λ matrix formulation applied to the hertz contact problem with finite friction in this paper we are concerned with coupled volterra integral equations for rigid bodies in the frame of the hertz contact model considering an appropriate integral operator as the variable of the matrix polynomial a l matrix corresponding to the hertz model is determined knowledge of the smith decomposition forms of the l matrices enables us to characterize a single integral equation which recovers the normal stress as well as the compliance factor the presented model shows a reliable behavior and an acceptable accuracy of the l matrix approach in comparison to the recent results in the literature

affine spaces of strong linearizations for rational matrices and the recovery of eigenvectors and minimal bases abstract the main aim of this paper is two fold first to define and analyze two affine spaces of matrix pencils associated with a realization of an n n rational matrix g and show that almost all of these pencils are strong linearizations of g second to describe the recovery of eigenvectors minimal bases and minimal indices of g from those of the strong linearizations of g the affine spaces of pencils are constructed from the vector spaces of linearizations of matrix polynomials defined and analyzed by mackey et al in siam j matrix anal appl 28 2006 pp 971 1004 we show that eigenvectors minimal bases and minimal indices of g can be easily recovered from those of the strong linearizations of g in particular we construct a symmetric strong linearization of g when g is regular and symmetric we also describe the recovery of pole zero structure of g at infinity from the pole zero structure at infinity of a strong linearization of g

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

an improved toeplitz algorithm for polynomial matrix null space computation in this paper we present an improved algorithm to compute the minimal null space basis of polynomial matrices a problem which has many applications in control and systems theory this algorithm takes advantage of the block toeplitz structure of the sylvester matrix associated with the polynomial matrix the analysis of algorithmic complexity and numerical stability shows that the algorithm is reliable and can be considered as an efficient alternative to the well known pencil state space algorithms found in the literature

an algorithm for computing the eigenstructure of a regular matrix polynomial abstract we give an algorithm to compute the finite zeros of a regular matrix polynomial p i e det p 0 the approach is close to that of the algorithm in 8 we use nonunitary elementary matrices instead of unitary matrices for the equivalence transformations which are somewhat cheaper in practice the danger of growth of nonunitary matrices seems to be more remote than usually supposed

effective equidistribution for closed orbits of semisimple groups on homogeneous spaces we prove effective equidistribution with polynomial rate for large closed orbits of semisimple groups on homogeneous spaces under certain technical restrictions notably the acting group should have finite centralizer in the ambient group the proofs make extensive use of spectral gaps and also of a closing lemma for such actions

on the direct construction of the inverse scattering operators of integrable nonlinear hamiltonian systems abstract we show that the mere knowledge of a single symmetry propagator would suffice to construct the lax operators for the inverse scattering scheme associated with an integrable physical system with one spatial dimension this construction supplements in an important way the integrability test scheme of chen lee and liu a discussion about the feasibility of the above scheme to the integrable systems with higher spatial dimensions is also presented

recursion operators and bi hamiltonian structures in multidimensions ii the algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied in particular the factorization of certain operators called recursion operators establishes the bi hamiltonian nature of all these equations recently we have presented the recursion operator and the bi hamiltonian formulation of the kadomtsev petviashvili equation a two spatial dimensional analogue of the korteweg devries equation here we present the general theory associated with recursion operators for bi hamiltonian equations in two spatial and one temporal dimensions as an application we show that general classes of equations which include the kadomtsev petviashvili and the davey stewartson equations possess infinitely many commuting symmetries and infinitely many constants of motion in involution under two distinct poisson brackets furthermore we show that the relevant recursion operators naturally follow from the underlying isospectral eigenvalue problems

m form numerical range and the computation of the structured singular value an equivalent expressions for the structures singular value is proposed leading to an alternative algorithm for its computation the approach is based to the geometric properties of the m form numerical range of certain tuples of matrices similar to previously considered schemes the algorithm proposed is proved to give the correct value for block structures of size up to three for larger sizes insight is gained into the question of the possible gap between the structured singular value and its known upper bound

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

an algebraic theory for design of controllers for linear multivariable systems part ii feedback realizations and feedback design the study of general linear multivariable systems with possibly different controlled and measured outputs is continued in this part of the paper the structure matrices defined in part i are used to solve the feedback realization problem feedback realizable transfer functions are then used to solve problems of regulator type it is shown that the solutions to problems like disturbance deeoupling output regulation and pole placement are all special cases of the solution to a more general problem finally it is shown how the results of part i and part ii can be combined to solve problems of servo type and of regulator type simultaneously

the eigenstructure of an arbitrary polynomial matrix computational aspects we give a new numerical method to compute the eigenstructure i e the zero structure the polar structure and the left and right null space structure of a polynomial matrix p these structural elements are of fundamental importance in several systems and control problems involving polynomial matrices the approach is more general than previous numerical methods because it can be applied to an arbitrary m n polynomial matrix p with normal rank r smaller than m and or n the algorithm is then shown to compute the structure of the left and right null spaces of p as well the speed and accuracy of this new approach are also discussed

theorem on linearized hamiltonian systems many nonlinear field equations can be written in hamiltonian form thus the equation tu k u can be written tu u h where h is an appropriate functional and is a poisson bracket frequently one is interested in the solution of the equation linearized about a given solution i e the equation t k where k d de k u e e 0 it is known that if a functional i is a constant of motion then u i is a solution recently more general solutions of this form have been found to prove these results it is very useful to have the answer to the following question if ii ij are two functionals and ki u ii what is k i kj the answer is ki kj u ii ij previously this was proved assuming that canonical coordinates can be introduced here a proof is given without any such assumption

a theorem about hamiltonian systems abstract a simple theorem in hamiltonian mechanics is pointed out one consequence is a generalization of the classical result that symmetries are generated by poisson brackets of conserved functionals general applications are discussed special emphasis is given to the kadomtsev petviashvili equation

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

on a new hierarchy of symmetries for the kadomtsev petviashvili equation abstract we present a new hierarchy of symmetries for the kadomtsev petviashvili equation these new symmetries depend on the space and time variables explicitly together with the previously known classical symmetries they constitute an infinite dimensional lie algebra

an algebraic theory for design of controllers for linear multivariable systems part i structure matrices and feedforward design in this two part paper a theory is presented in which several control problems can be solved the theory is applicable to a general class of linear multivariable systems where the measured output does not have to be equal to the controlled output or the state the system may be affected by nonmeasurable disturbances only controllers which stabilize the system and have proper transfer functions are allowed i e the controllers have to be physically realizable it is shown that the solutions to control problems of servo type e g problems of model matching decoupling and invertibility are special cases of the solution to a more general problem analogously the solutions to problems of regulator type e g disturbance decoupling output regulation and pole placement are also speclal cases of the solution to a more general problem it is shown that problems of servo type and regulator type can be solved independently of each other in part i generalized polynomials are introduced as a mathematical framework structue matrices which describe how well a system can be controlled are defined finally problems of servo type are solved part ii mainly deals with problems of regulator type