generalized blocks for symmetric groups we study via character theoretic methods an l analogue of the modular representation theory of the symmetric group for an arbitrary integer l 2 we find that many of the invariants of the usual block theory ie when l is prime generalize in a natural fashion to this new context

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

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

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

on direct versus indirect methods for reduced order controller design comparisons are obtained between direct parameter optimization and indirect controller reduction methods in reduced order controller design in particular the authors compare the controller canonical correlation coefficients method of c de villemagne and r e skelton 1988 to the optimal projection theory of d c hyland and d s bernstein 1984 it is noted that suboptimal methods may in certain cases be simpler to implement than optimal methods thus the choice of direct versus indirect methods can be viewed as a tradeoff between design simplicity and actual control system performance

bessel operators on jordan pairs and small representations of semisimple lie groups abstract we provide a uniform construction of l 2 models for all small unitary representations in degenerate principal series of semisimple lie groups which are induced from maximal parabolic subgroups with abelian nilradical this generalizes previous constructions to the case of a maximal parabolic subgroup which is not necessarily conjugate to its opposite and hence the previously used jordan algebra methods have to be generalized to jordan pairs the crucial ingredients for the construction of the l 2 models are the lie algebra action and the spherical vector working in the so called fourier transformed picture of the degenerate principal series the lie algebra action is given in terms of bessel operators on jordan pairs we prove that precisely for those parameters of the principal series where small quotients occur the bessel operators are tangential to certain submanifolds further we show that the small quotients are unitarizable if and only if these submanifolds carry equivariant measures in this case we can express the spherical vectors in terms of multivariable k bessel functions and some delicate estimates for these bessel functions imply the existence of the l 2 models

zeta distributions and boundary values of poisson transforms abstract let g be the conformal group of a non euclidean jordan algebra and let p be the maximal parabolic subgroup canonically associated to g standard intertwining operators between spherical degenerate principal series induced from p determine zeta distributions in this article we obtain a functional equations for zeta distributions by considering boundary values of poisson transforms we relate the constant occurring in the zeta functional equation to that occurring in the functional equation of wallach s generalized jacquet functionals

technical communique a descent anderson moore algorithm for optimal decentralized control a convergent version of the anderson moore algorithm for the optimal output feedback problem is applied to a class of optimal decentralized control problems the algorithm is based on a positive definite approximation of the second order taylor series expansion of the loss function numerical results show that the algorithm performs favourably when compared with the method of geromel and bernussou 1979 automatica 15 489 and with variable metric function minimization techniques

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

explicit hilbert spaces for certain unipotent representations iii abstract in this paper we construct a family of small unitary representations for real semisimple lie groups associated with jordan algebras these representations are realized on l2 spaces of certain orbits in the jordan algebra the representations are spherical and one of our key results is a precise l2 estimate for the fourier transform of the spherical vector we also consider the tensor products of these representations and describe their decomposition

singular unitary representations of classical groups on presente une description de la partie relativement singuliere du dual unitaire d un groupe classique de type i sur un corps local f de caracteristique autre que 2

explicit hilbert spaces for certain unipotent representations ii letg be the universal cover of the group of automorphisms of a symmetric tube domain and letp ln be its shilov boundary parabolic subgroup this paper attaches an irreducible unitary representation ofg to each of the finitely many l orbits onn the hilbert space of the representation consists of functions on the orbit which are square integrable with respect to a certainl equivariant measure the representation remains irreducible when restricted top and descends to a quotient ofg which is at worst thedouble cover of a linear group if thel orbit isnot open inn the construction gives a unipotent representation ofg

unitary representations of lie groups and operators of finite rank besides being a principal object of study in harmonic analysis the convolution algebra of ll functions on a locally compact group is traditionally used for investigating unitary group representations by methods of associative algebra with the development of the theory of c algebras this role was more and more taken over by the group c algebras a considerable amount of information concerning group c algebras in particular of lie groups has accumulated this article may be regarded as part of a program to use the obtained insights and methods in order to derive results in terms of more classical objects as ll functions or in the context of lie groups even smooth functions briefly to prove regularity theorems to make this more concrete let me describe two such regularity questions not to be treated in this paper the topology on the unitary dual g of a given locally compact group g can be characterized as follows a set a in g is closed if and only if for each ir e g a there exists an f e c g such that 7r f 0 and p f 0 for all p e a one may ask whether one can always find an f e l1 g with these properties it turns out that for some groups this is possible for instance for groups with polynomially growing haar measure for others it is not for instance for noncompact semisimple lie groups more information on this topic can be found in 2 secondly as pukanszky has shown 40 each primitive quotient c g p of the group c algebra of a connected lie group g has a unique faithful trace trp a priori it is not clear that there is an ll function f on g such that 0 trp f oo but charbonnel has proved 5 6 that one can find such an f even in d g cc g in this article we shall solve the following problem in the affirmative let ir be a continuous irreducible unitary representation of a connected lie group h and suppose that ir c h contains the compact operators on the representation space as i e the norm closure of ir l1 h contains the compact operators is it true that ir li h contains an operator of rank one actually we shall do somewhat better we shall construct a smooth function f on h such that ir f is an operator of rank one and such that f r

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

the xy centring algorithm for the dual lmi problem a new approach to fixed order control design many fixed order suboptimal control problems with stability performance and robustness specifications can be reduced to a search for a matrix x 0 satisfying a linear matrix inequality lmi while x 1 satisfies another lmi this paper defines a certain class of these problems we shall call the dual lmi problem and a computational algorithm to solve our dual lmi problem is given properties and limitations of the algorithm are discussed in comparison with the existing algorithm the min max algorithm an extension to optimal control problems is provided numerical examples for the fixed order stabilization problem and the static output feedback linear quadratic optimal control problem demonstrate the applicability of the proposed algorithm

on the brauer glauberman correspondence abstract the purpose of the present paper is two fold on the one hand to show the existence of a correspondence unifying brauer s and glauberman s ones see theorem 4 6 and on the other hand to give an alternative proof of watanabe s equivalence in atumi watanabe the glauberman character correspondence and perfect isometries for blocks of finite groups j algebra 216 1999 548 565 by the way we give a short proof of the coincidence of the clifford extensions associated with a pair of glauberman correspondent irreducible representations see corollary 4 16 a question that surprisingly enough has only been partially solved recently see morton harris markus linckelmann on the glauberman and watanabe correspondences for blocks of finite p solvable groups trans amer math soc 354 2002 3435 3453 and shigeo koshitani gerhard michler glauberman correspondence of p blocks of finite groups j algebra 243 2001 504 517

on the gap between h 2 and entropy performance measures in h control design abstract recent papers have considered the problem of minimizing an entropy functional subject to an h performance constraint since the entropy is an upper bound for the h 2 cost there remains a gap between entropy minimization and h 2 minimization in this paper we consider a generalized cost functional involving both h 2 and entropy aspects this approach thus provides a means for optimizing h 2 performance within h control design

structure of the degenerate principal series on symmetric r spaces and small representations abstract let g be a simple real lie group with maximal parabolic subgroup p whose nilradical is abelian then x g p is called a symmetric r space we study the degenerate principal series representations of g on c x in the case where p is not conjugate to its opposite parabolic we find the points of reducibility the composition series and all unitarizable constituents among the unitarizable constituents we identify some small representations having as associated variety the minimal nilpotent k c orbit in p c where k c is the complexification of a maximal compact subgroup k g and g k p the corresponding cartan decomposition

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

optimal low order controller design via lqg like parametrization abstract a new lqg like parametrization scheme is introduced for low order controller design descent based design methodologies are developed for optimizing an h 2 cost with respect to the controller design parameters in this case the reduced order regulator and estimator gain matrices in a modified version the reduced order model of the plant is also updated numerical experiments using large space structure models show the efficacy of this approach