lp parameter perturbation and design of robust controllers for linear systems in this paper linear systems with characteristic equations that are linearly dependent on some uncertain parameters are considered a new procedure is proposed for the calculation of d stability margins in the parameter space in general lp norms the procedure is simple and computationally efficient for several important regions of interest in the complex plane e g left hand plane sectors and circles centred at the origin it requires the solution of only one equation based on this result a new method is presented for the design of robust controllers robust placement of the closed loop poles inside the regions of interest is addressed the method provides a simple and computationally tractable solution to the robust controller design problem it can be used to synthesize robust controllers with general rational transfer functions for plants modelled as the ratio of two uncertain polynomials subjected to lp parameter perturbation

exactification of the asymptotics for bessel and hankel functions exactification is the process of showing how a complete asymptotic expansion can be evaluated to yield exact values of the original function it represents because the process does not involve neglecting the remainders of truncated component asymptotic series within a complete asymptotic expansion techniques for evaluating divergent series are required one such technique is borel summation but in many instances it can be computationally slow and consequently lacking in precision another is the numerical technique of mellin barnes regularization which is capable of evaluating divergent series with great precision far more rapidly than borel summation here both techniques are presented in the evaluation of exact values for bessel and hankel functions from their complete asymptotic expansions

exactification of the method of steepest descents the bessel functions of large order and argument the hadamard expansion procedure applied to laplace type integrals taken along contours in the complex plane enables an exact description of the method of steepest descents this mode of expansion is illustrated by the evaluation of the bessel functions j v x and y v v x of large order and argument when x is bounded away from unity the limit x 1 corresponding to the coalescence of the active saddles in the integral representations of the bessel functions translates into a progressive loss of exponential separation between the different levels of the hadamard expansion which renders computation in this limit more difficult it is shown how a simple modification to this procedure can be employed to deal with the coalescence of the active saddles when x 1

brief paper assigning closed loop invariant polynomials over polytopes for linear periodic systems this paper provides a parameterization of all output feedback periodic controllers providing closed loop invariant polynomials varying over some assigned polytopes for linear discrete time periodic plants using the notion of time invariant system associated to a periodic system the parameterization is provided in terms of the general solution of a suitably defined matrix diophantine equation

assigning invariant polynomials over polytopes this paper provides a parameterization of all output feedback controllers yielding closed loop invariant polynomials varying over some assigned polytopes

an algorithm for robust pole assignment via polynomial approach a computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented the analysis is based on transfer functions of characteristic polynomials and the problem is formulated as one of semi infinite programming an example of an application is given to illustrate this approach

the evaluation of bessel functions via exp arc integrals a standard method for computing values of bessel functions has been to use the well known ascending series for small argument and to use an asymptotic series for large argument with the choice of the series changing at some appropriate argument magnitude depending on the number of digits required in a recent paper d borwein j borwein and r crandall 1 derived a series for an exp arc integral which gave rise to an absolutely convergent series for the j and i bessel functions with integral order such series can be rapidly evaluated via recursion and elementary operations and provide a viable alternative to the conventional ascending asymptotic switching in the present work we extend the method to deal with bessel functions of general non integral order as well as to deal with the y and k bessel functions

on the use of hadamard expansions in hyperasymptotic evaluation differential equations of hypergeometric type we describe how a modication of a common technique for developing asymptotic expansions of solutions of linear di erential equations can be used to derive hadamard expansions of solutions of di erential equations hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions particularly that of having exponentially small remainders when truncated and as a consequence provide a useful computational tool for evaluating special functions the methods we discuss can be applied to linear di erential equations of hypergeometric type and may have wider applicability

on the use of hadamard expansions in hyperasymptotic evaluation of laplace type integrals ii complex variable we review and discuss the application of hadamard expansions to the hyperasymptotic evaluation of laplace integrals c ex p t f t dt x where for simplicity in this paper x is restricted to be a positive real variable the integration path c can be taken over both finite and semi infinite intervals in the complex plane in general these expansions take the form of compound expansions each associated with a different exponential level and involve absolutely convergent series containing the incomplete gamma function as a smoothing factor the early terms in each convergent expansion possess a rapid asymptotic like decay when the variable x is large with late terms that can be transformed into a rapid decay comparable with that of the early terms the hadamard expansion of the above integral when the phase function p t is linear is shown to depend significantly on the singularity structure of the amplitude function f t the application of the theory to laplace type integrals with quadratic cubic and nonpolynomial phase functions is considered in addition to the amplitude function the location of the saddle points satisfying p t 0 also plays a role in the detailed structure of the different exponential levels in the resulting hadamard expansion numerical examples are given to illustrate the accuracy that can be achieved with this new procedure

high precision evaluation of the bessel functions via hadamard series we present a method of high precision calculation of the bessel functions using hadamard series such series are absolutely convergent expansions involving the normalised incomplete gamma function p a z email protected a z c a and possess early terms that behave like those in an asymptotic expansion in the case of real variables the function p a z acts as a smoothing factor on the terms of the series we show how these series representing the bessel functions of complex argument can be chosen so as to produce rapidly convergent series that possess terms decaying at the geometric rate q k where 0 q 1 and k is the ordinal number of the series we give numerical examples with q 12 13 and 14 the theory is extended to cover the confluent hypergeometric functions f11 a b z and u a b z thereby dealing with many of the special functions arising in mathematical physics

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

on the use of hadamard expansions in hyperasymptotic evaluation of laplace type integrals iv poles this paper is one of a series considering the application of hadamard expansions in the hyperasymptotic evaluation of laplace type integrals of the form cexp email protected t f t dt for large values of z it is shown how the procedure can be employed to deal with the case when the amplitude function f t possesses poles which may coalesce with a saddle point of the integrand or approach the integration path c a novel feature introduced here is the reverse expansion procedure this results in contributions at each exponential level after the first of the expansion in the form of rapidly convergent series thereby enabling the high precision evaluation of the above integral in coalescence problems numerical examples are given to illustrate the procedure

robust characteristic polynomial assignment abstract in this paper a computational method for designing controllers which attempt to place the characteristic polynomial of an uncertain system inside some prescribed region is presented an objective function consisting of two terms is proposed penalizing both the distance to a given controller and the size of the uncertainty region developed to solve the robust assignment problem the algorithm is based on semi infinite programming theory and the special structure of the problem is exploited to get both simpler methods and convergence proof the way in which the uncertain parameters affect the plant coefficients is realistic since it includes multinomial dependence an example of application is given to illustrate the approach

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

hyperasymptotic evaluation of the pearcey integral via hadamard expansions we describe high precision computations of the pearcey integral pe x y for real x and y by means of hadamard expansions numerical results for x y situated in different regions of the x y plane are given to illustrate the levels of precision that can be achieved particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with pe x y across which there is either a coalescence of saddles or a stokes phenomenon

refined schur method for robust pole assignment with repeated poles schur type methods in 6 and 11 solve the robust pole assignment problem by employing the departure from normality of the closed loop system matrix as the measure of robustness they work well generally when all poles to be assigned are simple however when some poles are close or even repeated the eigenvalues of the computed closed loop system matrix might be inaccurate in this paper we present a refined schur method which is able to deal with the case when some or all of the poles to be assigned are repeated more importantly the refined schur method can still be applied when place 14 and robpole 28 fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

robust pole assignment abstract this paper presents new theorems on the theory of interval matrix inequalities and the theory of polynomials with interval roots and applies them to the problem of robust pole placement we formulate optimization problems and derive convergent iterative algorithms which allow the designer to find controllers that place closed loop poles within desired intervals for plants with unknown but bounded parameter uncertainties the algorithms are computationally reasonable and provide a useful addition to currently existing control cad tools

on the use of hadamard expansions in hyperasymptotic evaluation ii complex variables this paper extends the method of hyperasymptotic evaluation using absolutely convergent hadamard expansions developed in the first part to the confluent hypergeometric functions of complex argument z it is shown that the representation of this class of functions involves an infinite number of hadamard expansions associated with a decreasing sequence of subdominant exponential levels for large z numerical examples involving the bessel functions are given to illustrate the attainable levels of accuracy

pole assignment using dynamic output feedback compensators abstract the design of dynamic output feedback compensators for the pole assignment of linear time invariant multivariable systems is considered a systematic procedure is developed for the synthesis of the transfer function matrix of the compensator a certain number of poles can be arbitrarily assigned by the proposed compensator moreover in order to assign more poles using a compensator of the same order as before a new approximate assignment approach based on the least square error algorithm is proposed a numerical example is given to demonstrate the effectiveness of the proposed approaches