robustness of uncertain descriptor systems this paper considers a class of descriptor systems with perturbations it derives sufficient conditions for the uncertain systems to be impulse free regular and or asymptotically stable the problems of the impulse controllability and impulse observability and the so called robust impulsive controller ric of the uncertain system are considered numerical examples are presented to illustrate the results

robust stability of interval matrices a computational approach a simple computational procedure is given to determine the robust stability of matrices containing interval parameter uncertainty the computation consists of determining the maximal phase difference of the characteristic polynomial evaluated over the vertices of the uncertain parameter set at each point of the stability boundary and verifying that this maximal phase difference is less than radians this follows as a direct application of the mapping theorem which allows us effectively to treat rank one perturbations of matrices we discuss the conservatism of the method and show how the solution may be improved to any desired level of accuracy we give several numerical examples of systems with state space perturbations and compare our results with those obtained by other methods

improved stability robustness bounds using state transformation for linear discrete systems abstract sufficient condition bounds on the linear time varying perturbations for robust stability of an asymptotically stable linear time invariant discrete time system have been reported recently the development involves both schwartz and triangular inequalities and tends to give conservative results this paper uses state transformation to obtain improvement in these bounds both unstructured and structured perturbation bounds are shown to improve using transformations the proposed analysis is applied to a fourth order macroeconomic system model

characterization of robust controllers abstract this paper presents a procedure for designing a robust controller which is able to stabilize a multivariable system with interval uncertainties in the system parameters the uncertain parameters are assumed to lie within known intervals the fundamental idea behind the procedure is to characterize the set of robust controllers as a convex set by the new matrix inequalities result a suitable controller can then be chosen by means of an optimization algorithm the controller thus chosen will be able to ensure that the closed loop matrix lies within desired intervals for all the prescribed interval uncertainties in the system parameters

on robust stability of 2 d discrete systems presents a study on robust stability of two dimensional 2 d discrete systems in the fornasini marchesini f m state space setting a measure of stability robustness of a stable f m model is defined the relation of this measure to its counterpart in the roessor state space and related computational issues are addressed three lower bounds of the stability robustness measure defined are derived using a one dimensional parameterization approach and a 2 d lyapunov approach a numerical example is included to illustrate the main results obtained

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

qualitative indicator functions for imaging crack networks using acoustic waves we consider the problem of imaging a crack network embedded in some homogeneous background from measured multi static far field data generated by acoustic plane waves we propose two novel approaches that can be seen as extensions of linear sampling type methods and that provide indicator functions which are sensitive to local cracks densities the first approach uses multiple frequencies data to compute spectral signatures associated with artificially embedded localized obstacles the second approach also exploits the idea of incorporating an artificial background but uses data for a single frequency the indicator function is built using a similar concept as for differential sampling methods compare the solution of the interior transmission problem for healthy inclusion with the one with embedded cracks the performance of the methods is tested and discussed on synthetic examples and the numerical results are compared with the ones obtained using the classical factorization method

estimates for a measure of stability robustness via a lyapunov matrix equation the upper and lower bounds of an existing measure for stability robustness are obtained in terms of the solution to a lyapunov matrix equation for nominal systems this measure is exact in the sense that it gives a necessary and sufficient condition for the stability of perturbed systems for a certain class of perturbations the results enable us to assess the measure using the solution to a lyapunov equation

improved measures of stability robustness for linear state space models in this paper the aspect of stability robustness of linear systems is analyzed in the time domain a bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a lyapunov matrix equation solution the resulting bound is shown to be an improved bound over the ones recently reported in the literature also special cases of the nominal system matrix are considered for which the bound is given in terms of the nominal matrix thereby avoiding the solution of the lyapunov matrix equation examples given include comparison of the proposed approach with the recently reported results

conditions on the boundary of the zero set and application to stabilization of systems with uncertainty abstract we describe an analytic method for finding the location of the zero set of a vector valued function which depends on m real variables and n complex parameters we apply the method to robust stabilization of multivariable linear feedback systems we find exact measures of the extent of permissible perturbations in the plant and or the compensator that maintain feedback stability

limit cycles for rigid cubic systems we consider planar cubic systems with a unique rest point of center focus type and constant angular velocity for such systems we obtain an affine classification in three families and for two of them their corresponding phase portraits on the poincare sphere we also prove that for two of these families there is uniqueness of limit cycle with respect the third family we give the bifurcation diagram and phase portraits on the poincare sphere of a one parameter sub family exhibiting at least two limit cycles

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

steklov eigenvalues and quasiconformal maps of simply connected planar domains we investigate isoperimetric upper bounds for sums of consecutive steklov eigenvalues of planar domains the normalization involves the perimeter and scale invariant geometric factors which measure deviation of the domain from roundness we prove sharp upper bounds for both starlike and simply connected domains for a large collection of spectral functionals including partial sums of the zeta function and heat trace the proofs rely on a special class of quasiconformal mappings

existence of closed solutions for a polynomial first order differential equation we find new criteria for the existence of closed solutions in a first order polynomial differential equation which contains the abel equation as a particular case such results are applied to the problem of the existence of limit cycles in planar polynomial vector fields

explicit asymmetric bounds for robust stability of continuous and discrete time systems the problem of robust stability in linear systems with parametric uncertainties is considered explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems and inequalities with quadratic terms for discrete time systems cases where system parameters are nonlinear functions of an uncertainty are also examined

robustness measures for linear systems with application to stability radii of hurwitz and schur polynomials in this paper we consider robustness measures stability radii for system matrices which are subjected to structured real and complex perturbations of the form a a bdc where b c are given matrices our object is twofold a to present a number of new results mainly concerning the real stability radius and its differences from the complex one b to give an overview of our approach to the robustness analysis of linear state space systems including basic properties and characterizations of the complex stability radius applying the results to the special case where a is in companion form and b 0 0 0 1 t we are able to determine stability radii for hurwitz and schur polynomials under arbitrary complex and real affine perturbations of the coefficient vector computable formulae are obtained and illustrated by several examples

cubic systems and abel equations abstract we investigate cubic systems which can be transformed to an equation of abel form the conditions for the origin to be a centre and in particular an isochronous centre are obtained the maximum number of limit cycles which can bifurcate from a fine focus is determined and some information is obtained about the global phase portrait

new robustness bounds for discrete systems with random perturbations some new stochastic stability robustness bounds for state space models are reported nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness the methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one the results are compared with each other and with the exact stability region in an example

discontinuous galerkin methods of the non selfadjoint steklov eigenvalue problem in inverse scattering abstract in this paper we apply discontinuous galerkin methods to the non selfadjoint steklov eigenvalue problem arising in inverse scattering the variational formulation of the problem is non selfadjoint and does not satisfy h1 elliptic condition by using the spectral approximation theory of compact operators we prove the spectral approximation and optimal convergence order for the eigenvalues finally some numerical experiments are reported to show that the proposed numerical schemes are efficient for real and complex steklov eigenvalues

stekloff eigenvalues in inverse scattering we consider a problem in nondestructive testing in which small changes in the possibly complex valued refractive index n x of an inhomogeneous medium of compact support are to be determined from changes in measured far field data due to incident plane waves the problem is studied by considering a modified far field operator cal f whose kernel is the difference of the measured far field pattern due to the scattering object and the far field pattern of an auxiliary scattering problem with the stekloff boundary condition imposed on the boundary of a domain b where b is either the support of the scattering object or a ball containing the scattering object in its interior it is shown that cal f can be used to determine the stekloff eigenvalues corresponding to b where if b not d the refractive index is set equal to one in b setminus overline d a formula is obtained relating changes in n x to changes in the stekloff eigenvalues and numerical examples are given showing the effectiveness of determining changes to the refractive index in this way

the stability robustness of generalized eigenvalues the concept of stability radius is generalized to matrix pairs a matrix pair is said to be stable if its generalized eigenvalues are located in the open left half of the complex plane the stability radius of a matrix pair a b is defined to be the norm of the smallest perturbation delta a such that a delta a b is unstable the purpose is to estimate the stability radius of a given matrix pair depending on whether the matrices under consideration are complex or real the problem can be classified into two cases the complex case is easy and a complete solution is provided the real case is more difficult and only a partial solution is given

on the relationship between the spectral radius and stability radius for discrete systems the relationship between the spectral radius and the stability radius is established via elementary calculation the result gives a discrete counterpart of the existing result for continuous systems and provides an upper bound for the stability radius the main result of the calculation is summarized in the form of a theorem

improved robust stability bounds for discrete time linear regulators with computational delays abstract recently obtained stability robustness bounds on linear time varying perturbations of an asymptotically stable linear time invariant discrete time system are applied to linear regulators with computational delays the bounds were developed using lyapunov theory and singular value decomposition for unstructured and structured time varying perturbations the new structured perturbation bound may provide improved results for the elemental perturbations over a bound based on the unstructured perturbation bound of ishihara 1988 automatica 24 696 700 as indicated both by an example and by sufficient conditions

state space measures of robustness of pole locations for structured and unstructured perturbations abstract measures of pole location robustness for linear feedback systems are derived from a state space model of the system the robustness tests ensure that the eigenvalues of the perturbed systems matrix a e remain in a desired region d of the complex plane containing the eigenvalues of the nominal system matrix a the region d may be any open set of the complex plane whatsoever the results are expressed in terms of induced matrix norms and apply to structured perturbations of the form e b c where b and c define the structure of e and may be nonsquare matrices rank one perturbations e of minimal norm and with the given structure that will cause a e to have an eigenvalue outside of d are constructed for the cases when the matrix norm is induced by the vector 1 norm or the vector norm the advantages of having robustness measures for several matrix norms that can be computed are illustrated with a simple example that demonstrates how the conservatism of single tests can be reduced using several tests i e several matrix norms a method for computing numerically the robustness measures for particular norms is presented it can be used to compute with a guaranteed degree of accuracy the maximum of the norm of the frequency response of a system

steklov eigenvalues of reflection symmetric nearly circular planar domains we consider steklov eigenvalues of reflection symmetric nearly circular planar domains treating such domains as perturbations of the disc we obtain a second order formal asymptotic estimate in the domain perturbation parameter we conclude with a discussion of implications for isoperimetric inequalities namely our results corroborate the results of weinstock and brock that state respectively that the disc is the maximizer for the area and perimeter constrained problems they also support the result of hersch payne and schiffer that the product of the first two eigenvalues is maximal among all open planar sets of equal perimeter in addition our results imply that the disc is not the maximizer of the area constrained problems for higher even numbered steklov eigenvalues as suggested by previous numerical results

two grid discretizations and a local finite element scheme for a non selfadjoint stekloff eigenvalue problem abstract in this paper for a new stekloff eigenvalue problem which is non selfadjoint and not h 1 elliptic we establish and analyze two kinds of two grid discretization scheme and a local finite element scheme we present the error estimates of approximations of two grid discretizations we also prove a local error estimate which is suitable for the case that the local refined region contains singular points lying on the boundary of domain numerical experiments are reported finally to show the efficiency of our schemes

state space measures for stability robustness stability robustness measures for a perturbed linear feedback system are derived based on state space models of the system the system may be a continuous time or discrete time system the perturbations are modeled as additive perturbation matrices necessary and sufficient conditions for the stability of the perturbed closed loop system for all perturbations of norm bounded by some positive number are obtained the destabilizing perturbations of minimal norm are characterized it is shown by an example that there are cases when the destabilizing perturbations of minimal norm are all complex the results are expressed in terms of induced operator norms these are later specialized to the euclidean norm and expressed in terms of singular values a simple example is also included to illustrate an application of the results of this note

generalized edge theorem abstract in this paper we shall show that a family of analytic functions constructed from the convex hull of a finite number of vertex functions will have no zeros within a simply connected region in the complex plane if and only if all its edge functions have no zeros within the simply connected region the result is in fact a generalization of the edge theorem which has been derived for polynomial functions 1 2 7

stability robustness measures utilizing structural information this paper presents techniques of using weighted l1 and norms to incorporate the structural information of the return difference and the perturbation matrices in the measure of stability robustness of multivariable control systems the flexibility offered by these norms along with the use of non negative matrix theory enables one in most cases to reduce the conservatism which has been a typical concern with the use of singular value based stability robustness tests new stability robustness criteria are derived on the basis of weighted l1 and norms examples are given to demonstrate the merits of these methods over singular value tests

an algorithm for the computation of the structured complex stability radius abstract perturbed state space models of the form x a bdc x are considered where a b c are given matrices a is stable and d is an unknown complex perturbation matrix a reliable and efficient algorithm for the computation of the norm of the minimal norm destabilizing matrix d is presented the performance of the algorithm and possible applications are illustrated