minimization of a regulated response to a fixed input the problem of minimizing a regulated output due to a specific bounded input is solved in the siso single input single output discrete time case it is shown that in most situations the optimal solution will not exist but given any epsilon 0 it is possible to find a suboptimal solution with performance within epsilon of the optimal performance the proposed approach is extended to the problem of shaping the error transient response it is shown how time domain templates can be used in this problem in the same way that frequency weighting functions are used in the h sup infinity and h sup 2 problems

a global implicit function theorem without initial point and its applications to control of non affine systems of high dimensions control system design for non affine systems is a difficult problem because of the lack of mathematical tools the key to the problem is solving for an implicit function but the known results for implicit functions are not applicable for higher dimensional systems except for single input and single output systems in this paper a new version of a global implicit function theorem in higher dimension is presented and proved this result can be applied to show the controllability of a class of non affine multi input and multi output mimo system so that approximation based control system design can be applied with ease

a family of fourth order steffensen type methods with the applications on solving nonlinear odes abstract in this paper a family of fourth order steffensen type two step methods is constructed to make progress in including ren wu bi s methods h ren q wu w bi a class of two step steffensen type methods with fourth order convergence appl math comput 209 2009 206 210 and liu zheng zhao s method z liu q zheng p zhao a variant of steffensens method of fourth order convergence and its applications appl math comput 216 2010 1978 1983 as its special cases its error equation and asymptotic convergence constant are deduced the family provides the opportunity to obtain derivative free iterative methods varying in different rates and ranges of convergence in the numerical examples the family is not only compared with the related methods for solving nonlinear equations but also applied in the solution of bvps of nonlinear odes by the finite difference method and the multiple shooting method

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

a new technique to obtain derivative free optimal iterative methods for solving nonlinear equations abstract a new technique to obtain derivative free methods with optimal order of convergence in the sense of the kung traub conjecture for solving nonlinear smooth equations is described the procedure uses steffensen like methods and pade approximants some numerical examples are provided to show the good performance of the new methods

single input single output h control with time domain constraints standard h optimization cannot handle specifications or constraints on the time response of a closed loop system exactly in this paper the problem of h optimization subject to time domain constraints over a finite horizon is considered following an idea from helton and sideris 1989 ieee trans aut control ac 34 427 434 the problem is transformed into a finite dimensional optimization program that is shown to be convex although generically nondifferentiable the objective function is constructed via state space methods and several properties of the optimal constrained controller are discussed together with a robust algorithm for computation it is shown how satisfying the constraints over a finite horizon can imply overall good behavior

steffensen type methods for solving non linear equations families of steffensen type methods for solving non linear equations are obtained one family consists of second order method involving no derivatives while other consists of third order methods involving only the first derivatives also a derivative free third order method is provided the theory is supported by an example comparing the existing methods with the present one

state space approach to discrete time h control abstract state space solutions to a discrete time problem are given for a given number 0we give a characterization of all controllers such that the norm of the closed loop transfer function is less than the approach taken is based on the solution of two riccati equations using the stable deflating subspace of a symplectic pencil this ensures that no unnecessary assumptions on the a matrix on the realization of the transfer function are needed while the results are the direct analogues of those in the continuous time the state space derivation is considerably more difficult

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

infinite dimensional convex optimization in optimal and robust control theory many engineering problems can be shown to be equivalent to solving semidefinite programs sps i e convex optimization problems involving linear matrix inequalities lmis powerful computation tools are available for such problems in the finite dimensional case however the problems arising in optimal and robust control theory are often infinite dimensional and so adequate computation tools are not available the key to tackling such problems with finite computation tools is to have a primal dual formulation of the problem without duality gap in this paper we study infinite dimensional sps and present a lifting technique to recast sps as parameterized linear programs lps this enables the wealth of theoretical tools available for infinite dimensional lps to be extended to infinite dimensional sps in particular we develop some new sufficient conditions for the lack of a duality gap for infinite dimensional sps and give an exact characterization of the primal and dual problems for these cases both primal and dual problems are formed as infinite dimensional sp problems with finite truncations to each giving upper and lower bounds respectively on the exact solution to the infinite dimensional problem thus these results can form the basis of practical computation schemes for infinite dimensional problems which require only finite dimensional computation tools to illustrate the power of these tools we apply the results to two previously unsolved optimization problems namely minimizing the l sub 1 norm of a closed loop system subject to bounds on the frequency response magnitude at a finite number of points and or bounds on the h sub 2 norm

the four block model matching problem in l 1 and infinite dimensional linear programming the purpose of this work is fourfold first the reader is introduced to the present state of the theory behind the solution of the general model matching problem in l 1 this solution is based on the fact that the model matching problem can be recast as an infinite dimensional linear programming problem however the transformation into linear programming form is highly nonunique which leads to the second question of discussion namely how to find a good linear programming formulation it is shown that the presently available formulations contain some redundancies that limit the applicability of the theory and lead to linear programming systems containing unnecessary degeneracies the third object of this work is to study problems related to the computational complexity of two different approximation methods for the solution of the infinite dimensional linear programming systems both of these methods are needed in order to get two sided error bounds on the cutoff error one complication is that ev

a quadratic programming approach for solving the l sub 1 multiblock problem the authors present a new method to compute solutions to the general multiblock l sub 1 control problem the method is based on solving a standard h sub 2 problem and a finite dimensional semidefinite quadratic programming problem of appropriate dimension the new method has most of the properties that separately characterize many existing approaches in particular as the dimension of the quadratic programming problem increases this method provides converging upper and lower bounds on the optimal l sub 1 norm and for well posed multiblock problems ensures the convergence in norm of the suboptimal solutions to an optimal l sub 1 solution the new method does not require the computation of the interpolation conditions and it allows the direct computation of the suboptimal controller

minimization of the worst case peak to peak gain via dynamic programming state feedback case considers the problem of designing a controller that minimizes the worst case peak to peak gain of a closed loop system in particular we concentrate on the case where the controller has access to the state of a linear plant and it possibly knows the maximal disturbance input amplitude we apply the principle of optimality and derive a dynamic programming formulation of the optimization problem under mild assumptions we show that at each step of the dynamic program the cost to go has the form of a gauge function and can be recursively determined through simple transformations we study both the finite horizon and the infinite horizon case under different information structures the proposed approach allows us to encompass and improve earlier results based on viability theory in particular we present a computational scheme alternative to the standard bisection algorithm or gamma iteration that allows us to compute the exact value of the worst case peak to peak gain for any finite horizon we show that the sequence of finite horizon optimal costs converges as the length of the horizon goes to infinity to the infinite horizon optimal cost the sequence of such optimal costs converges from below to the optimal performance for the infinite horizon problem we also show the existence of an optimal state feedback strategy that is globally exponentially stabilizing and derive suboptimal globally exponentially stabilizing strategies from the solutions of finite horizon problems

an efficient derivative free family of fourth order methods for solving systems of nonlinear equations we present a derivative free two step family of fourth order methods for solving systems of nonlinear equations using the well known traub steffensen method in the first step in order to determine the local convergence order we apply the first order divided difference operator for functions of several variables and direct computation by taylor s expansion computational efficiencies of the methods of new family are considered and compared with existing methods of similar structure it is showed that the new family is especially efficient in solving large systems four numerical examples are given to compare the proposed methods with existing methods and to confirm the theoretical results

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

controllability results for the moore gibson thompson equation arising in nonlinear acoustics abstract we show that the moore gibson thomson equation t t t y t t y c 2 y b t y k t t y 2 t u is controlled by a force that is supported on an moving subset t of the domain satisfying a geometrical condition using the concept of approximately outer invertible map a generalized implicit function theorem and assuming that c 2 b 0 the local null controllability in the nonlinear case is established moreover the analysis of the critical value 0 for the linear equation is included

a variant of steffensen s method of fourth order convergence and its applications in this paper a variant of steffensen s method of fourth order convergence for solving nonlinear equations is suggested its error equation and asymptotic convergence constant are proven theoretically and demonstrated numerically the derivative free method only uses three evaluations of the function per iteration to achieve fourth order convergence its applications on systems of nonlinear equations and boundary value problems of nonlinear odes are showed as well in the numerical examples

model invalidation in spl lscr sub 1 using frequency domain data in this note we study the problem of invalidating uncertain models with an additive uncertainty the problem is to check the existence of an uncertainty and a measurement noise which fit to the given model structure and the uncertainty noise description as well as the experimental data used for invalidation we consider a mixed setting in which the uncertainty is characterized in time domain by the spl lscr sub 1 induced system norm while the available data are frequency response samples of the system we show that this problem which by formulation poses an infinite dimensional primal optimization problem can be solved in a dual finite dimensional space with finitely many constraints

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

lmi approach to an h sub spl infin control problem with time domain constraints over a finite horizon the discrete time h sub spl infin control problem is considered with time domain constraints over a finite horizon it is shown that a solution of this problem can be obtained from a system of linear matrix inequalities

sign weighted peak minimization problem for feedback systems this note studies the problem of minimizing a parameterized convex combination of the overshoot and undershoot of a single input single output siso discrete time system to a fixed input we provide a simple condition for the solution existence and characterize the structure of optimal solutions it is shown that a known l sub spl infin suboptimal scheme also works in our problem in addition we make a comparative analysis with the l sub spl infin problem

some novel optimal eighth order derivative free root solvers and their basins of attraction we present two families of derivative free methods with eighth order convergence for solving nonlinear equations each method of the families requires four function evaluations per full iteration that means the families are optimal in the sense of the hypothesis of kung traub 1974 computational results and comparison including cpu time with existing methods confirm the efficient and robust character of new methods moreover the presented basins of attraction also confirm equal or better performance of the methods as compared to other established methods in literature

h sub spl infin optimization with time domain constraints standard h sub spl infin optimization cannot handle specifications or constraints on the time response of a closed loop system exactly in this paper the problem of h sub spl infin optimization subject to time domain constraints over a finite horizon is considered more specifically given a set of fixed inputs w sup i it is required to find a controller such that a closed loop transfer matrix has an h sub spl infin norm less than one and the time responses y sup i to the signals w sup i belong to some prespecified sets spl omega sup i first the one block constrained h sub spl infin optimal control problem is reduced to a finite dimensional convex minimization problem and a standard h sub spl infin optimization problem then the general four block h sub spl infin optimal control problem is solved by reduction to the one block case the objective function is constructed via state space methods and some properties of h sub spl infin optimal constrained controllers are given it is shown how satisfaction of the constraints over a finite horizon can imply good behavior overall an efficient computational procedure based on the ellipsoid algorithm is also discussed

i 1 optimal control of multivariable systems with output norm constraints in this paper we consider the l1 optimal control problem for general rational plants it is shown that for plants with no poles or zeros on the unit circle an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs exactly or approximately optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed loop transfer function no assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators it is shown that constrained problems in which a set of outputs is regulated subject to l norm constraints on another set of outputs can be solved using a slight modification of the same algorithm

a class of two step steffensen type methods with fourth order convergence abstract based on steffensen s method we derive a one parameter class of fourth order methods for solving nonlinear equations in the proposed methods an interpolating polynomial is used to get a better approximation to the derivative of the given function each member of the class requires three evaluations of the given function per iteration therefore this class of methods has efficiency index which equals 1 587 kung and traub conjectured an iteration using n evaluations of f or its derivatives without memory is of convergence order at most 2 n 1 the new class of fourth order methods agrees with the conjecture of kung traub for the case n 3 numerical comparisons are made to show the performance of the presented methods

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

an optimal steffensen type family for solving nonlinear equations abstract in this paper a general family of steffensen type methods with optimal order of convergence for solving nonlinear equations is constructed by using newton s iteration for the direct newtonian interpolation it satisfies the conjecture proposed by kung and traub h t kung j f traub optimal order of one point and multipoint iteration j assoc comput math 21 1974 634 651 that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2 m 1 its error equations and asymptotic convergence constants are obtained finally it is compared with the related methods for solving nonlinear equations in the numerical examples

h sub infinity optimal control as a weighted wiener hopf problem it is shown that h sub infinity optimization is equivalent to weighted h sub 2 optimization in the sense that the solution of the latter problem also solves the former the weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state space realization the authors do not suggest transforming h sub infinity optimization problems to h sub 2 optimization problems as a computational approach rather their results reveal an interesting connection between h sub infinity and h sub 2 optimization problems which is expected to offer additional insight for example h sub 2 optimal controllers are known to have an optimal observer full state feedback structure the result obtained shows that the minimum entropy solution of h sub infinity optimal control problems can be obtained as an h sub 2 optimal solution therefore it can be expected that the corresponding h sub infinity optimal controller has an optimal observer full state feedback structure

controller design with multiple objectives in this paper we study multi objective control problems that give rise to equivalent convex optimization problems we develop a uniform treatment of such problems by showing their equivalence to linear programming problems with equality constraints and an appropriate positive cone we present some specialized results on duality theory and we apply them to the study of three multi objective control problems the optimal l sub 1 control with time domain constraints on the response to some fixed input the mixed h sub 2 l sub 1 control problem and the l sub 1 control with magnitude constraint on the frequency response what makes these problems complicated is that they are often equivalent to infinite dimensional optimization problems the characterization of the duality relationship between the primal and dual problem allows us to derive several results these results establish connections with special convex problems linear programming or linear matrix inequality problems uncover finite dimensional structures in the optimal solution when possible and provide finite dimensional approximations to any degree of accuracy when the problem does not appear to have a finite dimensional structure to illustrate the theory and highlight its potential several numerical examples are presented

a steffensen like method and its higher order variants for solving nonlinear equations we suggest a second order parametric steffensen like method which is derivative free and only uses two evaluations of the function in one step we also suggest a variant of the steffensen like method which is still derivative free and uses four evaluations of the function to achieve cubic convergence moreover a fast steffensen like method with super quadratic convergence and a fast variant of the steffensen like method with super cubic convergence are proposed by using a parameter estimation the error equations and asymptotic convergence constants are obtained for the discussed methods the numerical results and the basins of attraction support the proposed methods

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

a steffensen s type method in banach spaces with applications on boundary value problems in this paper a modified steffensen s type iterative scheme for the numerical solution of a system of nonlinear equations is studied two convergence theorems are presented the numerical solution of boundary value problems by the multiple shooting method using the proposed iterative scheme is analyzed

simplifying the h theory via loop shifting matrix pencil and descriptor concepts the 2 riccati h controller formulae and derivations are simplified via various loop shifting transformations that are naturally expressed in terms of a degree one polynomial system matrix psm closely related to the luenberger descriptor form of a system the technique enables one without loss of generality to restrict attention to the simple case in which d 11 0 d 22 0 d t 12 0 l d 21 0 l d l 12 c1 0 and b 1 d t 21 0 matrix fraction descriptions mfds for the algebraic riccati equation solutions afford another change of variables which brings the 2 riccati h controller formulae into a cleaner more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the riccati solutions pi and q blow up and in cases where l qp is nearly singular numerical difficulties previously associated with verifying the existence conditions p 0 q 0 and maxlpar qp 1 are largely eliminated by e

an optimal and efficient general eighth order derivative free scheme for simple roots abstract the main motivation of this study is to present an optimal scheme in a general way that can be applied to any existing optimal multipoint fourth order iterative scheme whose first substep employs steffensen s method or steffensen like method to further produce optimal eighth order iterative schemes a rational function approximation approach is used in the construction of proposed scheme in addition we also discussed the theoretical and computational properties of our scheme each member of the presented scheme satisfies the optimality conjecture for multipoint iterative methods without memory which was given by kung and traub in 1970 finally we also concluded on the basis of obtained numerical results that our methods have faster convergence in contrast to the existing methods of same order because they have minimum residual errors minimum error difference between two consecutive iterations and minimum asymptotic error constants corresponding to the considered test function

h control with time domain constraints the infinite horizon case abstract it has been shown recently that time domain constraints can be incorporated into h optimal control problems when the constraints are enforced over a finite horizon i e over a finite number of sample instants this is done in sideris and rotstein 1993 rotstein and sideris to appear where the finite horizon problem is reduced into a finite dimensional convex but generically nondifferentiable optimization program in this paper the infinite horizon case is addressed it is shown that when the horizon length goes to infinity the solutions to the finite horizon problems converge to a solution of the infinite horizon problem moreover a simple modification of the finite horizon problems guarantees convergence to a solution that is easily approximated by a finite dimensional transfer function

a higher order sufficient condition for local surjectivity soient 7b h et 7b n des espaces de banach reels et f 7b h 7b n une application telle que f 0 0 et f est c 1 frechet differentiable dans un voisinage ouvert de 0 7b h on donne une condition suffisante a la surjectivite locale qui peut s appliquer dans le cas ou df 0 n est pas surjective

a steffensen type method of two steps in banach spaces with applications this paper is devoted to the analysis of a steffensen type of two steps with order of convergence at least three the main advantage of this method is that it does not need to evaluate any frechet derivative or any bilinear operator the method includes extra parameters in the divided difference in order to ensure a good approximation to the first derivative in each iteration we prove using recurrence relations a semilocal convergence result in banach spaces and do a detailed study of the domain of parameters associated to this result finally some numerical results including differentiable and nondifferentiable operators are presented special attention is paid in the approximation of solutions of boundary problems using the multiple shooting method and in the approximation of a nonlinear model related with image processing

on the design of linear multivariable feedback systems via constrained nondifferentiable optimization in h sup infinity spaces the design discussed is of linear lumped time invariant multivariable feedback systems subject to various frequency and time domain performance specifications the approach is based on the use of stabilizing controller parametrizations which result in the formulation of feedback system design problems as convex nondifferentiable optimization problems these problems are solvable by recently developed nondifferentiable optimization algorithms for the constrained minimization of regular uniformly locally lipschitz continuous functions in r sup n

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

state space formulae for discrete time h optimization abstract state space formulae and proofs are given for ail the important steps in discrete time h 8 optimization the steps closely follow the algorithms for continuous time systems but there are some technically involved differences in the detail that make their derivation non trivial

general efficient class of steffensen type methods with memory for solving systems of nonlinear equations abstract there are a very small number of high quality derivative free methods with memory for solving a system of nonlinear equations numerically motivated and inspired by the fact we propose a more efficient general class of steffensen type multipoint methods with memory this proposed class requires one divided difference and inverse of only one matrix per full iteration we also demonstrate their applicability and illustrate that these methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations numerically for quantitative comparison we have also computed total number of convergent points and convergent percentage along with basins of attractions on a number of test problems to recommend the best quality algorithm

a necessary and sufficient condition for robust bibo stability abstract this paper is concerned with obtaining necessary and sufficient conditions for robustly stabilizing a class of plants characterized by a known linear shift invariant plant with additive perturbations of the form of possibly nonlinear time varying l stable operators we will show that in some sense the small gain theorem is necessary and sufficient even when the perturbations are restiricted to a class of linear operators

a characterization of all solutions to the four block general distance problem all solutions to the four block general distance problem which arises in h infty optimal control are characterized the procedure is to embed the original problem in an all pass matrix which is constructed it is then shown that part of this all pass matrix acts as a generator of all solutions special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all pass transfer functions as an application necessary and sufficient conditions are found for the existence of an h infty optimal controller following that a descriptor representation of all solutions is derived

an analysis of the pole zero cancellations in h optimal control problems of the first kind the aim of this paper is to study the pole zero cancellations which occur in a class of h infty optimal control problems which may be embedded in the configuration of fig 1 h infty control problems are said to be of the first kind if both p 12 s and p 21 s are square but not necessarily of the same size it is primarily this class of problems which will concern us here a general bound on the mcmillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies bf mathcal r s infty leqq rho rho need not be optimal in the l infty norm sense is derived as illustrated in fig 1 bf mathcal r s is the transfer function relating y 1 s to u 1 s if the mcmillan degree of p s in fig 1 is n we show that in the single loop siso case the corresponding unique h infty optimal controller never requires more than n 1 states in the multivariable case there is a continuum of optimal controllers whose mcmil

frequency response algorithms for h sub infinity optimization with time domain constraints a very broad framework for control system design is considered that encompasses frequency response methodologies for h sub infinity optimization that solve various aspects of the control design problem and that are less well known that state space methods the focus is on linear programming lawson s algorithm and trefethen s algorithm a modified lawson s algorithm is proposed and related to trefethan s method the modified algorithm is shown to be significantly faster than linear programming and lawson s algorithm it is also shown how to extend the modified lawson s algorithm so as to handle time domain constraints in addition to frequency domain specifications which distinguishes it from other h sub infinity optimization methods some steps are taken toward dealing with time domain constraints within an h sub infinity optimization framework

on a steffensen s type method and its behavior for semismooth equations abstract a generalization of steffensen s method is proposed our goal is to obtain similar convergence as newton s method but without to evaluate any derivative and without to have stability problems convergence analysis and numerical results for semismooth equations are presented