reduced order h filtering for linear systems with markovian jump parameters this paper addresses the reduced order h filtering problem for continuous time makovian jump linear systems where the jump parameters are modelled by a discrete time markov process sufficient conditions for the existence of the reduced order h filter are proposed in terms of linear matrix inequalities lmis and a coupling non convex matrix rank constraint in particular the sufficient conditions for the existence of the zero order h filter can be expressed in terms of a set of strict lmis the explicit parameterization of the desired filter is also given finally a numerical example is given to illustrate the proposed approach

optimal h model reduction via linear matrix inequalities continuous and discrete time cases necessary and sufficient conditions are derived for the existence of a solution to the continuous time and discrete time h model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set in addition an explicit parametrization of all reduced order models that correspond to a feasible solution is provided in terms of a contractive matrix these results follow from the recent solution of the h control design problem using lmis particularly simple conditions and a simple parametrization of all solutions are obtained for the zeroth order h approximation problem and the convexity of this problem is demonstrated computational issues are discussed and an iterative procedure is proposed to solve the h model reduction problem using alternating projections although global convergence of the algorithm is not guaranteed

reduced order multiple tuned mass damper optimization a bounded real lemma for descriptor systems approach abstract this paper presents a novel technique for multiple tuned mass damper optimization based on the dissipativity inequalities for a class of descriptor systems under the assumptions of regularity asymptotic stability and index one property of the descriptor system representing the structure with tuned mass dampers optimization criterion is defined in terms of h norm of the system in doing so special structure of the system matrices is utilized to eliminate some of the optimization variables to overcome its high computational cost and make it applicable for optimization of large scale structures a novel reduced order optimization algorithm is proposed unlike the existing approaches the presented optimization framework does not impose restrictions regarding regularity and constantness of the mass matrix and consequently allows simultaneous optimization of mass damping and stiffness matrices numerical examples which clearly illustrate the applicability and effectiveness of the proposed optimization procedure as well as the comparison with other methods are presented

alternating projections on manifolds we prove that if two smooth manifolds intersect transversally then the method of alternating projections converges locally at a linear rate we bound the speed of convergence in terms of the angle between the manifolds which in turn we relate to the modulus of metric regularity for the intersection problem a natural measure of conditioning we discuss a variety of problem classes where the projections are computationally tractable and we illustrate the method numerically on a problem of finding a low rank solution of a matrix equation

fixed structure discrete time h 2 h controller synthesis using the delta operator this paper considers the fixed structure discrete time mixed h 2 h x controller synthesis problem in the delta operator difference operator framework the differential operator and shift operator versions of the problem are reviewed for comparison and necessary conditions are derived for all three formulations a quasi newton continuation algorithm is then used to obtain approximate solutions to these equations controllers are synthesized for two numerical examples and the performance of the algorithm on the differential difference and shift operator versions of the problems is compared

simultaneous stabilization via static output feedback and state feedback in this paper the simultaneous stabilization problem is considered using the matrix inequality approach some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi input multi output mimo plants via static output feedback and state feedback are obtained in the form of coupled algebraic riccati inequalities it is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term a heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities the effectiveness of the approach is illustrated by numerical examples

analysis of a darcy flow model with a dynamic pressure saturation relation we consider a new model for groundwater flow the model differs from previous models in that the saturation pressure relation is extended with a dynamic term namely the time derivative of the saturation the resulting model equation is of nonlinear degenerate pseudoparabolic type we give a rigorous analysis of travelling wave solutions and the local behavior near fronts part of this analysis is then used in a formal asymptotic analysis of solutions with initial support in a half line as an illustrative special case we also consider heaviside initial data

robust control via concave minimization local and global algorithms this paper is concerned with the robust control problem of linear fractional representation lft uncertain systems depending on a time varying parameter uncertainty our main result exploits a linear matrix inequality lmi characterization involving scalings and lyapunov variables subject to an additional essentially nonconvex algebraic constraint the nonconvexity enters the problem in the form of a rank deficiency condition or matrix inverse relation on the scalings only it is shown that such problems but also more generally rank inequalities and bilinear constraints can be formulated as the minimization of a concave functional subject to lmi constraints first of all a local frank and wolfe 1956 feasible direction algorithm is introduced in this context to tackle this hard optimization problem exploiting the attractive concavity structure of the problem several efficient global concave programming methods are then introduced and combined with the local feasible direction method to secure and certify global optimality of the solutions computational experiments indicate the viability of our algorithms and in the worst case they require the solution of a few lmi programs

robust h sub 2 h sub spl infin state estimation for discrete time systems with error variance constraints this paper studies the problem of an h sub spl infin norm and variance constrained state estimator design for uncertain linear discrete time systems the system under consideration is subjected to time invariant norm bounded parameter uncertainties in both the state and measurement matrices the problem addressed is the design of a gain scheduled linear state estimator such that for all admissible measurable uncertainties the variance of the estimation error of each state is not more than the individual prespecified value and the transfer function from disturbances to error state outputs satisfies the prespecified h sub spl infin norm upper bound constraint simultaneously the conditions for the existence of desired estimators are obtained in terms of matrix inequalities and the explicit expression of these estimators is also derived a numerical example is provided to demonstrate various aspects of theoretical results

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

dynamical system design from a control perspective finite frequency positive realness approach nonminimum phase zeros are well known to limit the best achievable control performance when the control gain is allowed to be arbitrarily high on the other hand the phase crossover appears to be a limiting factor for performance when high gain controllers are not allowed in particular the positive realness in a finite frequency range seems crucial for achieving good performance in the presence of control constraints this paper will first give multiple reasons to support this conjecture and then develop a systematic method for designing mechanical systems to achieve the finite frequency positive real ffpr property specifically we present a state space characterization of the ffpr property by generalizing the well known kalman yakubovich popov lemma to deal with a class of frequency domain inequalities that are required to hold within a finite frequency interval the result is further extended for uncertain systems to give a sufficient condition for satisfaction of a robust ffpr property the nominal ffpr result is interpreted in the time domain in terms of input output signals finally we show that certain sensor actuator placement problems to achieve the ffpr property can be reduced to finite dimensional convex problems involving linear matrix inequalities the method is applied to the shape design of a swing arm for magnetic storage devices with the objective of maximizing the control bandwidth achievable with a limited actuator power

compensator design for stability enhancement with collocated controllers a continuum model rather than a finite element model is used the optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite dimensional theory developed by the author despite the lack of exponential stabilizability infinite dimensional steady state riccati equations characterizing the feedback control gain and the kalman filter gain operators can be solved explicitly the associated performance indexes including the mean square control effort are calculated in closed form as a first approximation the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies numerical calculations for the gain and bandwidths for a typical configuration are presented the performance of the compensator is evaluated when in fact in the true model there is no actuator noise the theoretical problem involved is to show that the infinite dimensional stochastic process is asymptotically stationary it is possible to calculate the steady state covariance in closed form and thereby calculate performance indexes of interest explicitly facilitating the choice of optimal design parameters

a linear programming approach to the synthesis of fixed structure controllers this paper describes a new approach to the synthesis of fixed structure and fixed order controllers such controllers are required in many practical applications a broad class of fixed structure controller synthesis problems can be reduced to the determination of a real controller parameter vector or simply a controller k k 1 k 2 k t so that a given set of real or complex polynomials of the form p s k po s k 1 p 1 s k t p t s is hurwitz the stability of the closed loop system requires a real characteristic polynomial to be hurwitz while several performance criteria can be satisfied by ensuring that a family of complex polynomials is hurwitz a novel feature of this paper is the exploitation of the interlacing property ip of hurwitz polynomials to construct arbitrarily tight approximations of the set of stabilizing controllers this is done by systematically constructing sets of linear inequalities in k the union of the feasible sets of linear inequalities provides an approximation of the set of all controllers k which render p s k hurwitz as the number of sets of linear inequalities increases and approaches infinity we show that the union of the feasible sets approaches the set of all stabilizing controllers of the desired structure the main tools that are used in the construction of the sets of linear inequalities are the hermite biehler theorem descartes rule of signs and its generalization we provide examples of the applicability of the proposed methodology to the synthesis of fixed order stabilizing controllers

alternating convex projection methods for covariance control design the problem of designing a static state feedback or full order dynamic controller is formulated as a problem of designing an appropriate plant state covariance matrix we show that closed loop stability and multiple output norm constraints imply that the plant state covariance matrix lies at the intersection of some specified closed convex sets in the space of symmetric matrices we address the covariance feasibility problem to determine the existence and compute a covariance matrix to satisfy assignability and output norm performance constraints we address the covariance optimization problem to construct an assignable covariance matrix which satisfies output performance constraints and is as close as possible to a given desired covariance we also treat inconsistent constraints where we look for an assignable covariance matrix which best approximates desired but non achievable output performance objectives we call this the infeasible covariance optimization problem all these problems are of a conve

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

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

suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs abstract as one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper we determine all the suborbits of a point stabilizer in the orthogonal group on the last subconstituent and calculate the length of each suborbit moreover we discuss the quasi strongly regular graphs and the association schemes based on the last subconstituent respectively

brief rbust control of linear systems with real parametric uncertainty we discuss the problem of robust controller synthesis to provide quadratic stability and a desirable disturbance attenuation level through an appropriately small l 2 gain for systems with time varying real parametric uncertainty through the use of skewsymmetric matrices the conservatism of standard scaled h approach is reduced while the full state feedback problem is convex the output feedback problem is not a set of conditions under which the design of output feedback controllers can be broken into two sequential convex problems is presented the results are compared with recent results concerning the design of parameter varying controllers and a simple result regarding the mixed problem where some of the unknown parameters can be measured on line is discussed

on h sub spl infin model reduction using lmis in this note we deal with the problem of approximating a given nth order linear time invariant system g by an rth order system g sub r where r n it is shown that lower bounds of the h sub spl infin norm of the associated error system can be analyzed by using linear matrix ineqaulity lmi related techniques these lower bounds are given in terms of the hankel singular values of the system g and coincide with those obtained in the previous studies where the analysis of the hankel operators plays a central role thus this note provides an alternative proof for those lower bounds via simple algebraic manipulations related to lmis moreover when we reduce the system order by the multiplicity of the smallest hankel singular value we show that the problem is essentially convex and the optimal reduced order models can be constructed via lmi optimization

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

damping parameter design optimization in structural systems using an explicit h norm bound abstract this paper examines the damping parameter design optimization problem for structural systems with collocated measurements and inputs so that h norm bound constraints are satisfied we utilize a particular solution of the bounded real lemma that provides an explicit upper bound on the h norm of a collocated structural system using this upper bound result the damping design is formulated as a linear matrix inequality lmi optimization problem with respect to the damping coefficients of the structural system the formulation is particularly useful for large scale structural systems where existing methods are computationally prohibitive numerical examples demonstrate the benefits and computational advantages of the proposed damping parameter design method

the buckley leverett equation with dynamic capillary pressure the buckley leverett equation for two phase flow in a porous medium is modified by including dependence of the capillary pressure on the rate of change of saturation this model due to hassanizadeh and gray results in a nonlinear pseudoparabolic partial differential equation phase plane analysis including a separation function to measure the distance between invariant manifolds is used to determine when the equation supports traveling waves corresponding to undercompressive shocks the riemann problem for the underlying conservation law is solved and the structures of the various solutions are confirmed with numerical simulations of the partial differential equation

a successive projection method it is of both theoretical and practical interest to find the projection of a point to the intersection of a finite number of closed convex sets by a sequence of projections to the individual sets successively in this paper we study such a method and analyze its convergence properties a main feature of the method is its capability to decompose the projection problem into several small ones for some structured sparse problems these small subproblems can be solved independently and the presented method has a potential use in parallel computation

computing a nearest symmetric positive semidefinite matrix the nearest symmetric positive semidefinite matrix in the frobenius norm to an arbitrary real matrix a is shown to be b h 2 where h is the symmetric polar factor of b a at 2 in the 2 norm a nearest symmetric positive semidefinite matrix and its distance 2 a from a are given by a computationally challenging formula due to halmos we show how the bisection method can be applied to this formula to compute upper and lower bounds for 2 a differing by no more than a given amount a key ingredient is a stable and efficient test for positive definiteness based on an attempted choleski decomposition for accurate computation of 2 a we formulate the problem as one of zero finding and apply a hybrid newton bisection algorithm some numerical difficulties are discussed and illustrated by example

association schemes based on the subspaces of type 2 1 0 in singular symplectic space over finite fields abstract in this paper we provide a construction of association scheme based on the subspaces of type 2 1 0 in singular symplectic space over finite fields moreover all parameters of the association scheme are computed

control of lpv systems with partly measured parameters the control of linear parameter varying lpv systems with time varying real uncertain parameters where only some of the parameters are measured and available for feedback is considered the control objectives are internal stability and disturbance attenuation in the sense of a bounded induced l sub 2 norm from the disturbance to the controlled output using parametric lyapunov functions the solvability conditions for dynamic output feedback controllers that depend on the measured parameters are expressed in terms of a set of linear matrix inequalities lmis and an additional coupling constraint which destroys the convexity of the overall problem by transforming the coupling constraint into a rank condition the problem is recast into a rank minimization problem with lmi constraints an example is included that demonstrates the application of the results

suborbits of m dimensional totally isotropic subspaces under finite singular classical groups it is well known that the set of all the totally isotropic subspaces with the same dimension in a singular classical space forms an orbit under the action of the corresponding classical group in this paper we determine all the orbitals and the rank of this action and calculate the length of each suborbit

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

generalized pole placement via static output feedback a methodology based on projections this paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form given n subsets of the complex plane find a static output feedback that places in each of these subsets a pole of the closed loop system the algorithm presented is iterative in nature and is based on alternating projection ideas each iteration of the algorithm involves a schur matrix decomposition a standard least squares problem and a combinatorial least squares problem while the algorithm is not guaranteed to always find a solution computational results are presented demonstrating the effectiveness of the algorithm

using scales in the multiobjective approach scales are used to reduce the conservatism encountered in most multiobjective approaches to control design the most general case i e matrix scales results in a nonconvex problem though the use of scalar scales leads to convex searches in the analysis and state feedback problems output feedback synthesis and other extensions are discussed numerical examples are provided to show the effectiveness of the suggested approach the article considers in particular h sup spl infin control

suborbits of subspaces of type m k under finite singular general linear groups abstract suppose f q n l denotes the n l dimensional vector space over a finite field f q and gl n l n f q denotes the corresponding singular general linear group all the subspaces of type m k form an orbit under gl n l n f q denoted by m m k n l n let be the set of all the orbitals of gl n l n f q m m k n l n then m m k n l n is a symmetric association scheme in this paper we determine all the orbitals and the rank of gl n l n f q m m k n l n calculate the length of each suborbit finally we compute all the intersection numbers of the symmetric association scheme m m k n l n where k 1 or k l 1

suborbits of a point stabilizer in the unitary group on the last subconstituent of hermitean dual polar graphs let be a dual polar graph in a unitary space it is well known that a point stabilizer in the unitary group is transitive on the last subconstituent of in this paper we determine all the suborbits of this action calculate its rank and the length of each suborbit note that the induced subgraph on is quasi strongly regular as an application of our results all its parameters are computed

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

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

stabilizing static output feedback receding horizon controls for linear discrete time invariant systems in this paper a stabilizing static output feedback receding horizon control rhc is proposed for linear discrete time invariant systems an inequality condition on the terminal weighting matrices is presented under which the closed loop stability of static output feedback receding horizon controls is guaranteed it is shown that the stabilizing static output feedback receding horizon control problem can be represented as a non linear minimization problem based on linear matrix inequalities lmis an algorithm for solving the presented non linear minimization problem is proposed in addition this result is extended to an arbitrary reference tracking problem that is one of the main features of receding horizon control finally the efficiency of the proposed algorithm is illustrated by numerical examples

lmi characterization of reduced order h controllers via invariant zero structure abstract in this paper we clarify a new relationship between invariant zeros of a generalized plant and the order reduction of h controllers by using linear matrix inequalities in both continuous time and discrete time cases in contrast with our recent paper where a relationship between an unstable transmission zero structure and the h controller order reduction is initiated in a fundamental manner results obtained in this paper are more flexible in two senses assumptions that are made for the generalized plant are relaxed and stable as well as unstable invariant zeros are characterized to obtain a reduced order h controller

l2 and l2 l model reduction via linear matrix inequalities necessary and sufficient conditions are derived for the existance of a solution to the continuous time and discrete time suboptimal l2 and l2 l model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint in addition explicit parametrizations of all reduced order models that correspond to a feasible solution are presented in terms of contractive matrices

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

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

solving rank constrained lmi problems with application to reduced order output feedback stabilization this paper presents an iterative penalty function method for solving rank constrained linear matrix inequality lmi problems and illustrates its application to reduced order output feedback stabilization we propose a penalized objective function to replace the rank condition so that a solution to the original nonconvex lmi feasibility problem can be obtained by solving a series of convex lmi optimization subproblems numerical experiments were performed to demonstrate the proposed method

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

output feedback decentralized stabilization ilmi approach in this paper the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach a necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time invariant large scale systems it is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality the extension of the result to h control is studied an iterative lmi algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain examples show the effectiveness of the algorithm

enhanced structural damage detection using alternating projection methods alternating projection algorithms are examined for the solution of damage detection problems in structures the damage detection problem is formulated as a feasibility problem to find a damaged stiffness matrix that is close to the refined stiffness matrix of the undamaged structure and that satisfies the necessary symmetry sparsity positive definiteness eigenequation and damage localization constraints alternating projection methods are proposed to utilize the orthogonal projections onto these constraint sets in an iterative fashion to find a solution that best satisfies these constraints in addition directional alternating projections that exploit the geometry of the damage detection feasibility problem are introduced to improve the computational efficiency of the approach the techniques are applied to detect damage in a simulated cantilever beam model and in the nasa eight bay truss damage detection experimental test bed

reduced order controllers for the h control problem with unstable invariant zeros this paper addresses the existence and design methods of reduced order controllers for the h control problem with unstable invariant zeros in the state space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output where the realization is induced from a stabilizable and detectable realization of the generalized plant this paper presents a new controller degree bound for the h control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region when the unstable invariant zero exists this paper shows that reduced order controllers with orders strictly less than that of the generalized plant exist if the h control problem is solvable moreover this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality based design methods algorithms for constructing the reduced order controllers the results developed in this paper are valid both for the continuous and discrete time h control problems

a newton like method for solving rank constrained linear matrix inequalities this paper presents a newton like algorithm for solving systems of rank constrained linear matrix inequalities though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases numerical experiments including application to an output feedback stabilization problem show the effectiveness of the algorithm

robust output feedback controller design via local bmi optimization the problem of designing a globally optimal full order output feedback controller for polytopic uncertain systems is known to be a non convex np hard optimization problem that can be represented as a bilinear matrix inequality optimization problem for most design objectives in this paper a new approach is proposed to the design of locally optimal controllers it is iterative by nature and starting from any initial feasible controller it performs local optimization over a suitably defined non convex function at each iteration the approach features the properties of computational efficiency guaranteed convergence to a local optimum and applicability to a very wide range of problems furthermore a fast but conservative lmi based procedure for computing an initially feasible controller is also presented the complete approach is demonstrated on a model of one joint of a real life space robotic manipulator

model reduction for state space symmetric systems in this paper the model reduction problem for state space symmetric systems is investigated first it is shown that several model reduction methods such as balanced truncation balanced truncation which preserves the dc gain optimal and suboptimal hankel norm approximations inherit the state space symmetric property furthermore for single input and single output siso state space symmetric systems we prove that the h norm of its transfer functions can be calculated via two simple formulas moreover the siso state space symmetric systems are equivalent to systems with zeros interlacing the poles zip under mild conditions

low order controller design for siso systems using coprime factors and lmi this paper develops a low order controller design method for linear continuous time invariant single input single output systems requiring only the solution of a convex optimization problem the technique integrates several well known results in control theory an important step is the use of coprime factors so that based on strictly positive real functions feedback stabilization using low order controllers becomes a zero placement problem which is convex from this result we develop algorithms to solve two optimal control problems

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

bregman monotone optimization algorithms a broad class of optimization algorithms based on bregman distances in banach spaces is unified around the notion of bregman monotonicity a systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block iterative surrogate bregman projection schemes another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of bregman monotonicity and to include the operators commonly found in bregman optimization methods special emphasis is placed on the viability of the algorithms and the importance of legendre functions in this regard various applications are discussed

a generalization of the formulas for intersection numbers of dual polar association schemes and their applications dual polar association schemes form an important family of association schemes whose intersection numbers were computed in wan et al studies in finite geometry and the construction of incomplete block designs science press beijing 1966 in chinese in this paper we generalize the formulas for the intersection numbers and introduce their applications to pooling designs cartesian authentication codes and vertex transitive graphs

association schemes based on maximal isotropic subspaces in singular classical spaces the paper provides the construction of association schemes on the sets of the maximal totally isotropic subspaces in singular classical spaces all intersection numbers of these schemes are computed

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

spectral bundle methods for non convex maximum eigenvalue functions second order methods we study constrained and unconstrained optimization programs for nonconvex maximum eigenvalue functions we show how second order techniques may be introduced as soon as it is possible to reliably guess the multiplicity of the maximum eigenvalue at a limit point we examine in which way standard and projected newton steps may be combined with a nonsmooth first order method to obtain a globally convergent algorithm with a fair chance to local superlinear or quadratic convergence

nonsmooth h_infty synthesis we develop nonsmooth optimization techniques to solve h infty synthesis problems under additional structural constraints on the controller our approach avoids the use of lyapunov variables and therefore leads to moderate size optimization programs even for very large systems the proposed framework is versatile and can accommodate a number of challenging design problems including static fixed order fixed structure decentralized control design of pid controllers and simultaneous design and stabilization problems our algorithmic strategy uses generalized gradients and bundling techniques suited for the h infty norm and other nonsmooth performance criteria we compute descent directions by solving quadratic programs and generate steps via line search convergence to a critical point from an arbitrary starting point is proved and numerical tests are included to validate our methods the proposed approach proves to be efficient even for systems with several hundreds of states

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

universal scaling of spontaneous imbibition for water wet systems 1 spontaneous counter current imbibition si is a key mechanism in many multiphase flow processes such as cleanup of nonaqueous phase liquids napls bioremediation or co2 storage for interpreting and upscaling laboratory si data and modeling and prediction purposes scaling groups are an essential tool the question of how to formulate a general scaling group has been debated for over 90 years here we propose the first scaling group that incorporates the influence of all parameters on si that are present in the two phase darcy model the group is derived rigorously from the only known exact analytical solution for spontaneous imbibition by relating the cumulative water phase imbibed to the normalized pore volume we show the validity of the group by applying it to 42 published si studies for water oil and water air experiments for a wide range of viscosity ratios different materials different initial water saturations and different length scales in all cases water was the wetting phase our group serves as a master equation whose generality allows the rigorous prediction of the validity of a large number of specialized scaling groups proposed during the last 90 years furthermore our results give strong evidence that the darcy model is suitable for describing si and that including dynamic effects in capillary pressure is not necessary for counter current si contrary to what has been hypothesized two key applications of the group are discussed first the group can serve as the long sought after general transfer rate for imbibition used in dual porosity models second it is the so far missing proportionality constant in imbibition germination models for plant seeds