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

optimal lines for railway systems abstract we discuss the optimal choice of traffic lines with periodic timetables on a railway system a chosen line system has to offer sufficient capacity in order to serve the known amount of traffic on the system the line optimization problem aims at the construction of a feasible line system optimizing certain objectives we introduce a mixed integer linear programming formulation for real world data we succeed in solving the model by means of suitable relaxations and sufficiently strong cutting planes with the commercial lp solver cplex 3 0

robust numerical algorithm to the european option with illiquid markets abstract in this paper we consider illiquid european call option which is arisen in nonlinear black scholes equation in this respect we apply the newton s method to linearize it based on the obtained linear equation we obtain the approximate solutions recursively in two steps finally based on the conditions of kantorovich theorem we investigate the convergence analysis of the newton s method on the proposed problem finally the positivity of the solution is discussed

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

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

robustness of pole assignment in a specified region an analysis of pole assignment is given for systems under linear time invariant perturbations based upon the lyapunov approach new techniques to calculate allowable element bounds for highly structured perturbations are presented under these allowable perturbations both stability robustness and a certain performance robustness are thus ensured examples are given to illustrate the proposed methods

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

exact maximum singular value calculation of an interval matrix in this note we present a method for calculating the maximum singular value of an interval matrix first we provide an algorithm for calculating the maximum singular value of a square interval matrix then based on this algorithm we extend the result to non square interval matrix case and to the case of computing the minimum singular value through numerical examples the validity of the suggested methods is illustrated particularly we compare the newly proposed method with an existing method to show that the new method finds the correct bound of the maximum singular value with no exception

pricing early exercise and discrete barrier options by fourier cosine series expansions we present a pricing method based on fourier cosine expansions for early exercise and discretely monitored barrier options the method works well for exponential levy asset price models the error convergence is exponential for processes characterized by very smooth rm c infty a b in mathbb r transitional probability density functions the computational complexity is o m 1 n log n with n a small number of terms from the series expansion and m the number of early exercise monitoring dates this paper is the follow up of fang and oosterlee in siam j sci comput 31 2 826 848 2008 in which we presented the impressive performance of the fourier cosine series method for european options

hybrid port hamiltonian systems from parameterized incidence matrices to hybrid automata abstract this paper shows how to formally design a hybrid automaton model for a wide class of dissipative physical systems with sources and switching topology this method is based on a mathematical representation of the dynamic network graph and of its dual graph using the hybrid incidence matrix and on a constructive method for analyzing admissible and constrained configurations the port hamiltonian representation associated with the set of hybrid system configurations parameterized by the discrete state of the switches is synthesized to be part of the hybrid automaton of the system this is a further step towards a generic control synthesis for physical switching systems

minimizing waiting times in integrated fixed interval timetables by upgrading railway tracks the integrated fixed interval timetable of a railway network guarantees none waiting times for passengers changing trains for a periodically served network such a timetable only exists if and only if the running times of the trains are feasible with a group equation system if the running times are infeasible with this equation system there will remain a certain amount of waiting time a modification of the running times can be achieved by reforming the actual state of certain track segments in this paper we discuss the cost benefit between the investigation for reforming track states and the quality of the resulting timetable measured by the remaining waiting times this leads to a complicated bi criteria optimization problem we generate sub optimal solutions by a hybrid genetic algorithm including fuzzy logic

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

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

discrete optimization in public rail transport many problems arising in traffic planning can be modelled and solved using discrete optimization we will focus on recent developments which were applied to large scale real world instances most railroad companies apply a hierarchically structured planning process starting with the definition of the underlying network used for transport one has to decide which infrastructural improvements are necessary usually the rail system is periodically scheduled a fundamental base of the schedule are the lines connecting several stations with a fixed frequency possible objectives for the construction of the line plan may be the minimization of the total cost or the maximization of the passengers s comfort satisfying certain regulations after the lines of the system are fixed the train schedule can be determined a criterion for the quality of a schedule is the total transit time of the passengers including the waiting time which should be minimized satisfying some operational constraints for each trip of the schedule a train consisting of a locomotive and some carriages is needed for service the assignment of rolling stock to schedule trips has to satisfy operational requirements a comprehensible objective is to minimize the total cost after all strategic and tactical planning the schedule has to be realized several external influences for example delayed trains force the dispatcher to recompute parts of the schedule on line

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

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

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

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

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

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

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

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

sufficient conditions for stability of interval matrices extremely simple sufficient conditions are presented for the stability of interval matrices these complement the necessary and sufficient conditions developed by bialas 1983 which become unwieldy for large matrices 4 4 and above

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

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

on the analysis of eigenvalue assignment robustness the robust eigenvalue assignment of systems subject to parameter perturbations is addressed based on some essential properties of induced norms and matrix measures the authors derive some sufficient conditions which ensure the assignment of the system s eigenvalues in the specified region irrespective of the system perturbations the robustness bounds for eigenvalue assignment are obtained without the need to solve the lyapunov equation an example is given to illustrate the effectiveness and ease of the proposed analysis methods

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

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

the steiner connectivity problem the steiner connectivity problem has the same significance for line planning in public transport as the steiner tree problem for telecommunication network design it consists in finding a minimum cost set of elementary paths to connect a subset of nodes in an undirected graph and is therefore a generalization of the steiner tree problem we propose an extended directed cut formulation for the problem which is in comparison to the canonical undirected cut formulation provably strong implying e g a class of facet defining steiner partition inequalities since a direct application of this formulation is computationally intractable for large instances we develop a partial projection method to produce a strong relaxation in the space of canonical variables that approximates the extended formulation we also investigate the separation of steiner partition inequalities and give computational evidence that these inequalities essentially close the gap between undirected and extended directed cut formulation using these techniques large steiner connectivity problems with up to 900 nodes can be solved within reasonable optimality gaps of typically less than five percent

robust stability bounds on time varying perturbations for state space models of linear discrete time systems the stability robustness of linear discrete time systems in the time domain is addressed using the lyapunov approach bounds on linear time varying perturbations that maintain the stability of an asymptotically stable linear time invariant discrete time nominal system are obtained for both structured and unstructured independent perturbations bounds are also derived assuming that various elements of the system matrix are perturbed dependently the result for the structured perturbation case is extended to the stability analysis of interval matrices

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

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

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

eigenvalue assignment robustness for systems with structured perturbations the eigenvalue assignment robustness problem of a linear time invariant uncertain system is considered allowable perturbations are obtained for ensuring the eigenvalues of a system with or without perturbations be retained in some distinct and arbitrarily shaped regions the presented criteria improve some of the previous results in the literature both for the transfer function model and the state space model

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

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

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

a numerical method for pricing discrete double barrier option by legendre multiwavelet in this article a fast numerical algorithm for pricing discrete double barrier option is presented according to blackscholes model the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution these recursive solutions are approximated by using legendre multiwavelets as orthonormal basis functions and expressed in operational matrix form the most important feature of this method is that its cpu time is nearly invariant when monitoring dates increase besides the rate of convergence of presented algorithm was obtained the numerical results verify the validity and efficiency of the numerical method

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

pole assignment in a specified disk the problem of assigning all poles of a closed loop system in a specified disk by state feedback is considered for both continuous and discrete systems a state feedback control law is determined by using a discrete riccati equation this kind of pole assignment problem is named d pole assignment and its relation to the optimal control problem and its robustness properties are discussed the gain and phase margins for all closed loop poles to stay inside the specified disk d are determined for the proposed control

numerical solution for the weakly singular fredholm integro differential equations using legendre multiwavelets an effective method based upon legendre multiwavelets is proposed for the solution of fredholm weakly singular integro differential equations the properties of legendre multiwavelets are first given and their operational matrices of integral are constructed these wavelets are utilized to reduce the solution of the given integro differential equation to the solution of a sparse linear system of algebraic equations in order to save memory requirement and computational time a threshold procedure is applied to obtain the solution to this system of algebraic equations through numerical examples performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation

a note on robust stability bounds the authors comment on stability robustness bounds for linear systems with multiple uncertain parameters which were obtained by means of lyapunov functions results obtained with quadratic and with vector lyapunov functions are compared simple examples are used to illustrate the effects of the choice of functions corresponding majorizations and system decompositions

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

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

expansion of det a b c and robustness analysis of discrete time state space systems in this paper the expansion of det a b c is given the robustness problem for discrete time state space systems with uncertain parameters is investigated by applying the schur stability theory of interval polynomials a stability robustness criterion for the uncertain systems is derived illustrative examples are presented

a double exponential fast gauss transform algorithm for pricing discrete path dependent options this paper develops algorithms for the pricing of discretely sampled barrier lookback and hindsight options and discretely exercisable american options under the black scholes framework the pricing of these options can be reduced to evaluation of a series of convolutions of the gaussian distribution and a known function we compute these convolutions efficiently using the double exponential integration formula and the fast gauss transform the resulting algorithms have computational complexity of o nn where the number of monitoring exercise dates is n and the number of sample points at each date is n and our results show the error decreases exponentially with n we also extend the approach and provide results for merton s lognormal jump diffusion model

on sufficient conditions for the stability of interval matrices using gershgorin s diagonal dominance theorem new sufficient conditions for the stability of interval matrices are obtained the new conditions remove a restriction in heinen s 1983 analysis and are applicable to a wider class of problems than previously possible

efficient and fast numerical method for pricing discrete double barrier option by projection method in this paper we introduce a new and considerably fast numerical method based on projection method in pricing discrete double barrier option according to the blackscholes framework the price of option in each monitoring dates is the solution of well known partial differential equation that can be expressed recursively upon the heat equation solution these recursive solutions are approximated by projection method and expressed in operational matrix form the most important advantage of this method is that its computational time is nearly fixed against monitoring dates increase afterward in implementing projection method we use legendre polynomials as an orthogonal basis finally the numerical results show the validity and efficiency of presented method in comparison with some others

numerical valuation of discrete double barrier options in the present paper we explore the problem for pricing discrete barrier options utilizing the black scholes model for the random movement of the asset price we postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method thus the problem is reduced to the estimation of a multi dimensional integral whose dimension corresponds to the number of the monitoring dates we propose a fast and accurate numerical algorithm for its valuation our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in finance and literature a desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers the method has a simple computer implementation and it permits observing the entire life of the option

a robust stability bound of linear systems with structured uncertainty the robust stability of linear uncertain systems with multiple uncertain parameters is considered a sphere norm bound condition on the uncertainties which assures stability of the systems is derived this bound is shown to be less conservative than existing ones a necessary condition to maximize this bound is also given

near optimal control for time varying linear discrete systems with additive nonlinearities and random gains in this technical note the near optimal control problem is investigated for a class of time varying linear discrete systems subject to additive nonlinearities and random gains first certain upper bound on the cost function is proposed to quantify the control performance subsequently in virtue of the time varying discrete riccati like recursions drlrs the near optimal control strategy is designed such that this upper bound is minimized over the finite horizon to reflect the steady state behavior of the dynamic system the upper bound of the derived time varying drlrs is also analyzed over the infinite horizon by resorting to the semidefinite programming method finally a numerical example is provided to verify the validity and advantages of the proposed methodology

numerical method for discrete double barrier option pricing with time dependent parameters in this paper the main purpose is pricing of discrete double barrier option under black scholes framework with time dependent parameters by some conventional transforms in each monitoring interval the problem is reduced to well known black scholes partial differential equations with convenient constant coefficient such that the solution can be expressed recursively upon the heat equation solution finally a numerical method is proposed to compute the obtained recursive formula efficiently also the greeks of contract are calculated

lyapunov approach to robust pole assignment analysis abstract the robust pole assignment of systems with linear time invariant perturbations is considered based upon the lyapunov approach new techniques for calculating the robustness bounds for pole assignment in any chosen region are presented these take account not only of stability robustness but also of certain types of performance robustness examples are presented to illustrate the merit of the proposed analysis methods

numerical solution based on hybrid of block pulse and parabolic functions for solving a system of nonlinear stochastic ito volterra integral equations of fractional order abstract in this study an effective numerical approach based on the hybrid of block pulse and parabolic functions pbpfs is suggested to obtain an approximate solution of a system of nonlinear stochastic ito volterra integral equations of fractional order for this aim we first introduce these functions and express some of their properties and then calculate fractional and stochastic operational matrices of integration based on these functions using the properties of pbpfs and obtained operational matrices the system of nonlinear stochastic ito volterra integral equations of fractional order converts to a nonlinear system of algebraic equations which can be easily solved by using newton s method moreover in order to show the rate of convergence of the suggested approach we present several theorems on convergence analysis and error estimation which demonstrate the rate of convergence of the proposed method for solving this nonlinear system is o h 3 finally two examples are included to illustrate the validity applicability and efficiency of the proposed technique

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

on smoothing of the crank nicolson scheme and higher order schemes for pricing barrier options most option pricing problems have nonsmooth payoffs or discontinuous derivatives at the exercise price discrete barrier options have not only nonsmooth payoffs but also time dependent discontinuities in pricing barrier options certain aspects are triggered if the asset price becomes too high or too low standard smoothing schemes used to solve problems with nonsmooth payoff do not work well for discrete barrier options because of discontinuities introduced in the time domain when each barrier is applied moreover these unwanted oscillations become worse when estimating the hedging parameters e g delta and gamma we have an improved smoothing strategy for the crank nicolson method which is unique in achieving optimal order convergence for barrier option problems numerical experiments are discussed for one asset and two asset problems time evolution graphs are obtained for one asset problems to show how option prices change with respect to time this smoothing strategy is then extended to higher order methods using diagonal m m pade main schemes under a smoothing strategy of using as damping schemes the 0 2m 1 subdiagonal pade schemes

reduced conservatism in stability robustness bounds by state transformation this note addresses the issue of conservatism in the time domain stability robustness bounds obtained by the lyapunov approach a state transformation is employed to improve the upper bounds on the linear time varying perturbation of an asymptotically stable linear time invariant system for robust stability this improvement is due to the variance of the conservatism of the lyapunov approach with respect to the basis of the vector space in which the lyapunov function is constructed improved bounds are obtained using a transformation on elemental and vector norms of perturbations i e structured perturbations as well as on a matrix norm of perturbations i e unstructured perturbations for the case of a diagonal transformation an algorithm is proposed to find the optimal transformation several examples are presented to illustrate the proposed analysis