root locus approach to the stability analysis of interval matrices a new approach called the root locus approach is developed for the stability analysis of perturbed matrices the basic idea of this approach is to ensure that the root loci of a continuously perturbed matrix remain in the open left half complex s plane based on this approach new techniques are presented to analyse the stability of interval matrices examples are given to demonstrate the merit of the proposed theorems

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

numerical solution method for general interval quadratic programming abstract recently liu and wang described an interesting numerical method to a special class of interval quadratic programming where the linear term in objective function and constraints involved interval coefficients s t liu r t wang a numerical solution method to interval quadratic programming applied mathematics and computation 189 2007 1274 1281 in this paper we generalize liu and wang s method to general interval quadratic programming where all coefficients in the objective function and constraints are interval numbers although the interval quadratic programming model considered in this paper is more general the proposed method requires less computing compared with liu and wang s method numerical examples are presented to illustrate the whole idea

comments on robust stability in linear state space models abstract this note shows that the resuh of jiang 1988 for the robust stability of linear state space models is not new as claimed

robustness analysis a case study the stability test of polynomials whose coefficients depend multilinearly on interval parameters is considered the authors describe and compare four brute force solution approaches these are eigenvalue calculation zero exclusion from a specified value set algebraic tests of real and complex hurwitz roots and the parameter space method they are applied to a simple example with two parameters and third order polynomial an interesting feature of the example is that it can have an isolated unstable point the example may be useful as a benchmark for future approaches to the multilinear problem all four methods are shown to be feasible for the simple example but they require effort

the stability of the grey linear system this paper discusses the stability problem of linear systems whose state matrices are interval matrices and presents some sufficient conditions whereby the stability of the systems can be guaranteed examples are given to illustrate the points

stability analysis of interval matrices another sufficient condition a sufficient condition for the stability of interval matrices is presented based on a lyapunov approach the condition while requiring the solution of a lyapunov matrix equation removes the restrictions imposed by heinen 1984 examples given illustrate the improvement of the proposed condition over the ones given by heinen and bialas 1983 and daoyi 1985

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

a necessary and sufficient condition for the stability of nonnegative interval discrete systems the stability of nonnegative discrete systems with interval uncertainty is discussed for this class of system a necessary and sufficient condition for the stability is provided when all elements of the system matrix are assumed to be specified by intervals an illustrative example is used as a guideline to demonstrate the effectiveness of the result simple computational tests are suggested and their usefulness in this framework is discussed the possible extension of this result to more general classes of systems is addressed

another sufficient condition for the stability of interval matrices a sufficient condition for the stability of interval matrices is presented which is based on the condition given by yedavalli 1985 b examples are given which illustrate the improvement of the proposed condition over that given by yedavalli 1986

comments on sufficient and necessary condition for the asymptotic stability of discrete linear interval systems abstract in a recent paper by jiang 1988 a necessary and sufficient condition for asymptotic stability of the interval matrix of discrete time systems is presented in this contribution it is shown that this condition is not true in general a counter example is given and additional remarks are made

several solution methods for the generalized complex eigenvalue problem with bounded uncertainties abstract the aim of this paper is to evaluate the effects of uncertain but bounded parameters on the complex eigenvalues of the non proportional damping structures by combining the interval mathematics and the finite element analysis the mass matrix the damping matrix and the stiffness matrix were represented as the interval matrices firstly with the help of the optimization theory we presented an exact solution the vertex solution theorem for determining the exact upper bounds or maximum values and exact lower bounds or minimum values of complex eigenvalues of structures where the extreme values are reached on the boundary of the interval mass damping and stiffness matrices then an interval perturbation method was proposed which needs less computational efforts a numerical example of a seven degree of freedom spring damping mass system was used to illustrate the computational aspects of the presented vertex solution theorem and the interval perturbation method in comparison with deif s method

sufficient conditions on stability of interval matrices connections and new results the stability properties of interval matrices are discussed sufficient conditions are given for these properties based upon gershgorin s theorem and its extension and they are shown to improve previous results the derivation helps clarify relations between certain previously available results and shows they can be derived using gershgorin s theorem furthermore the problem of determining the stability of interval matrices is related to that of characterizing certain nonsingular m matrices

counter example to a recent result on the stability of interval matrices by s bialas abstract in bialas 1983 a condition is given which is supposedly necessary and sufficient for the stability of interval matrices we demonstrate via a counter example that the condition given is in fact not sufficient

stabilization of perturbed systems via linear optimal regulator linear quadratic state feedback regulators make the resulting closed loop systems stable enough i e they realize robust stabilization many attempts at robust stabilization using linear quadratic regulators have been reported one of the major trends of formulating uncertainty in systems is to express perturbed parameters as the sum of two terms i e nominal values and the deviation from them in this paper it is assumed that the upper and lower bounds for each uncertain parameter can somehow be estimated this enables us to dispense with nominal values the main aim is to contrive a robust feedback stabilization law for systems with parameters falling into certain ranges via a linear quadratic regulator based only upon information on their bounds the systems under consideration are therefore those having interval system matrices in which each element has the above mentioned two sided bounds a certain feedback law is a stabilizing law for a system with an interval system matrix if and only if the

stability of a polytope of matrices counterexamples while there have been significant breakthroughs for the stability of a polytope of polynomials since v l kharitonov s 1978 seminal result on interval polynomials for a polytope of matrices the stability problem is considered far from completely resolved counterexamples are provided for three conjectures that are directly motivated by the results in the polynomial case these counterexamples illustrate the fundamental differences between polynomial stability and matrix stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail

stability analysis of dynamic interval systems abstract the stability analysis of interval matrices with certain stability margins is considered by means of similarity transformation and gershgorin s theorem new criteria are developed and illustrated by examples we also demonstrate a counter example to a recent result by argoun 1986

simple criteria for stability of interval matrices in this paper the simple sufficient conditions are presented for the stability of a constant real matrix whose elements are not known precisely but we know the upper and lower bounds of intervals in which the elements of matrix a are confined these conditions are also applied in determining the stability and the degree of stability of a matrix

necessary and sufficient conditions for stability of a matrix polytope with normal vertex matrices abstract it is shown that the eigenvalue set of a matrix polytope with normal vertex matrices is a subset of the convex hull of eigenvalues of the vertex matrices

sufficient conditions for the stability of interval matrices the stability of interval dynamical systems is studied sufficient conditions for the polytope of interval matrices are examined and some of the proofs are greatly simplified more generally sufficient conditions are obtained and the approach taken in the new proofs has the potential for further generalizations of the result obtained in this paper

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

high order numerical methods to two dimensional delta function integrals in level set methods in this paper we design and analyze a class of high order numerical methods to delta function integrals appearing in level set methods in two dimensional case the methods comprise approximating the mesh cell restrictions of the delta function integral in each mesh cell the two dimensional delta function integral can be rewritten as a one dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral and thus is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals proposed in x wen high order numerical methods to a type of delta function integrals j comput phys 226 2007 1952 1967 we establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub algorithms and has better accuracy under an assumption on the zero level set of the level set function which holds generally numerical examples are presented showing that the second to fourth order methods implemented in this paper achieve or exceed the expected accuracy and demonstrating the advantage of using our high order numerical methods

stability of interval parameter matrices the stability of interval matrices has been studied by many authors in this paper the stability of interval parameter matrices is introduced and some criteria for this stability are given our results are effective for testing the stability of interval matrices and are more general than previous results furthermore criteria for the stability of time varying matrices are obtained

robust interval stability persistence and partial stability on lotka volterra systems with time delay abstract lotka volterra ecological systems with discrete time delays are studied where the information about the biological vital parameters such as the rates of birth death and interaction between species is incomplete but their upper and lower bounds are known by using stability theory of the interval dynamical systems and constructing suitable liapunov functionals robust stability partial robust stability and robust persistence of those lotka volterra systems are investigated and sufficient conditions are obtained respectively

a two operator approach to robust stabilization of linear systems on robust non fragile feedback stabilization is studied for causal linear time invariant lti input output systems defined in an l 2 signal space setup or equivalently in an l 2 j setup in the frequency domain two operator descriptions for the plant and the controller are used with bounded operators defined on the full space l 2 basic properties of causal lti operators on weighted l 2 spaces l 2 w which are relevant to stabilization theory are also established for different choices of the weighting function w weighted l 2 spaces allow the inclusion of persistent signals such as steps and thus provide the potential of important generalizations of the robust stabilization theory on l 2 in particular it is shown that there is a large class of weights w for which the l 2 w setup leads to h optimization this implies that robust h design can be applied to a large class of weighted l 2 spaces on problems of closability of unstable causal lti convolution operators are discussed t

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

convergence property of interval matrices and interval polynomials in association with robust control system design and analysis the hurwitz property of interval matrices and interval polynomials has recently been actively investigated however its discrete counterpart the convergence property has seemingly not been much discussed in this paper this property is studied in comparison with the hurwitz counterpart some conditions under which interval matrices or interval polynomials are convergent are derived

necessary and sufficient conditions for stability of a class of interval matrices in this paper some necessary and sufficient conditions for stability complete instability and composite stability type of a class of interval matrices are given

comments on a necessary and sufficient condition for the stability of interval matrices in a recent paper by bialas a new proof of a known result concerning interval polynomials was given this result is summarized here and a much stronger result is mentioned bialas main theorem on the stability of interval matrices is shown to be false