brief paper a dual optimization procedure for linear quadratic robust control problems this paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system the model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional this problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found although the direct solution of this problem will be discussed briefly the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available

a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

robust controller synthesis using kharitonov s theorem the authors present a method based upon kharitonov s theorem for synthesizing robustly stabilizing feedback controllers the approach is based upon a multiple plant model formulation with a quadratic cost functional sufficient conditions are obtained for characterizing robustly stabilizing static output feedback proportional controllers for mimo multiple input multiple output plants with denominator polynomial uncertainty

an algorithm for simultaneous stabilization using decentralized constant gain output feedback an algorithm which solves numerically the simultaneous stabilization problem using a constant gain decentralized control law is presented the algorithm is determined from the necessary conditions for minimizing an optimal control problem the optimal control problem consists of n plant models each with its own cost function the costs are summed to create an average cost function and equality constraints are added to yield the decentralized control structure the algorithm can start with any stabilizing full state feedback gain for each model and will converge to the optimal constant feedback gain for all models assuming a solution exists examples of the algorithm are given for kharitonov synthesis and optimal gain scheduled control law synthesis using output feedback

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

the functor of p permutation modules for abelian groups let k be a field of characteristic p where p is a prime number let pp k g be the grothendieck group of p permutation kg modules where g is a finite group and let cpp k g be pp k g tensored with the field of complex numbers c in this article we find all the composition factors of the biset functor cpp k restricted to the category of abelian groups

the coset poset and probabilistic zeta function of a finite group abstract we investigate the topological properties of the poset of proper cosets xh in a finite group g of particular interest is the reduced euler characteristic which is closely related to the value at 1 of the probabilistic zeta function of g our main result gives divisibility properties of this reduced euler characteristic

a study of a simple p permutation functor abstract in this article we are going to give a description of a simple p permutation functor s 1 c we can prove the existence of an isomorphism between this functor and the functor which sends a group to the image of the cartan homomorphism this fact allows us to link the evaluation of s 1 c with the image of the cartan matrix of comack k g and gives us an explicit formula for the dimension of this evaluation

a remark on the dade group and the burnside group abstract the object of this note is to show that the formula for tensor induction of relative syzygies in the dade group stated in s bouc j reine angew math 523 2000 113 can be viewed as a special case of a functorial homomorphism from the dual b of the burnside group to the subgroup d of the dade group generated by relative syzygies it follows that there exists a short exact sequence of functors 0 r q b d d tors 0 where r q is the functor of rational representations this may be viewed as an improvement from q to z of theorem d of invent math 139 2000 275

counterexamples to analytic hypoellipticity for domains of finite type consider the hypersurface z1 z2 q z2 p zi cc c2 where p r is a subharmonic nonharmonic polynomial such a surface is pseudoconvex more precisely is the boundary of a pseudoconvex domain and of finite type it is the boundary of a model domain f z2 p zi so called because such domains provide good approximations to general pseudoconvex domains of finite type in c2 see 37 11 a nonvanishing antiholomorphic tangent vector field is a oaz 1 2i ap oaz i o a29z as coordinates for the surface we use c x jr 3 z t z t ip z the vector field pulls back to l o oz i op 9z a3 t equip c x jr with lebesgue measure and consider the orthogonal projection from l2 onto its intersection with the kernel of l the intersection of this kernel with the schwartz space may be shown to have infinite dimension and it is well known that l fails to be c hypoelliptic however c hypoellipticity does hold in a modified form see 30 if lu e c in an open set and if in addition u lv for some v e l2 where l is the formal adjoint of l then u e c there our main purpose is to point out that the analogous assertion for real analytic hypoellipticity is false if p z rz m m an even integer 4 specifically for p a general homogeneous subharmonic nonharmonic polynomial let s z t w s be the szeg6 kernel that is the distribution kernel associated to the operator defined by the orthogonal projection of l2 c x jr with respect to lebesgue measure onto the kernel of l we shall see in section 5 that this projection maps co to c further s is smooth off the diagonal by 37 define the distribution

simultaneous control of linear systems by state feedback in this paper a new method for finding a state feedback matrix in order to control simultaneously a collection of linear systems of the same size by using similarity operations is presented for stabilization of all the systems it is necessary that the eigenvalues of the closed loop systems lie inside a specified region in the left hand side of the complex plane this aim is achieved by solving linear and nonlinear parametric systems of equations using nonlinear programming the presented method is implemented in two examples and the results are verified in view of the norm of the state feedback matrix and stabilizability

representations of the double burnside algebra and cohomology of the extraspecial p group ii abstract let e be the extraspecial p group of order p 3 and exponent p where p is an odd prime we determine the mod p cohomology h x f p of a summand x in the stable splitting of p completed classifying space be in the previous paper hida and yagita 2014 7 we determined this cohomology modulo nilpotence in this paper we consider the whole of the cohomology moreover we consider the stable splittings of bg for some finite groups with sylow p subgroup e related to the three dimensional linear group l 3 p

tensor product of correspondence functors abstract as part of the study of correspondence functors the present paper investigates their tensor product and proves some of its main properties in particular the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors and a converse also holds

borel smith functions and the dade group we show that there is an exact sequence of biset functors over p groups 0 cb jb d 0 where cb is the biset functor for the group of borel smith functions b is the dual of the burnside ring functor d is the functor for the subgroup of the dade group generated by relative syzygies and the natural transformation is the transformation recently introduced by the first author in s bouc a remark on the dade group and the burnside group j algebra 279 2004 180 190 we also show that the kernel of mod 2 reduction of is naturally equivalent to the functor b of units of the burnside ring and obtain exact sequences involving the torsion part of d mod 2 reduction of cb and b

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

maximal subgroups of direct products we determine all maximal subgroups of the direct product g n of n copies of a group g if g is finite we show that the number of maximal subgroups of g n is a quadratic function of n if g is perfect but grows exponentially otherwise we deduce a theorem of wiegold about the growth behaviour of the number of generators of g n

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

convergence of a numerical algorithm for calculating optimal output feedback gains a sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes including the standard lq case the primary contribution is a proof that the algorithm converges to a local minimum under nonrestrictive assumptions numerical examples illustrate the theory the second example demonstrates an important lq design technique which permits the designer to prespecify the feedback structure subject to the requirement of output feedback stabilizability

the functor of rational representations for p groups abstract let k be a field of characteristic p 0 let c p k be the category whose objects are the finite p groups morphisms are the k linear combinations of bisets and composition of morphisms is obtained by k linear extension from the usual product of bisets let f p k denote the category of k linear functors from c p k to the category of k vector spaces this paper investigates the structure of the functor kr q mapping a p group p to kr q p k z r q p as an object of f p k where r q p is the grothendieck group of the category of finite dimensional q p modules the main result is an explicit description of the lattice of all subfunctors of kr q in particular for p odd it is shown that kr q is a uniserial object in f p k for p 2 the lattice of subfunctors of kr q can be described as the lattice of closed subsets of a graph whose vertices are the 2 groups of normal 2 rank 1 in both cases a composition series of kr q is obtained which leads to a formula giving the dimension of the evaluations sq k p of the simple objects sq k of f p k associated to p groups q of normal p rank 1 different from cp this formula can be phrased in terms of rational representations of p but also in terms of the geometry of the lattice of subgroups of p using the notions of basic subgroups and origins for example if p 2 the dimension of s 1 k p is equal to the number of absolutely irreducible q p modules