on the structure of h sup infinity control systems and related extensions an existence condition of a h sup infinity controller which achieves a prescribed norm bound of the closed loop transfer function is derived in the frequency domain based on a generalization of the notion of j lossless systems this condition is regarded as a frequency domain representation of the well known existence condition in the state space represented in terms of the two algebraic riccati equations a notion of j orthogonal complement which is introduced as a generalization of the usual orthogonal complement play an important role in clarifying the fundamental frequency domain structure of the model matching problem and simplifying the computation of controllers the results are extended to the nonstandard case where the direct feedthrough from the input to the error or from the exogenous signal to the output is no longer of full rank it is shown that the proper controller achieving the prescribed norm bound exists even in this case in nonstandard cases the controller order can be smaller than the plant order

one step extension approach to optimal hankel norm approximation and h sup infinity optimization problems a methodology is presented for hankel approximation and h sup infinity optimization problems that is based on a new formulation of a one step extension problem which is solved by the sarason interpolation theorem the parameterization of all optimal hankel approximants for multivariable systems is given in terms of the eigenvalue decomposition of an hermitian matrix composed directly from the coefficients of a given transfer function matrix phi rather than starting with the state space realization of phi the authors use polynomial coefficients of phi as input data in terms of these data a natural basis is given for the finite dimensional sarason model space and all computations involve only manipulations with finite matrices

strong convergence to global solutions for multidimensional flows of compressible viscous fluids with polytropic equations of state and discontinuous initial data we extend to general polytropic pressures p k 1 the existence theory of 8 for isothermal 1 flows of navier stokes fluids in two and three space dimensions with fairly general initial data specifically we require that the initial density be close to a constant in l2 and l and that the initial velocity be small in l2 and bounded in l2n in two dimensions the l2 norms must be weighted slightly solutions are obtained as limits of approximate solutions corresponding to mollified initial data the key point is that the approximate densities are shown to converge strongly so that nonlinear pressures can be accommodated even in the absence of any uniform regularity information for the approximate densities

robust stabilization of linear multivariable systems relations to approximation the stabilization of a linear system modelled as g a where g is a known rational transfer function and a is a perturbation satisfying w a2 g1 or equivalently there does not exist g with fewer poles in c than g such that w1 g g w2 a simple characterization of all robustly stabilizing controllers is then derived and state space formulae for maximally robust controllers are given finally reduced order controllers are considered

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

selection of variables for stabilizing control using pole vectors for a linear multivariable plant it is known from earlier work that the easy computable pole vectors provide useful information about in which input channel actuator a given mode is controllable and in which output channel sensor it is observable in this note we provide a rigorous theoretical basis for the use of pole vectors by providing a link to previous results on performance limitations for unstable plants

existence of the global solution for the parabolic monge ampere equations on compact riemannian manifolds abstract on a compact riemannian manifold m g we consider the existence and nonexistence of global solutions for the parabolic monge ampere equation t log det g hess det g p f x x 0 0 x here p 1 and are real parameters f 0 m 0 are smooth functions on m if 0 then the solution of exists for all times t and t t converges exponentially towards a solution of its stationary equation as t in the case of 0 it does not have the global solution of thus we obtain the nonexistence of the positive solution for the stationary equation of

a state space formulation for optimal hankel norm approximations the optimal hankel norm approximation problem studied in 1 is reformulated in a state space setting the crucial extension theorem is reestablished in this framework the minimal degree optimal approximation is then derived in terms of state space parameters

a duality theory for robust stabilization and model reduction fuhrmann 1991 1993 developed a duality theory in the context of hanel norm approximation and nehari complementation problems the class of functions involved were the scalar antistable transfer functions this work was extended using normalized coprime factorizations by fuhrmann and ober 1993a to the class of all minimal transfer functions in this paper we extend the scope of the duality theory significantly the paper presents a unified approach to problems of hankel norm approximation model reduction and robust control of rational multivariable transfer functions the unification is achieved by considering two classes of transfer functions and corresponding normalized coprime factorization using the youla kucera parametrization of all stabilizing controllers we single out a unique controller by imposing a mcmillan degree minimization restriction on the doubly coprime factorizations with this controller we construct an associated stable transfer function which we call the characteristic function many problems on the original system can be reduced to the study of the characteristic function

on the robust stability of linear time invariant plants with unstructured uncertainty we consider general families of linear time invariant plants described by a nominal plant model with unstructured uncertainty we show under a rather weak assumption that when a family of systems is not robustly stabilizable by any linear time invariant feedback controller then no nonlinear time varying controller can robustly stabilize the given family

remarks on orthogonal polynomials and balanced realizations given a proper antistable rational transfer function g a balanced realization of g is constructed as a matrix representation of the abstract shift realization introduced by fuhrmann 1976 the required basis is constructed as a union of sets of polynomials orthogonal with respect to weights given by the squares of the absolute values of minimal degree schmidt vectors of the corresponding hankel operators this extends results of fuhrmann 1991 obtained in the generic case

on spherically symmetric solutions of the compressible isentropic navier stokes equations we prove the global existence of weak solutions to the cauchy problem for the compressible isentropic navier stokes equations in n n 2 3 when the cauchy data are spherically symmetric the proof is based on the exploitation of the one dimensional feature of symmetric solutions and use of a new multidimensional property induced by the viscous flux the present paper extends lions existence theorem 15 to the case 1 n for spherically symmetric initial data where is the specific heat ratio in the pressure n 3 2 for n 2 and n 9 5 for n 3 dedicated to professor rolf leis on the occasion of his 70th birthday

l optimization and hankel approximation an important l infty optimization problem arising in feedback system design is shown to be equivalent to an optimal hankel norm approximation problem this enables the problem to be solved using state space methods based on balanced realizations

h model reduction for discrete time singular systems this paper investigates the problem of h sub infinity model reduction for linear discrete time singular systems without decomposing the original system matrices necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set when these conditions are feasible an explicit parametrization of the desired reduced order models is given particularly a simple lmi condition without rank constraint is derived for the zeroth order h sub infinity approximation problem finally an illustrative example is provided to demonstrate the applicability of the proposed approach

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

robust stabilization of discrete generalized systems the robust stabilization problem for generalized discrete time systems described by polynomial or improper transfer function matrices subject to perturbations acting on the normalized coprime factors is solved the maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate riccati equations

robust synchronization of coprime factor perturbed networks this paper deals with robust synchronization of directed and undirected multi agent networks with uncertain agent dynamics given a network with identical nominal dynamics we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics these perturbations are assumed to be stable and have h infinity norm that is bounded by an a priori given desired tolerance we derive state space equations for dynamic observer based protocols that achieve robust synchronization in the presence of such uncertainty we obtain an achievable interval i e an interval such that for each value of the tolerance contained in this interval there exists a robustly synchronizing protocol c 2016 elsevier b v all rights reserved

h optimal control part 2 solution for controllers abstract the problem is considered of bounding the h norm of the transfer function t y1u1 relating the output y 1 to the input u 1 for the feedback configuration shown in fig 1 subject to the closed loop system being internally stable a new criterion for internal stability is derived in terms of the q parameterization where q k i p22 k 1 by means of such a stability theory it is shown that the h control problem can be decomposed into two one sided model matching problems of the form considered in part 1 hung 1989 of the paper a closed form state space solution with a tight mcmillan degree bound is obtained for h optimal or suboptimal controllers an iterative algorithm for obtaining the h optimal controller is provided computationally the algorithm requires the solution of only two algebraic riccati equations in each iteration for which the upper bound on t y1u1 is adjusted

a computational algorithm for the super optimal solution of the model matching problem abstract in this paper we develop a computational algorithm to implement the strengthened minimization technique 1 in the model matching problem which arises in robust controller design and weighted sensitivity minimization a general algorithm is proposed for constructing unitary matrices and the extremal functions for the h optimization problem are diagonalized using the constructed unitary matrices we impose stronger minimization conditions to force the solution of the optimization problem to be unique and explain their physical significance

existence results for viscous polytropic fluids with vacuum abstract we consider the full navier stokes equations for viscous polytropic fluids with nonnegative thermal conductivity we prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition the initial density need not be positive and may vanish in an open set moreover our results hold for both bounded and unbounded domains

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

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

global well posedness of classical solutions with large oscillations and vacuum to the three dimensional isentropic compressible navier stokes equations we establish the global existence and uniqueness of classical solutions to the cauchy problem for the isentropic compressible navier stokes equations in three spatial dimensions with smooth initial data that are of small energy but possibly large oscillations with constant state as far field which could be either vacuum or nonvacuum the initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large in particular the initial density can even have compact support these results generalize previous results on classical solutions for initial densities being strictly away from vacuum and are the first for global classical solutions that may have large oscillations and can contain vacuum states 2012 wiley periodicals inc

finite dimensional controller design for infinite dimensional systems the circle criterion approach abstract the hilbert space generalization of the circle criterion is used for the finite dimensional compensator design for unstable infinite dimensional systems a design algorithm which generalizes the small gain based algorithm in 5 is presented

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

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

a modification of the nevanlinna algorithm on the solution of the h sup infinity sub m n optimization problem a modification of the nevanlinna algorithm is presented for the solution of the h sup infinity sub m m optimization problem this is an essential modification when the nevanlinna algorithm is applied to find the extremal function of the matrix h sup infinity interpolation problem which deals with the case that the interpolation points have multiplicities for the computation of the minimal h sup infinity norm a pure matrices computational algorithm is used where the formulation is solely in terms of the coefficients of the inner function

maximally robust controllers for multivariable systems the set of all optimal controllers which maximize a robust stability radius for unstructured additive perturbations may be obtained using standard hankel norm approximation methods these controllers guarantee robust stability for all perturbations which lie inside an open ball in the uncertainty space say of radius r 1 necessary and sufficient conditions are obtained for a perturbation lying on the boundary of this ball to be destabilizing for all maximally robust controllers it is thus shown that a worst case direction exists along which all boundary perturbations are destabilizing by imposing a parametric constraint such that the permissible perturbations cannot have a projection of magnitude larger than 1 delta r 1 0 delta leq1 in the most critical direction the uncertainty region guaranteed to be stabilized by a subset of all maximally robust controllers can be extended beyond the ball of radius r1 the choice of the best maximally robust controller in the sense that the uncertainty region guaranteed to be stabilized becomes as large as possible is associated with the solution of a superoptimal approximation problem expressions for the improved stability radius are obtained and some interesting links with mu analysis are pursued

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

robust control of flexible structures a case study a comparison is made between three partial differential equation models for a flexible beam with different types of damping and varying parameter values robust controllers can be designed to stabilize all linear systems whose transfer functions lie within a ball in the l norm given a nominal model for our flexible beam we calculate which sets of models can be stabilized by the same finite dimensional robust controller by stabilize we mean here that the poles of the system are moved to the left of the line re s 0

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

functional models in linear algebra abstract this paper examines the role of functional models in linear algebra and some related areas of application notably linear systems theory this approach adopts an intermidiate level of abstraction somewhere between abstract module theory on the one hand and matrix theory on the other it is a powerful method which simplifies many proofs provides insights and illuminates the less obvious connections between linear algebra and operator theory approximation theory moment problems interpolation and control theory

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

global existence for 1d compressible isentropic navier stokes equations with large initial data we prove the global existence of weak solutions of the cauchy problem for the navier stokes equations of compressible isentropic flow of a polytropic gas in one space dimension the initial velocity and density are assumed to be in l2 and l2 n bv respectively modulo additive constants in particular no smallness assumptions are made about the intial data in addition we prove a result concerning the asymptotic decay of discontinuities in the solution when the adiabatic constant exceeds 3 2

boundary asymptotical behavior of large solutions to complex hessian equations we consider the exact asymptotic behavior of subharmonic solutions to boundary blow up problems for the complex hessian equation in bounded domains

an elementary state space approach to rh optimal control this paper presents a new elementary approach to the h infinity optimal control problem no knowledge about function spaces is needed to derive the solutions only a few results in linear system theory some matrix manipulations and the classical cauchy integral theorem are used

frequency domain uncertainty and the graph topology a new metric on linear time invariant systems is defined this metric is no greater than the gap metric and is in fact the smallest metric for which a certain robust stabilization result holds unlike other known metrics which induce the graph topology it has a clear frequency response interpretation this allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric

remarks on computing coprime factors for distributed parameter systems presents an indirect method for computing coprime factors for a class of linear time invariant distributed parameter systems the method overcomes the numerical instability of an existing direct decomposition method it is shown that coprime factorization can be reduced to constructing simultaneously stabilizing finite dimensional controllers for which an efficient iterative procedure is developed

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

the general distance problem in h optimal control theory abstract the general distance problem that arises in h optimal control theory is considered transformations that reduce the general h problem to the general distance problem are reviewed and an iterative scheme called iteration is considered in which the general distance problem is reduced to a standard best approximation problem the iteration is viewed as a problem of finding the zero crossing of a function this function is shown to be continuous monotonically decreasing convex and bounded by some very simple functions these properties make it possible to obtain very rapid convergence of the iterative process the issues of model reduction and approximation in h synthesis will also be addressed

on the robust stabilizability of uncertain linear time invariant plants using nonlinear time varying controllers abstract we consider general families of linear time invariant plants described by a nominal plant model with additive or multiplicative unstructured modeling uncertainty we show that such families of plants are robustly uniformly stabilizable by nonlinear time varying controllers if and only if they are robustly stabilizable by linear time invariant ones some auxiliary results on hankel and l norm approximation are also obtained

the failure on continuous dependence on initial data for the navier stokes equations of compressible flow it is shown that physical solutions of the navier stokes equations for one dimensional compressible flow need not depend continuously on their initial data at least when vacuum states are allowed specifically two fluid regions initially separated by a third region of very low density 6 are considered it is shown that as delta to 0 the unique solutions corresponding to delta 0 do not in fact converge to a physical solution but rather to a nonphysical weak solution in which the two fluids cannot collide independent of their initial velocities and whose separate momenta need not be conserved a particular consequence is that solutions of the cavity problem delta 0 are not unique

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

uncertain feedback loops and robustness in general linear systems abstract our main results are a riccati equation based robust stability criterion and a robust stabilization scheme in systems with uncertain loop gain these issues are considered in the general framework of time varying and possibly infinite dimensional linear systems the current analysis is consequential to the recent development of a time domain variational approach to h control the report includes also remarks on the trade off between the type of uniform stability required lyapunov vs exponential and the type of perturbations considered real vs complex and on the small gain criterion in time varying systems

a simple algorithm on minimal balanced realization for transfer function matrices given a transfer function matrix it is shown that its minimal balanced realization can be obtained directly from the singular values and the singular vectors of a constant matrix constructed from the coefficients of the least common denominator polynomial the algorithm is based on the close relationship of controllability and the observability gramians to the singular value decomposition of the associated infinite block hankel matrix

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

global well posedness of classical solutions to the compressible navier stokes equations in a half space abstract in this paper we establish the global well posedness of classical solutions to the half space problem with the boundary condition proposed by navier for the isentropic compressible navier stokes equations in three spatial dimensions initial data are of small energy but possibly large oscillations

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 output regulation for a class of linear multivariable systems in the design of robust regulators the solution of anh norm optimization problem of the formmin q r h t11 t12qt21 is needed to get an optimal controller a difficulty in doing this is that t12 j will be singular at the poles of the external signals in 11 a lower bound for this norm has been found in this paper it will be shown that for stable plants this bound is an infimum and can be approximated as near as possible thus a necessary and sufficient condition for robust regulation is found for a class for a class of linear mimo systems moreover if the external signals are step functions an h optimal controller can be obtained

blowup of smooth solutions to the compressible navier stokes equation with compact density we present a sufficient condition on the blowup of smooth solutions to the compressible navier stokes equations in arbitrary space dimensions with initial density of compact support as an immediate application it is shown that any smooth solutions to the compressible navier stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support and an upper bound which depends only on the initial data on the blowup time follows from our elementary analysis immediately another implication is that there is no global small decay in time or even bounded in the case that all the viscosity coefficients are positive smooth solutions to the compressible navier stokes equations for polytropic fluids no matter how small the initial data are as long as the initial density is of compact support this is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum the blowup of smooth solutions to the compressible euler system with initial density and velocity of compact support is a simple consequence of our argument 1998 john wiley sons inc

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

pointwise stabilizability of families of linear time invariant plants the topic of robust pointwise stabilizability of families of linear time invariant lti plants arising from unstructured modeling uncertainty is addressed the results presented extend some earlier work and show that there is no advantage in using general nonlinear time varying nltv controllers over lti ones for certain problems of robust pointwise stabilization

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

the explicit structure of inner matrices and its application in h sup infinity optimization an expression for inner matrices is obtained which allows a detailed investigation of their structure the expression is used to solve the h sup infinity interpolation problem in a simple way a solution to this problem is obtained explicitly in terms of interpolation parameters without solving any equation it is found that the resulting solution encounters a reduction in its order at the critical point and the characteristics of the resulting reduced order solution are investigated

directional interpolation approach to h optimization and robust stabilization it is shown that under a mild condition h infty optimization and robust stabilization are equivalent to a directional interpolation problem which is a matrix extension of the classical pick nevanlinna interpolation problem a classical iterative method which is an extension of the schur nevanlinna algorithm is given for solving the problem this method does not require the inner outer factorization nor the balanced realization of the original plant a circuit theoretical parameterization of all solutions is derived that is expected to enhance the physical insight to the h infty optimal control and robust stabilization this parameterization has the degree much less than the one obtained previously

the complex monge ampere equation with infinite boundary value abstract in this article we consider the complex monge ampere equation with infinite boundary value in bounded pseudoconvex domains we prove the existence of strictly plurisubharmonic solution to the problem in convex domains under suitable growth conditions we also obtain for general pseudoconvex domains some nonexistence results which show that these growth conditions are nearly optimal

some uniform estimates and blowup behavior of global strong solutions to the stokes approximation equations for two dimensional compressible flows abstract this paper concerns the global existence and the large time behavior of strong and classical solutions to the two dimensional 2d stokes approximation equations for the compressible flows we consider the unique global strong solution or classical solution to the 2d stokes approximation equations for the compressible flows together with the space periodicity boundary condition or the no stick boundary condition or cauchy problem for arbitrarily large initial data first we prove that the density is bounded from above independent of time in all these cases secondly we show that for the space periodicity boundary condition or the no stick boundary condition if the initial density contains vacuum at least at one point then the global strong or classical solution must blow up as time goes to infinity

the robust optimal control of uncertain systems state space method the robust optimal control of linear uncertain systems with l sub 2 bounded uncertainties is addressed the optimal state feedback control law in the so called worst disturbance case is derived the lql method minimax state estimation maximin state feedback closed loop control scheme lql means linear quadratic l sub 2 bounded uncertainties is proposed in a sense the lql method uses the idea of the linear quadratic gaussian lqg method to treat h sub infinity optimizing design problems

a polynomial approach to hankel norm and balanced approximations abstract a new unified approach to problems of hankel norm and balanced approximations is presented which is based on a combination of polynomial algebra and the geometry of invariant subspaces contrary to state space methods where contact with external properties of systems is indirect the approach presented yields new insights into basic properties of hankel norm approximation and balanced realizations several approximation results are interpreted geometrically in terms of projections also duality results in this area are printed out

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given

minimax frequency domain performance and robustness optimization of linear feedback systems it is shown that feedback system design objectives such as disturbance attenuation and rejection power and bandwidth limitation and robustness may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis this leads to a minimax frequency domain optimization problem whose solution is reduced to the solution of a polynomial equation

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