity as in 21 which was used for the first time by 23

invariance of a strict hurwitz property for uncertain polynomials with dependent coefficients this note is concerned with the invariance of strict hurwitz property for uncertain polynomials having dependent coefficients a feasible test criterion is provided which reduces the conservatism of the kharitonov theorem

results on the stability robustness of systems with state space perturbations abstract some considerations on the stability robustness of a state space description for perturbed linear systems are presented on the basis of a determinantal criterion the two problems of the stability domain and of checking in the parameter space are considered and a number of computationally simple results are derived an extension to a general pole placement problem and some numerical examples are also proposed

a note on the spectral characterization of θ graphs we consider graphs that is graphs obtained by subdividing the edges of the multigraph consisting of 3 parallel edges it is shown that any graph g is determined by the spectrum the multiset of eigenvalues except possibly when it contains a unique 4 cycle

strictly hurwitz property invariance of quartics under coefficient perturbation in this note it is shown how the maximum interval centered around each of the coefficients of a prescribed fourth degree strictly hurwitz polynomial may be determined so that the strictly hurwitz property remains invariant when each coefficient might be perturbed to any arbitrary value within its permissible interval

a dual result to kharitonov s theorem a dual problem to kharitonov s problem involving a diamond instead of a rectangle is considered the results show that a family of polynomials with coefficients varying in the diamond is strictly hurwitz if and only if eight one dimensional exposed edges of the diamond are strictly hurwitz

robustness analysis of interval matrices based on kharitonov s theorem this paper deals with the robustness analysis problem of interval matrices expansion of det a b is used to get characteristic polynomials of two corresponding systems kharitonov s theorem is applied to test hurwitz properties of the two polynomials a new sufficient condition for all eigenvalues of the interval matrix to lie in a damping cone on complex plan is derived illustrative examples are given

root clustering of interval polynomials in the left sector abstract we examine the root clustering property of interval polynomials in particular we shall show that a family of interval polynomials will have only zeros within the left sector if and only if a finite number of specially chosen vertex polynomials have only zeros in the left sector the number of required vertex polynomials is a linear function of the orders of the polynomial but is independent of the damping margins of the left sector

strong kharitonov theorems for low order polynomials the root clustering property of low order interval polynomials is examined and it is shown that the number of polynomials required to check root clustering within the left sector may be reduced if the order of the interval polynomial is low specifically the reduction is possible if n phi

an overview of extremal properties for robust control of interval plants abstract this paper provides an overview of recent results on the problem of robust stability and performance of feedback control systems in the presence of plant perturbations the widely studied class of interval plants is considered and an effort is made to cover different types of plant perturbations by incorporating in addition to the interval plant description unstructured norm bounded perturbations extremality results for these classes of uncertain systems are provided in a unifying framework robust performance of control systems is addressed in the paper and a number of extremal results are given for the computation of the structured singular value function for feedback systems with interval plants also classical frequency response analysis for interval plant controller families of open loop transfer functions is surveyed with the aim of providing extremal results for the computation of specification parameters such as phase or gain margins and sensitivity and complementary sensitivity peaks

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

maximal polytopic stability domains in parameter space for uncertain systems abstract some results on the stability and pole location of families of uncertain systems with characteristic polynomial coefficients affected by structured perturbations are presented the case in which the coefficients are affine in a set of system physical parameters is considered assuming that the parameters are subject to polytopic perturbations of a given structure for these cases which often arise in system stability robustness analysis as for example in the robustification of controllers for multivariable closed loop systems a procedure is given to estimate maximal stability polytopic regions in the space of parameters this result is also used to derive simple necessary and sufficient conditions for the discrete time stability of convex combinations of two polynomials

signless laplacian spectral characterization of the cones over some regular graphs abstract let g be an r regular graph of order n we prove that the cone over g is determined by its signless laplacian spectrum for r 1 n 2 for r 2 and n 11 for r n 3 we show that the cone over g is determined by its signless laplacian spectrum if and only if the complement of g has no triangles a class of q cospectral graphs are also given

frequency response of uncertain systems with interval plants frequency domain properties of uncertain rational functions depending on two independent interval polynomials are investigated several simplifications for efficient computation of the envelope of the nyquist plots of the uncertain family are reported stronger computational reduction results are given for the bode magnitude and phase plots of an interval plant controller family of transfer functions these results allow for a clear understanding of the extremality properties of several frequency domain performance specifications commonly used in control system design

stability of families of polynomials geometric considerations in coefficient space the stability robustness of both continuous and discrete time dynamical systems is tantamount to the stability of a whole family of characteristic polynomials the authors treat such families as sets in coefficient space and examine some of their geometric properties specifically they examine cases where the stability of the extreme points of a set implies the stability of the complete family they are also concerned with the construction and convexity of the stability region in coefficient space

on robust stability of interval control systems the authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty the basic system considered is that of the classical lur e problem of nonlinear control theory a robust version of the lur e problem consisting of a family of linear time invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector bounded nonlinear gains is presently treated by using the kharitonov theorem to develop some extremal results on positive realness of interval transfer functions i e a family of rational transfer functions with bounded independent coefficient perturbations the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed these calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations

on the spectral characterization of t shape trees a graph g is said to be determined by its spectrum if any graph having the same spectrum as g is isomorphic to g a t shape is a tree with exactly one of its vertices having maximal degree 3 in this paper we show that all t shape trees are determined by their spectra except for a few well defined cases

convexity properties of polynomials with assigned root location this paper presents some geometrical results on the domain of generalized stability for a family of nth order polynomials regions of root location such that the convex hull of the corresponding domain of stability in the coefficient space is a polyhedron are investigated and specific regions for which the convex hull is an n 1 vertex polyhedron are derived the discrete time stability domain falls in the latter class of regions implications of the results for the design of filters solving the robust strict positive realness for families of rational transfer functions with uncertainty in the numerator are also developed

generalized kadomtsev petviashvili equation with an infinite dimensional symmetry algebra abstract a generalized kadomtsev petviashvili equation describing water waves in oceans of varying depth density and vorticity is discussed a priori it involves 9 arbitrary functions of one or two variables the conditions are determined under which the equation allows an infinite dimensional symmetry algebra this algebra can involve up to three arbitrary functions of time it depends on precisely three such functions if and only if it is completely integrable

robust strict positive real stabilization and asymptotic hyperstability robustness abstract this paper is devoted to the study of robust strict positive real stabilization of siso uncertain systems i e finding a single controller that not only robustly stabilizes a plant with uncertainties under unity feedback but also makes the closed loop system robustly strictly positive real it is proved that there must exist a stable controller achieving robust strict positive real stabilization of uncertain systems with both parameter variations and unstructured uncertainties under some reasonable assumptions the propemess of the controller is guaranteed when the largest relative degree of an uncertain system is retricted by applying these results to nonlinear systems some significant conclusions on asymptotic hyperstability robustness are given

expansion of det a b and robustness analysis of uncertain state space systems in this note an expansion for the determinant of the sum of two matrices det a b is given a robustness analysis approach for state space systems with uncertain parameters is investigated by using kharitonov s theorem some useful results are obtained several illustrative examples are given

frequency response of interval plant controller families abstract in this paper a general frequency domain result for families of interval plant with a fixed linear controller is given it is shown that the locus of the polar diagrams of frequency responses of the transfer functions of an interval plant controller family is bounded by the polar plots relative to the 32 segments of transfer functions of the interval plant family easy proofs of several important results such as the generalization of the theorem of kharitonov for feedback systems with interval plants or the robust version of the small gain theorem for the same class of systems are constructed by using the general result more importantly an immediate consequence of the main theorem is that extremal phase gain margins or sensitivity complementary sensitivity peaks for systems of the family can be deduced from those of the 32 segments of the interval plant family

robust stability of a family of disc polynomials in his well known theorem v l kharitonov established that hurwitz stability of a set f1 of interval polynomials with complex coefficients polynomials where each coefficient varies in an arbitrary but prescribed rectangle of the complex plane is equivalent to the hurwitz stability of only eight polynomials in this set in this paper we consider an alternative but equally meaningful model of uncertainty by introducing a set fd of disc polynomials characterized by the fact that each coefficient of a typical element p s in fd can be any complex number in an arbitrary but fixed disc of the complex plane our result shows that the entire set is hurwitz stable if and only if the center polynomial is stable and the h norms of two specific stable rational functions are less than one our result can be readily extended to deal with the schur stability problem and the resulting condition is equally simple

homoclinic orbits for asymptotically linear hamiltonian systems we study the existence of homoclinic orbits for first order time dependent hamiltonian systems z jhz z t where h z t depends periodically on t and hz z t is asymptotically linear in z as z we also consider an asymptotically linear schrodinger equation in rn

a new parameterization of stable polynomials in this note we develop a new characterization of stable polynomials specifically given n positive ordered numbers frequencies we develop a procedure for constructing a stable degree n monic polynomial with real coefficients this construction can be viewed as a mapping from the space of n ordered frequencies to the space of stable degree n monic polynomials the mapping is one one and onto thereby giving a complete parameterization of all stable degree n monic polynomials we show how the result can be used to generate parameterizations of stabilizing fixed order proper controllers for unity feedback systems we apply these results in the development of stability margin lower bounds for systems with parameter uncertainty

parametric absolute stability of lur e systems the concept of parametric stability is extended to include lur e type nonlinear control systems with uncertain parameters and constant reference inputs conditions for parametric absolute stability are derived which guarantee that the system remains stable despite uncertainty of equilibrium location caused by parametric uncertainties and values of the reference input the conditions can be tested by computing value sets using the polygon interval arithmetic algorithm

robust absolute stability of lur e control systems in parameter space abstract this paper deals with the problem of robust absolute stability analysis for nonlinear lur e control systems in the presence of system parameter variations the well known popov criterion for absolute stability is used in order to characterize the boundary of the region of absolute stability in the parameter plane when the coefficients of the transfer function of the linear plant are polynomial functions of the uncertain parameters for a scalar parameter a method is given to determine the maximal interval of variation around a fixed nominal value preserving absolute stability this result is also used to derive a technique for checking absolute stability of lur e systems with parameters in given planar uncertainty sets numerical examples showing the application of the method are reported

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

frequency domain criteria for l sup p robust stability of continuous linear systems necessary and sufficient criteria in the frequency domain for robust stability are given under the assumption that coefficients of a characteristic polynomial belong to a transformed l sup p ball three cases are considered in detail p infinity interval uncertainty p 2 ellipsoidal uncertainty and p 1 octahedral uncertainty it is shown that frequency domain stability criteria are efficient when one deals with robust stability problems the frequency domain approach considered can be extended to various problems of robust stability

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

existence regularity and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient kadomtsev petviashvili equation in this paper we establish some results concerning the existence regularity and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient kadomtsev petviashvili equation variational methods are used to get an existence result as well as to study the concentration phenomenon while the regularity is more delicate because we are leading with functions in an anisotropic sobolev space

robust stability of multivariable interval control systems in this paper we will give necessary and sufficient conditions for the hurwitz stability of mimo interval systems as a consequence of this result we will give a precise bound on the h norm of unstructured perturbations that can be tolerated by mimo interval systems connected in feedback with these perturbations we will also consider the robust version of the popov problem that considers interval mimo systems subject to nonlinear time invariant sector bounded perturbations and in turn obtain a robust stability condition of the popov problem with mixed perturbations

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

robustness of pole location in perturbed systems abstract in this paper we present some results on robustness of location of roots of polynomials in given regions of the complex plane for unknown but bounded perturbations on the polynomial coefficients a geometric approach in coefficient space is exploited to derive maximal deviations in a given class of admissible perturbations of characteristic polynomial coefficients of an uncertain linear system from their nominal values preserving system poles in a given region of the complex plane it is also shown that the solution of this problem can be used to give computationally feasible necessary and sufficient conditions such that all the roots of the members of a family of polynomials lie in a given open region of the complex plane this last result can be considered an extension of the result of the well known theorem of kharitonov it is also outlined how the proposed technique can be used to deal with families of polynomials with linearly correlated coefficient perturbations

starlike trees are determined by their laplacian spectrum in this paper we show that if g is a starlike tree then it is determined by its laplacian spectrum moreover we prove some facts about trees with the same adjacency spectrum as a starlike tree

robust hurwitz l sup p stability of polynomials with complex coefficients necessary and sufficient conditions for robust stability of a family of polynomials with complex coefficients are provided this work generalizes a frequency domain criteria for robust stability of continuous linear systems reported on by y z tsypkin and b t polyak 1991

kharitonov s theorem extension to interval polynomials which can drop in degree a nyquist approach this paper studies the hurwitz stability of interval polynomials which can drop in degree from a nyquist point of view these families make it possible to deal with system families taking into account different dynamic behaviors in the modeling of a plant the behavior of the interval polynomials is studied and it is proven that kharitonov s theorem can be extended

solutions of a variable coefficient kadomtsev petviashvili equation via computer algebra we apply the truncated painleve expansion and computer algebra to a type of the variable coefficient kadomtsev petviashvilli equations and find a class of the analytical solutions along with the corresponding constraints on the variable coefficients shown in this class are the physically meaningful solutions which possess the usual soliton profile

stability conditions for polytopes of polynomials in considering the stability or performance of linear systems with uncertain parameters one is led to consider the simultaneous stability of families of polynomials for a general stability region in the complex plane the author gives a stability criterion for polytopes of polynomials in terms of the stability of a minimal number of corners and edges of the polytope the testing set of edges and corners depends entirely on the edge directions of the polytope hence the results are particularly applicable to problems with fixed directions but varying lengths and positions of the edges applications to robust pole placement of uncertain systems and computation of worst case h sub infinity norms are demonstrated

an alternative proof of kharitonov s theorem an alternative proof is presented of kharitonov s theorem for real polynomials the proof shows that if an unstable root exists in the interval family then another unstable root must also show up in what is called the kharitonov plane which is delimited by the four kharitonov polynomials this fact is proved by using a simple lemma dealing with convex combinations of polynomials then a well known result is utilized to prove that when the four kharitonov polynomials are stable the kharitonov plane must also be stable and this contradiction proves the theorem

the robust root locus abstract in this paper a simple technique is described for generating the root loci of a feedback system which includes perturbations q rl entering affine linearly into the coefficients of the plant denoting the perturbed plant by p s q and the compensator by c s we address the following problem given a bounding set q rl for q find the locus of points z in the complex plane such that 1 kp z q c z 0 for some k 0 and some q q such points z are said to lie on the robust root locus one of the strengths of the technique presented in this paper is that it avoids the combinatoric explosion synonymous with gridding the l dimensional set q and plotting a large number of ordinary root loci associated with gridding the points instead the technique given here exploits only a 2 dimensional gridding of a bounded subset of the complex plane for the more general case when perturbations enter multilinearly into the coefficients a certain convex hull robust root locus is constructed finally the robust root locus technique is illustrated using a model of a supersonic transport plane

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

a novel approach to the analysis and synthesis of controllers for parametrically uncertain systems this paper presents a novel characterization of hurwitz polynomials and demonstrates its usefulness in analyzing parametrically uncertain systems and synthesizing robust controllers for such systems the characterization is a variant of the nyquist stability theorem but unlike this theorem it can prove a polynomial is hurwitz from only approximate knowledge of the polynomial s phase at finitely many points along the imaginary axis

nondefinite least squares and its relation to h sub infinity minimum error state estimation the problem of recursive nondefinite least squares state estimation of continuous time stationary processes is solved by applying pontryagin s maximum principle a comparison of the derived solution to the result that is obtained for the h sub infinity minimum error estimation suggests a new interpretation for the h sub infinity optimal estimation mechanism according to this interpretation the estimator tries to optimally estimate the required combination of the states in the l sub 2 norm sense against the worst disturbance signal that stems from a fictitious measurement of this combination

spectral characterizations of lollipop graphs abstract the lollipop graph denoted by h n p is obtained by appending a cycle c p to a pendant vertex of a path p n p we will show that no two non isomorphic lollipop graphs are cospectral with respect to the adjacency matrix it is proved that for p odd the lollipop graphs h n p and some related graphs h n p are determined by the adjacency spectrum and that all lollipop graphs are determined by its laplacian spectrum

existence of solution for two classes of elliptic problems in r n with zero mass in this paper we show the existence of a positive solution for the following class of elliptic equations u k x f u in rn where f is a continuous function with quasicritical growth and k is a nonnegative function verifying some conditions of two kinds we analyze the problem with k asymptotically periodic k periodic and k belonging to some lr

computer aided stability analysis renders popov criterion obsolete a class of multipliers that can be used for producing alternative stability tests for systems having a single incrementally conic nonlinearity f x has been nearly parameterized by zames and falb 1 the present note demonstrates how linear programming can be used to compute optimal multipliers leading to a frequency domain stability criterion that is less conservative than the standard graphical criteria

robust stability of control systems with polytopical uncertainty a nyquist approach for technical plants a bounded continuum of parameter values describes admissible process models a robust controller guarantees the observance of minimal requirements for all of the allowed process models in this paper a frequency domain approach is proposed that permits the instability of a family of polynomials to be checked this method can be extended in an easy manner to investigate the instability of a closed loop the plant is thereby described by a family of models with a polytopical region of uncertainty in the parameter space as an important special case of the general d stability the hurwitz stability of the closed loop is investigated and a minimal set of necessary and sufficient conditions for robust hurwitz stability is given a generalization for other stability domains is possible besides an algebraic criterion based on a zero inclusion check for a minimal set of exposed edges of the polytopical region a graphic criterion of nyquist type can also be used

on the sixty four polynomials of djaferis to stabilize an interval plant this paper shows that 32 of the 64 polynomials developed by djaferis to stabilize an interval plant with a controller are superfluous thus it is sufficient to stabilize 32 polynomials simultaneously moreover the construction developed in this note allows the implementation of these polynomials in a simple way

an elementary proof of kharitonov s stability theorem with extensions gives an elementary proof of kharitonov s theorem using simple complex plane geometry without invoking the hermite bieler theorem kharitonov s theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval the result states that the whole class is hurwitz if and only if four special well defined polynomials are hurwitz the paper also gives elementary proofs of two previously known extensions for polynomials of degree less than six the requirement is reduced to fewer than four polynomials and the theorem is generalized to polynomials with complex coefficients