on the antimaximum principle for the p laplacian with indefinite weight this paper is concerned with the antimaximum principle for the quasilinear prob 1 mathrm e mathrm m delta p u lambda m x u p 2 u h x delta p is the laplacian and m x is aweight function which may change sign we will in particular investigate the question of the uniformity of this principle and provide avariational characterization for the interval of uniformity an identity of picone s type for the mathrm p laplacian plays an important role in our approach

the existence of multiple equilibrium points in a global attractor for some p laplacian equation abstract in this paper we are mainly concerned with some properties of the global attractor for some p laplacian equation with a lyapunov function in a banach space under some suitable assumptions we prove the existence of multiple equilibrium points in a global attractor for some p laplacian equation

explicit solution to the singular discrete time stationary linear filtering problem a closed form solution to the stationary discrete time linear filtering problem is obtained explicitly in terms of the system state space matrices in the limiting singular case where the measurement noise tends to zero simple expressions in closed form are obtained for the kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the kalman filter closed loop matrix is derived the minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure and a remarkably different behavior of the solution in the minimum and nonminimum phase cases is found

a regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its l norm the i th singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one we show that near a local maximum however the largest singular value has a lipschitz second derivative but need not have a third derivative using this regularity result we give a quadratically convergent algorithm for computing the l norm of a transfer matrix

analysis and design of linear multivariable feedback systems in the presence of additive perturbations the paper introduces the concept of normal approximations to the analysis of uncertain linear multivariable feedback systems in order to derive a new criterion for the stability of plants subject to additive perturbations this criterion permits a complete assessment of stability margins in that it provides a measure of tolerance to uncertainty as well as providing a measure of gain phase margins the proposed approach leads to a systematic design procedure which minimizes the effects of uncertainty by attaining the condition of normality or which improves the stability margins by robust gain phase sharing the results presented in this paper are insensitive to small perturbations on the nominal plant model and provide the means for a consideration of information concerning the structure of uncertainty

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

loop transfer recovery techniques for discrete time optimal regulators using prediction estimators for discrete time lqg optimal regulators using current estimators it has been shown that perfect recoveries of the loop transfer matrices at the input or at the output are possible for square minimum phase systems however current estimators cannot be used when the processing time of the controller is significant in this note the loop transfer recoveries using prediction estimators for square minimum phase systems are considered it is shown that although the perfect recoveries are impossible the feedback properties obtained by the recovery techniques are those that can be recovered best in the presence of the delay in the controller

multivariable feedback a personal reminiscence my involvement in the development of linear multivariable feedback theory and its applications is described from a highly personal point of view concentrating on the origin of key ideas and their development in association with many colleagues detailed references are given to all my papers and books and explanatory notes provided where further material may be found

an explicit expression for the minimum phase image of transfer function matrices a simple expression is obtained for the transfer function matrix of the minimum phase image of a left invertible continuous time invariant system with zeros in the right half plane that may be of multiplicities greater than one this expression is obtained by multiplying the system transfer function matrix from the right by a special inner matrix and it is explicitly given in terms of the input zero directions that correspond to the zeros of the system in the right half plane the result provides a simple expression for the inner outer factorization of transfer function matrices and it can thus be used in h sub infinity optimal control

a multiplicity theorem for problems with the p laplacian abstract we consider nonlinear elliptic equations driven by the p laplacian differential operator using degree theoretic arguments based on the degree map for operators of type s we prove the existence of two nontrivial smooth solutions one of which is of constant sign

a sensitivity tradeoff for plants with time delay in this paper we show that the sensitivity function of a scalar feedback system must satisfy an integral constraint when the open loop transfer function is strictly proper and contains a time delay the integral constraint is identical to the classical bode sensitivity integral which holds provided the open loop gain has greater than a one pole rolloff the design implications of the two constraints are somewhat different however and this difference is discussed the relation between open loop phase and a conflict between bandwidth and sensitivity properties is explored

cantor and band spectra for periodic quantum graphs with magnetic fields we provide an exhaustive spectral analysis of the two dimensional periodic square graph lattice with a magnetic field we show that the spectrum consists of the dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant lyapunov function of a suitable kronig penney hamiltonian in particular between any two dirichlet eigenvalues the spectrum is a cantor set for an irrational flux and is absolutely continuous and has a band structure for a rational flux the dirichlet eigenvalues can be isolated or embedded subject to the choice of parameters conditions for both possibilities are given we show that generically there are infinitely many gaps in the spectrum and the bethe sommerfeld conjecture fails in this case

a new stable compensator design for exact and approximate loop transfer recovery abstract in this paper a new compensator structure for loop transfer recovery ltr is proposed the proposed compensator a is open loop stable b guarantees closed loop stability and above all c requires much smaller values of gain than the conventional observer based controller for the same degree of loop transfer recovery the fact that the new compensator requires much smaller values of gain than the conventional controller results in several practical advantages the most important among them being the reduction in controller band width and freedom from the woes of saturation the trade off between the value of gain and the degree of loop transfer recovery as well as the bounds on singular values of sensitivity and complementary sensitivity functions is shown clearly both full and reduced order compensators for ltr when the design specifications are reflected either at the input or at the output point of the given plant are considered numerical examples illustrate the advantages of the new compensator structure the new compensator structure is inspired by a careful and clear understanding of how loop transfer recovery occurs when conventional observer based controllers are used to motivate and deduce our new compensator structure a unified treatment of observer theory for ltr is presented in the context of such a unification some new results are also given

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

spectral properties of the periodic magnetic schrodinger operator in the high energy region two dimensional case the goal is to investigate spectral properties of the operator h i a x 2 a0 x in the two dimensional situation a x a0 x being periodic we construct asymptotic formulae for bloch eigenvalues and eigenfunctions in the high energy region describe properties of isoenergetic curves in the space of quasimomenta and give a new proof of the bethe sommerfeld conjecture

on pseudo algebraically closed extensions of fields abstract the notion of pseudo algebraically closed pac extensions is a generalization of the classical notion of pac fields in this work we develop a basic machinery to study pac extensions this machinery is based on a generalization of embedding problems to field extensions the main goal is to prove that the galois closure of any proper separable algebraic pac extension is its separable closure as a result we get a classification of all finite pac extensions which in turn proves the bottom conjecture for finitely generated infinite fields the secondary goal of this work is to unify proofs of known results about pac extensions and to establish new basic properties of pac extensions e g transitiveness of pac extensions

absolute continuity of the periodic magnetic schrodinger operator we prove that the spectrum of the schrodinger operator with periodic electric and magnetic potentials is absolutely continuous

asymptotically linear elliptic equations without nonresonance conditions abstract in this paper we are concerned with the existence of nontrivial solutions of a semilinear elliptic equation when the nonresonance condition at infinity is not satisfied we consider a strongly resonant case in the first part and a sort of resonance under density assumptions in the second part

logarithmic integrals interpolation bounds and performance limitations in mimo feedback systems we study performance limitation issues found in linear multivariable feedback systems our main contributions include bode and poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions these results characterize and quantify explicitly how open loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance the role of time delay is also studied in this context most notably we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros and in particular on how pole and zero directions are aligned the latter is characterized by angles measuring the mutual orientation between zero and pole directions and it is shown to play a crucial role in multivariable system design

performance limitations in the robust servomechanism problem for discrete time lti systems fundamental limitations for error tracking regulation are obtained for the robust servomechanism problem rsp for a sampled system in studying this problem the cheap control problem for a multi input multi output discrete time system is considered and explicit expressions are obtained for the limiting steady state solution of its associated algebraic riccati equation are as the weight on the control energy tends to zero application of these results is then made to obtain explicit expressions for the limiting performance costs associated with error tracking regulation in the rsp these limitations can be characterized by the system order the dimension of the outputs the number of the system s transmission zeros and the location of the system s nonminimum phase transmission zeros

uniform sobolev inequalities and absolute continuity of periodic operators we establish certain uniform l p l q inequalities for a family of second order elliptic operators of the form d k a d k t on the d torus where d i k c d and a is a symmetric positive definite d x d matrix with real constant entries using these sobolev type inequalities we obtain the absolute continuity of the spectrum of the periodic dirac operator on r d with singular potential the absolute continuity of the elliptic operator div x on d with a positive periodic scalar function x is also studied

robustness of zero shifting via generalized sampled data hold functions in this paper we study robustness and sensitivity properties of a sampled data feedback system with a generalized sampled data hold function gshf we argue that shifting non minimum phase zeros using gshf control can lead to difficulties unless the zero is outside the closed loop bandwidth

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

existence of three nontrivial solutions for asymptotically p linear noncoercive p laplacian equations abstract we consider a nonlinear elliptic problem driven by the p laplacian where the right hand side nonlinearity exhibits a p linear behavior near infinity and the euler functional of the problem need not be coercive and in fact can be indefinite using a combination of minimax arguments with truncation techniques and morse theory we show that the problem has at least three nontrivial smooth solutions two of which have a constant sign our method of proof uses some results on critical groups and the spectrum of the p laplacian due to perera and dancer perera

multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential abstract in this paper we study a nonlinear elliptic problem at resonance driven by the p laplacian and with a nonsmooth potential hemivariational inequality our approach is variational and it is based on the nonsmooth critical point theory for locally lipschitz functions due to chang we prove a theorem guaranteeing the existence of one solution which is smooth and strictly positive then by strengthening the assumptions we establish a multiplicity result providing the existence of at least two distinct solutions our hypotheses permit resonance and asymmetric behavior at and as a byproduct of our analysis we obtain an nonlinear and nonsmooth generalization of a result of brezis nirenberg about h 0 1 versus c 0 1 minimizers of a smooth functional

the periodic schrodinger operators with potentials in the morrey class we consider the periodic schrodinger operator v x in rd d 3 with potential v in the morrey class let be a periodic cell for v we show that for p d 1 2 d 2 there exists a positive constant e depending only on the shape of p and d such that iflim supr 0supx r21 b x r b x r v y pdy1 p e then the spectrum of v is purely absolutely continuous we obtain this result as a consequence of certain weighted l2 sobolev inequalities on the d torus it improves an early result by the author for potentials in ld 2 or weak ld 2 space

asymptotic recovery for discrete time systems an asymptotic recovery design procedure is proposed for square discrete time linear time invariant multivariable systems which allows a state feedback design to be approximately recovered by a dynamic output feedback scheme both the case of negligible processing time compared to the sampling interval and of significant processing time are discussed in the former case it is possible to obtain perfect recovery if the plant is minimum phase and has the smallest possible number of zeros at infinity in other cases good recovery is frequently possible new conditions are found which ensure that the return ratio being recovered exhibits good robustness properties

principal gains and principal phases in the analysis of linear multivariable feedback systems the concepts of principal gain and principal phase are introduced for linear multivariable systems and their use in the analysis of feedback behavior is demonstrated a sufficient nyquist type stability criterion is presented in terms of these quantities and is used to characterize the robustness of the closed loop stability property when the system model is subjected to a linear perturbation either multiplicative or additive at any point in the feedback configuration the results presented are less conservative than those obtained via the small gain theorem

absolute continuity of the spectrum of a landau hamiltonian perturbed by a generic periodic potential consider a non degenerate lattice in mathbb r 2 and a constant magnetic field b with a flux though a cell of that is a rational multiple of 2 we prove that for a generic periodic potential v the spectrum of the landau hamiltonian with magnetic field b and periodic potential v is purely absolutely continuous

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

existence of multiple solutions for quasilinear and semilinear elliptic equations has been studied by many authors cf l 3 4 161 under the assumption that g r r is a continuous function such that g t t closes finite many eigenvalues when t varies from 0 to a the existence of one nontrivial solution for 1 2 was proved by amann and zehnder 3 and thews 21 the existence of two nontrivial solutions was studied by castro and lazer lo and ambrosetti and mancini 4 most of the multiplicity results for problem 1 2 are based on the fact that 1 2 can be rewritten as

design of delta sigma modulators via generalized kalman yakubovich popov lemma this paper is concerned with the design of delta sigma modulators via the generalized kalman yakubovich popov lemma the shaped noise transfer function ntf is assumed to have infinite impulse response and the optimization objective is minimizing the maximum magnitude of the ntf over the signal frequency band by virtue of the gkyp lemma the optimization of an ntf is converted into a minimization problem subject to quadratic matrix inequalities and then an iterative algorithm is proposed to solve this alternative minimization problem each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by the existing numerical software packages moreover specifications on the ntf zeros are also integrated in the design method a design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal to noise ratio

on absolute continuity of the spectrum of three and four dimensional periodic schrodinger operators we consider schrodinger operators in with electric potentials v and magnetic potentials a being periodic functions with a common period lattice and prove absolute continuity of the spectrum of the operators in question when and when the function v has relative bound zero with respect to the free schrodinger operator in the sense of quadratic forms if n 3 and the electric potential v has relative bound zero with respect to the operator if n 4

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

discrete time lqg ltr technique for systems with time delays loop transfer recovery ltr is applied for lqg controllers with prediction estimators for a class of square minimum phase discrete time linear systems with time delays we consider the class of plants described by the triple a b c whose time delay structure is characterized by the following hypothesis on the plant impulse response cb cab cad 2b 0 det cad 1b 0 when the estimator gain is fixed by recovery technique it is shown that the loop transfer matrix at the plant input is equal to the transfer matrix obtained with the optimal digital regulator having d sample controller delays described in 6 the dual result corresponding to the situation where the feedback gain is fixed by recovery technique is also analysed

positive measure spectrum for schrodinger operators with periodic magnetic fields we study schrodinger operators with periodic magnetic field in r2 in the case of irrational magnetic flux positive measure cantor spectrum is generically expected in the presence of an electric potential we show that even without electric potential the spectrum has positive measure if the magnetic field is a perturbation of a constant one

second order nonsmooth optimization for h synthesis the standard way to compute h feedback controllers uses algebraic riccati equations and is therefore of limited applicability here we present a new approach to the h output feedback control design problem which is based on nonlinear and nonsmooth mathematical programming techniques our approach avoids the use of lyapunov variables and is therefore flexible in many practical situations

tradeoffs in linear time varying systems an analogue of bode s sensitivity integral bode s integral characterizes some of the tradeoffs imposed by the open loop dynamics of a linear time invariant system here we present an analogous time domain characterization applicable to time varying systems

remarks on multiple nontrivial solutions for quasi linear resonant problems in this paper morse theory and local linking are used to study the existence of multiple nontrivial solutions for a class of dirichlet boundary value problems with double resonance at infinity and at 0

diamond theorem for a finitely generated free profinite group we extend haran s diamond theorem to closed subgroups of a finitely generated free profinite group this gives an affirmative answer to problem 25 4 9 of fried and jarden in field arithmetic 2nd edn springer berlin heidelberg new york 2005

multiple solutions for quasilinear elliptic problems via critical points in open sublevels and truncation principles abstract we study a quasilinear elliptic problem depending on a parameter of the form p u f u in u 0 on we present a novel variational approach that allows us to obtain multiplicity regularity and a priori estimate of solutions by assuming certain growth and sign conditions on f prescribed only near zero more precisely we describe an interval of parameters for which the problem under consideration admits at least three nontrivial solutions two extremal constant sign solutions and one sign changing solution our approach is based on an abstract localization principle of critical points of functionals of the form e on open sublevels 1 r combined with comparison principles and the sub supersolution method moreover variational and topological arguments such as the mountain pass theorem in conjunction with truncation techniques are the main tools for the proof of sign changing solutions

multiple constant sign and nodal solutions for nonlinear elliptic equations with the p laplacian we consider a nonlinear elliptic equation driven by the p laplacian with dirichlet boundary conditions using variational techniques combined with the method of upper lower solutions and suitable truncation arguments we establish the existence of at least five nontrivial solutions two positive two negative and a nodal sign changing solution our framework of analysis incorporates both coercive and p superlinear problems also the result on multiple constant sign solutions incorporates the case of concave convex nonlinearities

crossover frequency limitations in mimo nonminimum phase feedback systems this paper investigates limitations and design tradeoffs of the closed loop sensitivity performance of linear time invariant nonminimum phase uncertain multiple input multiple output plants with i inputs and m outputs where m spl les l it is shown that if rows i sub 1 i sub k of the plant transfer function form a k spl times l nonminimum phase transfer matrix and if the design is such that the sensitivity gain of k 1 rows among the rows i sub 1 i sub k of the closed loop transfer function is low then by necessity the sensitivity gain of the remaining row is high this sensitivity constraint is quantified with the help of the crossover frequency restriction of a specially constructed single input single output transfer function that includes the right half plane zeros and poles of the k spl times l transfer matrix

on the structure of spectra of periodic elliptic operators the paper discusses the problem of absolute continuity of spectra of periodic elliptic operators a new result on absolute continuity for a matrix operator of schrodinger type is obtained it is shown that all types of operators for which the absolute continuity has previously been established can be reduced to this one it is also discovered that some natural generalizations stumble upon an obstacle in the form of non triviality of a certain analytic bundle on the two dimensional torus

on the spectrum of a class of second order periodic elliptic differential operators under an additional symmetry condition we prove that the spectrum of a second order self adjoint elliptic differential operator with periodic coefficients is purely absolutely continuous

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

sensitivity integrals and transformation techniques a new perspective we provide alternative proofs for the classical bode and poisson type sensitivity integrals and their extensions for both continuous time and discrete time systems our derivation uses the well known properties of laplace and z transformations this derivation helps establish a connection between bode and poisson type sensitivity integrals and laplace and z transforms hence providing an alternative perspective in interpreting these fundamental integral results

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

integral constraints and performance limits on complementary sensitivity discrete time systems abstract we study performance limitation issues for multivariable discrete time feedback systems the complementary sensitivity function is employed as a performance measure and bode and poisson type integral inequalities and h type performance limits are derived the results exhibit frequency dependent constraints as well as best achievable limits on the complementary sensitivity function which are shown to be determined by nonminimum phase zeros unstable poles and time delays in particular the directions of such zeros and poles are seen to play a central role to this effect

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

an overview of periodic elliptic operators the article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas close attention is paid to studying analytic properties of bloch and fermi varieties which influence significantly most properties of such operators the approaches described are applicable not only to the standard model example of schrodinger operator with periodic electric potential v x but to a wide variety of elliptic periodic equations and systems equations on graphs operator and other operators on abelian coverings of compact bases many important applications are mentioned however due to the size restrictions they are not dealt with in details

logarithmic integrals and system dynamics an analogue of bode s sensitivity integral for continuous time time varying systems a new time domain interpretation of bode s integral is presented this allows for a generalization to the class of time varying systems which possess an exponential dichotomy it is shown that the sensitivity function is constrained on average by the spectral values in the dichotomy spectrum of the antistable component of the open loop dynamics

generalizations of browder s degree theory the starting point of this paper is the recent important work of f e browder who extended degree theory to operators of monotone type the degree function of browder is generalized to maps of the form t f g where t is maximal monotone f is of class s bounded and g is an u s c compact multifunction it is also generalized to maps of the form f ng with f of class s and ng the nemitsky operator of a multifunction g x r satisfying various types of sign conditions some examples are also included to illustrate the abstract results

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

guaranteed stability margins for the discrete time linear quadratic optimal regulator the stability properties of the linear quadratic deterministic optimal regulator are investigated in the discrete time case guaranteed phase and gain margins are obtained for the regulator in terms of the singular values of the matrices of the regulator state space description these margins are compared to their continuous time counterparts and their implication on the regulator robustness is discussed

fucik spectrum sign changing and multiple solutions for semilinear elliptic boundary value problems with resonance at infinity in this paper we use fucik spectrum ordinary differential equation theory of banach spaces to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity especially with resonance at infinity and obtain new results on the existence of multiple solutions and sign changing solutions with a weakening of the p s condition in one case we get up to seven nontrivial solutions the techniques have independent interest

analytic properties of the singular values of a rational matrix abstract it is shown that the singular values of a rational matrix g s where s x jy are locally a set of real analytic functions of x and y a brief discussion is given of their global properties

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

discrete time loop transfer recovery for systems with nonminimum phase zeros and time delays abstract the purpose of this paper is to study what happens when the discrete time loop transfer recovery ltr procedure is applied to plants with nonminimum phase zeros and with uniform time delay in all channels explicit expressions are given for the asymptotic behavior of the resulting sensitivity function and loop transfer function these results yield a better understanding of the mechanism of the discrete time loop transfer recovery procedure and the design limitations due to nonminimum phase zeros and time delays

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

technical communique controller synthesis with guaranteed closed loop phase constraints in this paper we present an analysis and synthesis approach for guaranteeing that the phase of a single input single output closed loop transfer function is contained in the interval a a for a given a 0 at all frequencies specifically we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint next we use the kalman yakubovich popov theorem to derive an equivalent time domain condition in the case where a p2 we show that frequency and time domain sufficient conditions specialize to the positivity theorem furthermore using linear matrix inequalities we develop a controller synthesis approach for guaranteeing a phase constraint on the closed loop transfer function finally we extend this synthesis approach to address mixed gain and phase constraints on the closed loop transfer function

constraints on sensitivity characteristics in linear multivariable discrete time control systems abstract this paper is concerned with the limitations on the sensitivity characteristics for linear multivariable discrete time control systems some integral type constraints and the lower bounds of the weighted h norm imposed by the unstable poles the unstable zeros and their directions of the open loop system or the given plant are developed by a factorization approach these constraints and bounds which are tighter than those in the previous work are also characterized by the state space representations the descriptions are closely related to a special type of the algebraic riccati equation and the relation between the sampling period and the sensitivity performance is discussed for digital control systems the constraints on the more general function mixed sensitivity function are investigated in a similar way

ltr design of discrete time proportional integral observers applies the proportional integral pi observer in connection with loop transfer recovery ltr design for discrete time systems both the prediction and the filtering versions of the pi observer are considered we show that a pi observer makes it possible to obtain time recovery i e exact recovery for t spl rarr spl infin under mild conditions two systematic ltr design methods one based on an extension of the linear quadratic gaussian loop transfer recovery lqg ltr and the other based on linear matrix inequality lmi are derived for the discrete time pi observer case explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations