time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

examples of extreme cases in i 1 and h optimization abstract we are guided by the simple bound h l1 2n 1 h h established in 1 for finite dimensional systems where h l1 is the peak gain of the system and h h is the maximum frequency response of the system and n is the mcmillan degree to establish bounds on closed loop systems resulting from l1 and h minimization furthermore we illustrate that the effectiveness of adding frequency constraints in addition to the interpolation constraints in the l 1 minimization problem depends on the bandwidth of the plant

approximation methods of scalar mixed h sub 2 l sub 1 problems for discrete time systems the scalar mixed h sub 2 l sub 1 problem for discrete time systems is considered the continuity property of the optimal value with respect to changes in the l sub 1 constraint is studied an upper approximation method and a lower approximation method of the optimal value are given suboptimal values and superoptimal values of the problem can be obtained by solving a sequence of finite dimensional quadratic programming problems

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

definable sets in ordered structures on introduit la notion de theorie o minimale des structures ordonnees une telle theorie etant telle que les sous ensembles definissables de ses modeles soient particulierement simples

on nonlinear state feedback controllers for persistent disturbance rejection abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant in the state feedback case there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance in the case of d 12 square and invertible we show that it is enough to have the nonlinearity on a particular substate which can be used to significantly simplify the design problem

non minimal factorization approach to the l gain of discrete time linear systems a method is presented to compute the gain of discrete time linear mimo systems which is based on a newly derived sequence of factorizations for g z by resorting to a chain scattering representation of the system the proposed approach offers a criterion enabling one to cope with the static output feedback 1 control design by solving a finite set of linear inequalities numerical examples are reported as well as an application to the synthesis of a performing decentralized 1 controller

finite time blow up for a thin film equation with initial data at arbitrary energy level abstract in this paper we consider the initial boundary value problem for a class of thin film equations in r n with a p laplace term and a nonlocal source term u q 2 u 1 u q 2 u dx we prove that there exist weak solutions for the problem with arbitrarily initial energy that blow up in finite time we also obtain the upper bounds for the blow up time

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

approximation and identification of continuous time systems an approximation approach to the identification of stable continuous time possibly infinite dimensional systems is studied for this purpose concrete exponential leg endre series methods are proposed and analysed here for the l1 and l2 approximations of continuous time systems rate of approximation results are given for the proposed methods for an important class of delay systems the proposed exponential legendre series method for the l2 approximation has a certain optimal rate of approximation property for this class of delay systems these results show that exponential legendre series techniques have promising properties in connection with the l1 and l2 identifications of stable continuous time systems the proposed l1 identification method has a direct application to the robust design of control systems

h optimal feedback controllers for linear multivariable systems this paper treats the problem of designing for a linear multivariable plant a feedback controller which minimizes the h infty norm of a weighted sensitivity matrix there exists a family of optimal improper feedbacks this family is determined by application of a theory of ball and helton a method for computing optimal feedbacks is described in detail and a numerical example is included it is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

robust fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances a novel decoupled approach unlike the l 2 gain h control case the l gain control problem is dealing with persistent bounded disturbances this study introduces l gain fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables do not depend on the state variables estimated by a fuzzy observer a novel decoupled method is proposed in this study to transform the non lmi conditions into some lmi forms by the proposed decoupled method and the genetic algorithm the l gain fuzzy observer based fuzzy control problem can be easily solved by an lmi based method

a rigorous solution of the infinite time interval lq problem with constant state tracking a linear quadratic constant state tracking problem is considered over an infinite time horizon it is shown that the solution cannot be obtained as a limit from a finite time horizon problem as in general the limiting problem is ill posed to obtain a rigorous solution the problem is split in two natural well posed subproblems one optimal control problem addresses the transient and the other optimal control problem concerns the steady state behavior it is shown that the transient problem and the steady state problem are solved by the same control law

rational approximation of l sub 1 optimal controllers for siso systems the l sub 1 optimal control problem with rational controllers for continuous time systems is considered in which it is shown that the optimal l sub 1 performance index with rational controllers is equal to that of irrational controllers a sequence of rational controllers that approximates the optimal index is constructed convergence properties of such a sequence are studied that the corresponding sequence of objective transfer functions is shown to converge in weak topology in bv r sub in the time domain and uniformly in a wider sense in the frequency domain

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

robust fuzzy observer based fuzzy control design for nonlinear discrete time systems with persistent bounded disturbances to date nonlinear l infin gain control problems have not been solved by the conventional control methods for nonlinear discrete time systems with persistent bounded disturbances this study introduces fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer to deal with the nonlinear l infin gain control problem the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables first the takagi sugeno t s fuzzy model is employed to represent the nonlinear discrete time system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l infin gain of the closed loop system under some nonlinear matrix inequality non lmi constraints a novel decoupled method is proposed in this study to transform the non lmi conditions into some linear matrix inequality lmi forms by the proposed decoupled method and the genetic algorithm the l infin gain fuzzy observer based fuzzy control problem for the nonlinear discrete time systems can be easily solved by an lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l infin gain control problems from linear discrete time systems to nonlinear discrete time systems a simulation example is given to illustrate the design procedures and to confirm the l infin gain performance of the proposed method

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

h sub 2 optimal zeros although the problem of pole placement has received enormous attention the problem of zero placement has been relatively neglected the latter however could be of substantial importance in some design problems such as actuators and sensors positioning in this paper the authors characterize the zeros that ensure h sub 2 optimality of transfer functions and analyze qualitative properties of the resulting systems

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