the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

explicit characterization of decentralized coprime factors this paper is concerned with parametrization of all decentralized stabilizing controllers the auxiliary diagonal system which is defined by the diagonal elements of bezout factors plays an important role in the parametrization of decentralized controllers this paper gives an explicit characterization of the auxiliary system

quadratic stabilizability of switched linear systems with polytopic uncertainties in this paper we consider quadratic stabilizability via state feedback for both continuous time and discrete time switched linear systems that are composed of polytopic uncertain subsystems by state feedback we mean that the switchings among subsystems are dependent on system states for continuous time switched linear systems we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices then the switched system is quadratically stabilizable via state feedback for discrete time switched linear systems we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non negative scalars and a common positive definite matrix for both continuous time and discrete time switched systems we propose the switching rules by using the obtained common positive definite matrix

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

a heuristic approach to solving a class of bilinear matrix inequality problems abstract many canonical and modern control problems can be recast into the problem of a group of matrix inequalities some of them are in the form of linear matrix inequalities lmis which can be solved very efficiently by the powerful lmi toolbox in matlab but some others are in the form of bilinear matrix inequalities the characteristic of this latter class of problems is that when the so called communicating variables are fixed the overall problem will be reduced to the problem in lmis thus how to find the communicating variables is the key to solve the whole problem in this paper an optimal estimate for the communicating variables is presented we will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems numerical examples are provided to show the effectiveness of the proposed method

robust controller synthesis via non linear matrix inequalities over thelastseveralyears fixed structure multiplier versions of mixed structured singular value mssv theory have been developed and have led to the development of linear matrix inequalities lmis for the analysis of robust stability and performance these lmis have in turn led to the development of bilinear matrix inequalities bmis for the synthesis of robust controllers the bmi formulation in practice requires the multiplier to lie in the span of a stable basis potentially introducing significant conservatism this paper uses the lmi approach to mssv analysis to develop an approach to robust controller synthesis that is based on the stable factors of the multipliers and does not require the multipliers to be restricted to a basis it is shown that this approach requires the solution of non linear matrix inequalities nmis a continuation algorithm is presented for the solution of nmis this algorithm may be used to solve nmis in general and its usefulness is not limited to the robust controller synt

automorphism invariant representations of real reductive groups we characterize representations of a connected real reductive group which are invariant under an automorphism of finite order the intertwining operators constructed in this characterization are then used to prove a paley wiener theorem for a class of real reductive groups twisted by involutions

brief paper unification of independent and sequential procedures for decentralized controller design this paper is concerned with decentralized control problems there are two typical procedures to design decentralized controllers independent and sequential design procedures as the concepts and the techniques in these two approaches are too different from each other there have been no attempts to unify these approaches this paper proposes an iterative independent design procedure for decentralized control systems which is a unified approach to these conventional approaches

design of nonlinear interconnections guaranteeing the absence of periodic solutions abstract in this paper a novel methodology for scheming interconnection structure for a class of nonlinearly interconnected systems is proposed to guarantee the absence of a specific kind of periodic solutions those types of systems can be viewed as an interconnection of single input single output isolated subsystems with the interconnection structure specified by a square matrix frequency domain inequalities conditions as well as linear matrix inequalities lmis conditions for nonexistence of limit cycles of the second kind in the entire interconnected system are established the main results also define the frequency range on which cycles of the second kind of the system cannot exist based on this lmi approach an estimate of the largest bound of the frequency of cycles of the second kind can be explicitly computed by solving a generalized eigenvalue minimization problem numerical results show the effect of the nonlinear interaction on system behavior and the applicability and validity of the proposed method

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

real paley wiener theorems and local spectral radius formulas we systematically develop real paley wiener theory for the fourier transform on d for schwartz functions l p functions and distributions in an elementary treatment based on the inversion theorem as an application we show how versions of classical paley wiener theorems can be derived from the real ones via an approach which does not involve domain shifting and which may be put to good use for other transforms of fourier type as well an explanation is also given as to why the easily applied classical paley wiener theorems are unlikely to be able to yield information about the support of a function or distribution which is more precise than giving its convex hull whereas real paley wiener theorems can be used to reconstruct the support precisely albeit at the cost of combinatorial complexity we indicate a possible application of real paley wiener theory to partial differential equations in this vein and furthermore we give evidence that a number of real paley wiener results can be expected to have an interpretation as local spectral radius formulas a comprehensive overview of the literature on real paley wiener theory is included

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

special decentralized control problems in discrete time interconnected systems composed of two subsystems in this paper some special decentralized control problems are addressed for discrete time interconnected systems first it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases then a special kind of decentralized control problem is studied this kind of problem can be viewed as harmonic control among independent subsystems research results show that two unstable systems can generate a stable system through some effective cooperations in addition a decentralized controller design method based on linear matrix inequality is also given by using parameter dependent lyapunov function method developed for the study of robust stability a special linear star coupled dynamical network is also considered the central subsystem must be unstable to stabilize the whole network under a special coupling several examples are given to illustrate the results

brief decentralized h controller design a matrix inequality approach using a homotopy method this paper considers a decentralized h control problem for multi channel linear time invariant systems our interest is focused on dynamic output feedback the control problem is reduced to a feasibility problem of a bilinear matrix inequality bmi the objective of this paper is to propose an algorithm for solving the bmi by using the idea of the homotopy method where the controller s coefficient matrices are deformed from full matrices defined by a centralized h controller to block diagonal matrices of specified dimensions which describe a decentralized h controller when a feasible decentralized h control problem is considered it can be expected that there always exists a centralized h controller for which the algorithm converges and presents a desired solution to find such a suitable centralized h controller random search in a parametrized set of h controllers with a proper dimension is suggested the efficiency of the proposed algorithm is demonstrated by an example

a parametrization approach to optimal h 2 and h decentralized control problems the paper proposes a two stage design approach to optimal h2 and h decentralized control problems in the first stage an optimal centralized controller is computed then in the second stage based on the optimization results for centralized controllers the parameter that decentralizes the controller is optimized the design approach is applied to an observer based decentralized controller optimality conditions are derived and examples are given to illustrate the design

large eddy simulation of turbulent obstacle flow using a dynamic subgrid scale model we apply the dynamic subgrid scale model to a large eddy simulation of turbulent channel flow with a square rib mounted on one wall the reynolds number re is 3 21 x 10 3 based on the mean velocity above the obstacle and the obstacle s height near wall structures are resolved with the no slip boundary condition the results show better agreement with direct numerical simulation than large eddy simulation with a fixed model constant verifying the value of the dynamic subgrid scale model for simulating complex turbulent flows arge eddy simulation les is an accurate method of simulating complex turbulent flows in which the large flow structures are computed while small scales are modeled the rationale behind this method is based on two observations most of the turbulent energy is in the large structures and the small scales are more isotropic and universal therefore les may be more general and less geometry dependent than reynolds averaged modeling although it comes at higher cost even though les has been used by many investigators most research has been limited to flows with simple geometry in engineering applications however one encounters more complicated geometries here we shall consider a rectangular parallelepiped mounted on a flat surface related flows are those over surfaces protruding from submarines conning towers or control fins wind flows around buildings and airflows over computer chips among others the most distinctive features associated with these flows are three dimensionality flow separation due to protruding surfaces and large scale unsteadiness as a model flow we consider a plane channel flow in which a two dimensional obstacle is mounted on one surface see fig 1 this relatively simple geometry contains flow separation and reattachment flow in this geometry has been studied by tropea and gackstatter1 for low re and werner and wengle2 and dimaczek et al 3 for high re among others recently germano et al 4 suggested a dynamic subgridscale model dsgsm in which the model coefficient is dynamically computed as computation progresses rather than specified a priori this approach is based on an algebraic identity between the subgrid scale stresses at two different filter levels and the resolved turbulent stresses they applied the model to transitional and fully turbulent channel flows and showed that the model contributes nothing in laminar flow and exhibits the correct asymptotic behavior in the nearwall region of turbulent flows without an ad hoc damping function this is a significant improvement over conventional subgrid scale modeling

paley wiener subspace of vectors in a hilbert space with applications to integral transforms article history the goal of this article is to introduce an analogue of the paley wiener space of bandlimited functions pw in hilbert spaces and then apply the general result to more specific examples guided by the role that the differentiation operator plays in some of the characterizations of the paley wiener space we construct a space of vectors using a self adjoint operator d in a hilbert space h and denote this space by pw d t he article can be virtually divided into two parts in the first part we show that the space pw d has similar properties to those of the space pw including an analogue of the bernstein inequality and the riesz interpolation formula we also develop a new characterization of the abstract paley wiener space in terms of solutions of cauchy problems associated with abstract schrodinger equations finally we prove two sampling theorems for vectors in pw d one of which uses the notion of hilbert frames and the other is based on the notion of variational splines in h in the second part of the paper we apply our abstract results to integral transforms associated with singular sturm liouville problems in particular we obtain two new sampling formulas related to one dimensional schrodinger

sur le theoreme de paley wiener d arthur the fourier transform of a c function f with compact support on a real reductive lie group g is given by a collection of operators o p e ip e f for a suitable family of representations of g which depends on a family indexed by p in a finite set of parabolic subgroups of g of pairs of parameters e varying in a set of discrete series e lying in a complex finite dimensional vector space the ip e are generalized principal series induced from p it is easy to verify the holomorphy of the fourier transform in the complex parameters also it satisfies some growth properties moreover an intertwining operator between two representations ip e ip e of the family implies an intertwining property for o p e and o p e there is also a way to introduce hsuccessive partial derivatives h of the family of representations ip e along the parameter e and intertwining operators between subquotients of these successive derivatives imply the intertwining property for the successive derivatives of the fourier transform o we show that these properties characterize the collections of operators p e o p e which are fourier transforms of a c function with compact support for g linear the proof which uses harish chandra fs plancherel formula rests on a similar result for left and right k finite functions which is due to j arthur we give also a proof of arthur fs result purely in term of representations involving the work of a knapp and e stein on intertwining integrals and langlands and vogan fs classifications of irreducible representations of g

optimal model matching control for time delay systems model matching control for time delay systems is formulated as an optimization problem in h2 norm space as well as h norm space wiener hopf techniques and the theory of optimal interpolation are successfully employed to treat this model matching problem including perfect and imperfect model matching cases prior to this work for time delay systems only the problem of perfect model matching control had been considered and no attempt had been made to examine that of imperfect model matching control with the optimization approach presented here an optimal model matching control scheme is constructed for the imperfect model matching case to produce perfect model matching results whenever possible

large eddy simulation of an equilibrium three dimensional turbulent boundary layer large eddy simulation has been applied to prediction of an equilibrium three dimensional turbulent boundary layer tbl subgrid scale stresses were parameterized using a lagrangian dynamic mixed model the predicted mean velocities and second order statistics are in good agreement with direct numerical simulation results single point statistics are also generally similar to those found in other equilibrium three dimensional tbls such as the flow over a rotating disk and the turbulent ekman layer the modification of shear stress producing structure by mean flow three dimensionality was also investigated

decentralized h_ 2 control for multi channel stochastic systems this technical note investigates a decentralized h 2 control problem for multi channel linear time invariant stochastic systems governed by ito s differential equation after using a stochastic algebraic riccati equation sare to establish the necessary conditions for the existence of the optimal strategy set that minimizes an h 2 norm we show that the necessary conditions can also be expressed using a linear matrix inequality lmi the equivalence between the solvability of the sare and the feasibility of the lmi is proved for the first time using a karush kuhn tucker kkt condition furthermore the static output feedback solution was also studied a numerical example is given to demonstrate the usefulness of the obtained features

sampled data control of continuous time systems with an h optimality criterion abstract the synthesis of sampled data controllers for continuous time systems is studied in the context of h control theory the sampled data h optimal control problem consists of finding a sampled data controller which minimizes the l2 induced norm from the continuous time disturbance to the continuous time output the problem is here solved via a discrete system representation this is achieved by describing the closed loop system as a discrete system with finite state dimension and with a representation of the disturbance and the output signals of the discrete system as sequences of elements of certain infinite dimensional spaces via finite rank approximations of a compact integral operator associated with the system the sampled data h control problem can be solved to any degree of accuracy from the structure of the problem it follows that irrespective of the order of the approximation a feasible sampled data controller can be found which has the same order as the system

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

static output feedback stabilisation with h performance for a class of plants in this paper the problem of static output feedback control of a linear system is considered the existence of a static output feedback control law is given in terms of the solvability of two coupled lyapunov inequalities which result in a non linear optimisation problem however using state coordinate and congruence transformations and by imposing a block diagonal structure on the lyapunov matrix we will see that the determination of a static output feedback gain reduces for a specific class of plants to finding the solution of a system of linear matrix inequalities the class of plants considered is those which are minimum phase with a full row rank markov parameter the method is extended to incorporate h performance objectives this results in a sub optimal static h control law found by non iterative means the simplicity of the method is demonstrated by a numerical example

paley wiener type theorems for a class of integral transforms abstract a characterization of weighted l 2 i spaces in terms of their images under various integral transformations is derived where i is an interval finite or infinite this characterization is then used to derive paley wiener type theorems for these spaces unlike the classical paley wiener theorem our theorems use real variable techniques and do not require analytic continuation to the complex plane the class of integral transformations considered is related to singular sturm liouville boundary value problems on a half line and on the whole line

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

positivity and stability analysis for linear implicit difference delay equations abstract this paper deals with positivity and stability of linear implicit difference delay equations being different from the lyapunov function approach commonly used in stability analysis the method employed in this paper gives a way to solve the exponential stability of linear implicit difference equations with time varying delay by decomposition state space and mathematical induction method new necessary and sufficient conditions for positivity and stability of such systems are derived numerical examples are given to illustrate the proposed results

a homotopy method for eigenvalue assignment using decentralized state feedback this paper addresses the following problem given an interconnected system m composed of n subsystems of the form a i b i k i i 1 n a i b i a controllable pair and where the off diagonal blocks of m lie in the image of the appropriate b i then is it possible to arbitrarily assign the characteristic polynomial of m by a suitable selection of the characteristic polynomials of a i b i k i moreover is it possible to compute the appropriate characteristic polynomials of the a i b i k i or equivalently construct the k i needed to do so the first question is answered by constructing a mapping f r n rightarrow r n which maps a prescribed set of n of the feedback gains elements of k i i 1 n to the n coefficients of the characteristic polynomial of m the question then becomes given a p in r n does f x p have a solution the answer is found by constructing a homotopy h r n x o 1 rightarrow r n where h x 1 f x and h x 0 is some trivial function degree theory is then applied to guarantee that there exists an x t such that h x t t p for all t in 0 1 the parameterized sard s theorem is then utilized to prove that with probability 1 x t is a smooth curve and hence can be followed numerically from x 0 to x 1 by the solution of a differential equation davidenko s method

a j spectral factorization approach to control necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with mathcal h infty control j control are derived using j spectral factorization theory the existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled j spectral factorization problems with the second factor providing a parametrization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of nonnegative definite stabilizing solutions to two indefinite algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given a virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework and no additional auxiliary riccati equations are required

global low rank enhancement of decentralized control for large scale systems this note proposes a new control strategy which is computationally attractive for systems of large dimensions the main idea is to supplement decentralized feedback with a global additive term which is computed as a product of two low rank matrices this feature is of critical importance for systems that cannot be adequately stabilized using standard decentralized control the low rank matrices can be efficiently obtained using linear matrix inequalities and the resulting control is suitable for implementation in a multiprocessor environment simulations on a platoon of vehicles demonstrate that such a control can significantly improve the robustness of the closed loop system with respect to uncertain nonlinearities

some applications of small gain theorem to interconnected systems based on small gain theorem decentralized control of interconnected systems is studied linear matrix inequality conditions are given for stabilizability of interconnected systems interconnections can be used to improve system robustness in the sense of small gain theorem an example is given to illustrate the results finally interconnected systems composed of symmetric subsystems are studied

implicit large eddy simulation of non wall bounded turbulent flows based on the multiscale properties of a high order finite volume method in this paper it is presented the application of a higher order finite volume method based on moving least squares approximations fv mls to the resolution of non wall bounded compressible turbulent flows our approach is based on the monotonically implicit large eddy simulation miles the main idea of miles methodology is the absence of any explicit subgrid scale sgs model in the numerical algorithm to solve turbulent flows in the case of the fv mls method we take advantage of the multiresolution properties of moving least squares approximations and we show that they can be used as an implicit sgs model the numerical results are encouraging the third order fv mls method is able to reproduce the inertial subrange and it obtains better results than other usual numerical schemes in les computations such as the muscl scheme we note that in the present state of this research the numerical method is not yet suited for wall bounded flows this paper is the first step in the application of the fv mls method to general turbulent flows

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

h control for fuzzy singularly perturbed systems in this paper both the state feedback and static output feedback h controllers for fuzzy singularly perturbed systems are investigated we give sufficient conditions for the existence of h controller such that the closed loop fuzzy control system is globally stable and achieves a prescribed level of disturbance attenuation for sufficiently small perturbation parameters the linear matrix inequality lmi approach is proposed to obtain the state feedback gains and a homotopy based iterative lmi algorithm is developed to get the static output feedback gains simulation results for two examples are included to demonstrate the effectiveness of the proposed approaches

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

a novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows abstract this paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models the approximate deconvolution ad procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the smagorinsky and leith models the novel idea here is to estimate the modeling parameters using the ad method rather than the traditionally used test filtering approach first a priori and a posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem the proposed model is then applied to a wind driven quasigeostrophic four gyre ocean circulation problem which is a standard prototype of more realistic ocean dynamics results show that the proposed model captures the quasi stationary ocean dynamics and provides the time averaged four gyre circulation patterns taking locally resolved flow characteristics into account the model dynamically provides higher eddy viscosity values for lower resolutions

intermittent redesign of analog controllers via the youla parameter the paper studies digital redesign of linear time invariant analog controllers under intermittent sampling the sampling pattern is only assumed to be uniformly bounded but otherwise irregular and unknown a priori the contribution of the paper is twofold first it proposes a constructive algorithm to redesign any analog stabilizing controller so that the closed loop stability is preserved second it is shown that when applied to sub optimal boldsymbol h 2 and boldsymbol h infty controllers the algorithm produces sub optimal sampled data solutions under any a priori unknown sampling pattern the proposed solutions are analytic computationally simple implementable and transparent transparency pays off in showing the optimality under a fixed sampling density of uniform sampling for both performance measures studied

stabilization and h control of symmetric systems an explicit solution abstract in this paper we address the h control analysis the output feedback stabilization and the output feedback h control synthesis problems for state space symmetric systems using a particular solution of the bounded real lemma for an open loop symmetric system we obtain an explicit expression to compute the h norm of the system for the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state space symmetric systems for the h control synthesis problem we derive an explicit expression for the optimally achievable closed loop h norm and the optimal control gains extension to robust and positive real control of such systems are also examined these results are obtained from the linear matrix inequality formulations of the stabilization and the h control synthesis problems using simple matrix algebraic tools

brief decentralized h controller design in this paper a decentralized h controller design problem for two channel systems is considered a parametrization of all decentralized stable factors is proposed with the parametrization of all decentralized stable factors the class of decentralized compensators is parametrized the decentralized h controller design procedure is built upon the j spectral factorization approach to h control a class of decentralized suboptimal controllers satisfying the h norm bound is parametrized a design procedure for decentralized suboptimal h controllers is suggested

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

weight selection in feedback design with degree constraints we present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint performance is cast as an interpolation problem with bounded analytic functions minimizers of a certain weighted entropy functional provide interpolants having degree less than the number of constraints the choice of weight parameterizes all such bounded degree solutions however the relationship between the weights and the shape of corresponding transfer functions is not direct thus in this paper we develop a formalism that guides weight selection

memoryless h controller design for switched non linear systems with mixed time varying delays this article deals with the h control problem for a class of switched non linear systems with mixed time varying delays the novel features here are that the system in consideration is non linear perturbation with discrete and distributed delays the time varying delay is also involved in the observation output and the controllers to be designed satisfy some exponential stability constraints on the closed loop poles by using lyapunov razumikhin functional approach new sufficient conditions for the h control with exponential stability constraint are derived in terms of the solution of riccati type equations the approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

a new decentralised controller design method for a class of strongly interconnected systems abstractin this paper two interconnected structures are first discussed under which some closed loop subsystems must be unstable to make the whole interconnected system stable which can be viewed as a kind of strongly interconnected systems then comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown a new approach for the design of decentralised controllers is presented by determining the lyapunov function structure previously which allows the existence of unstable subsystems by fully utilising the orthogonal space information of input matrix some new understandings are presented for the construction of lyapunov matrix this new method can deal with decentralised state feedback static output feedback and dynamic output feedback controllers in a unified framework furthermore in order to reduce the design conservativeness and deal with robustness a new robust decentralised controller design method is given by combining with the parameter depend

on the game riccati equations arising in h_ infty control problems in the state space approach to h infty optimal control feasible closed loop gains gamma are characterized via a pair of game riccati equations depending on gamma this paper is concerned with the properties of these equations as gamma varies the most general problem is considered d 11 neq 0 and the variations of the riccati solutions are thoroughly analyzed insight is gained into the behavior near the optimum and into the dependence on gamma of the suboptimality conditions in addition concavity is established for a criterion that synthesizes the three conditions x geq 0 y geq 0 and rho xy gamma 2 this suggests a numerically reliable newton scheme for the computation of the optimal gamma most results presented here are extensions of earlier contributions the main concern is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically sound algorithms

decentralized control through parameter space optimization the decentralized control problem for linear dynamic systems is revisited using a parameter space approach which enables the definition of the decentralized feedbacks from the existence of non empty parameter convex sets the convexity property enables the derivation of efficient numerical algorithms based on standard approaches in convex programming the continuous time and discrete time cases are investigated and the decentralized control design is also treated to meet other important assignments such as optimal h2 performance index absolute stability h prescribed attenuation and robustness against actuator failures some numerical experiments illustrate the potential of this new control design

integrated design of structural and control systems with a homotopy like iterative method we consider an integrated design problem of structural and control systems it is well known that even the simplest formulation of this problem results in a kind of a bmi problem in this paper homotopy like iterative design method based on lmis is proposed to obtain an optimal plant and a controller simultaneously for a full order output feedback problem we can deal with a multiobjective problem e g control problem etc in the proposed design method we can also optimize structural design parameters appearing non linearly in the coefficient matrices of the plant state space form using the first order approximation of the non linear dependence in the proposed algorithm several design examples show that the proposed algorithm works quite effectively for various integrated design problems

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

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

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

continuation methods theory and applications this paper surveys in a tutorial fashion theoretical and applications aspects of the confirmation method for the solution of large scale system engineering problems the continuation method is motivated and defined the existence of the method is formulated in terms of degree theory a la algebraic topology examples are given throughout the paper and applications to engineering and economic problems are cited and described

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

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

a double homotopy method for decentralised control design an iterative algorithm that is based on the idea of two homotopy paths is proposed for output feedback decentralised control design the approach follows a bilinear matrix inequality bmi formulation of the decentralised control problem along one homotopy path the bmi problem which is non convex is locally linearised and solved along the second homotopy path the controller is deformed at each step so that in the end it attains a decentralised structure the proposed computational algorithm can also be applied to obtain reduced order decentralised controllers numerical examples are used to demonstrate the efficacy of the proposed algorithm

decentralized control of symmetric systems abstract this paper is concerned with the stabilizability problem of symmetric systems by means of decentralized controllers it is shown that the set of decentralized fixed modes of a symmetric system is equal to the set of uncontrollable and unobservable modes of the system and implies that the stabilizability of a state space symmetric system by means of a decentralized controller is equivalent to the stabilizability for the system by means of a centralized controller

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

on the minimization of sensitivity to additive disturbances for linear distributed parameter mimo feedback systems the problem of minimizing the sensitivity of the output or input of a plant under a feedback control with respect to external additive disturbances is considered the mathematical model assumed for the plant is a rectangular matrix of transfer functions which can arise from both lumped parameter and distributed parameter systems including time delays the feedback controller is assumed to guarantee the closed loop stability it is shown that an arbitrarily small sensitivity function on a compact set of complex frequencies can be obtained by a suitable choice of feedback transfer function provided no zero of the plant transfer function is in this set additionally the sensitivity function can be designed to be bounded on an unbounded region containing the imaginary axis if there are no zeros of the plant in the right half plane and a certain hypothesis holds multiplicative delays are not excluded if there are zeros in the right half plane the latter design is not realizable since minimizing the sen

linear feedback systems and the graph topology it is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed loop stability and closed loop performance are robust properties in earlier works similar topological results were obtained by exploiting the existence of particular coprime factor system representations not known to exist in general by contrast the development here does not rely on any specific system representations systems are simply characterized as subspaces of norm bounded input output pairs and the analysis hinges on the underlying geometric structure of the feedback stabilization problem unlike other work developed within such a framework fundamental issues concerning the causality of feedback interconnections are discussed explicitly the key result of this paper concerns the difference between linear feedback interconnections with identical controllers in terms of a performance robustness related closed loop mapping upper and lower bounds on the induced norm of this difference are derived allowing for possibly infinite dimensional input output spaces and time varying behavior the bounds are both proportional to the gap metric distance between the plants which clearly demonstrates the gap to be an appropriate measure of the difference between open loop systems from the perspective of closed loop behavior to conclude an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

further results on limitations to the capability of feedback in this paper we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non linear autoregressive control systems the size of the structural uncertainty is characterized by multiple lipschitz constants say l 1 l 2 lp of the uncertain non linear function it is shown that if l 1 l 2 lp satisfy certain algebraic conditions then there exists no globally stabilizing feedback control law for the corresponding uncertain systems the result here is an extension of the previous result obtained by zhang and guo 2002

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

prediction of the high reynolds number flow over a two dimensional bump large eddy simulation les has been applied to prediction of the high reynolds number boundary layer flowing over a bump approximate boundary conditions were used in the les to model the wall layer in which the instantaneous wall stress is correlated with the velocity at the first layer of grid points two formulations of the approximate boundary conditions were employed in the first formulation a constrained relation was used in which the mean wall shear stress is specified a priori either from experimental measurements or from a separate solution of the reynolds averaged navier stokes rans equations in the second formulation an unconstrained relation which is based on an instantaneous power law velocity profile was used calculations were also performed in which the wall stress was computed directly i e as if the near wall flow were resolved in the region resolved by the les the strong distortions of the mean flow stream wise fluctuations and turbulent shear stress are reasonably well predicted and the relatively rapid recovery downstream of the trailing edge is also captured however neither les nor rans reproduces the plateau in skin friction measured upstream of the bump summit attributed to early relaminarization in the experiments les predictions of the mean flow and turbulence intensities using the dynamic eddy viscosity model are relatively insensitive to the particular formulation of approximate boundary conditions however in calculations without a subgrid model les predictions exhibit large errors compared to experiments and the quantitative levels of such errors are also sensitive to the choice of wall layer model

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

computational complexity of a problem arising in fixed order output feedback design this paper is concerned with a matrix inequality problem which arises in fixed order output feedback control design this problem involves finding two symmetric and positive definitive matrices x and y such that each satisfies a linear matrix inequality and that xy i it is well known that many control problems such as fixed order output feedback stabilization h control guaranteed h2 control and mixed h2 h control can all be converted into the matrix inequality problem above including static output feedback problems as a special case we show however that this matrix inequality problem is np hard

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

brief the weighted incremental norm approach from linear to nonlinear h control weighted induced norms can be used to handle robustness and sensitivity requirements in the linear context as shown by zames in its seminal work this paper deals with an attempt to extend linear h control concepts to the nonlinear context making use of a weighted incremental norm it is shown how these concepts make it possible to handle basic requirements such as robust stability disturbance attenuation and steady state behaviors

robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback the objective of this note is to propose a dynamic output control scheme within the lmi framework for robust decentralized stabilization of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints the procedure utilizes the general linear dynamic feedback structure and consists of two steps the first giving a block diagonal lyapunov matrix together with the robustness degree and the second the controller parameters a numerical example illustrates the applicability of the method

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest