limit cycle oscillation of missile control fin with structural non linearity non linear aeroelastic characteristics of a deployable missile control fin with structural non linearity are investigated a deployable missile control fin is modelled as a two dimensional typical section model doublet point method is used for the calculation of supersonic unsteady aerodynamic forces and aerodynamic forces are approximated by using the minimum state approximation for non linear flutter analysis structural non linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method the linear and non linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio from the non linear flutter analysis various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary the non linear flutter characteristics and the non linear aeroelastic responses are investigated

riccati differential equation in optimal filtering of periodic non stabilizable systems this paper discusses the periodic solutions of the matrix riccati differential equation in the optimal filtering of periodic systems special emphasis is given to non stabilizable systems and the question addressed is the existence and uniqueness of a steady state periodic non negative definite solution of the periodic riccati differential equation which gives rise to an asymptotically stable steady state filter the results presented show that the stabilizability is not a necessary condition for the existence of such a periodic solution the convergence of the general solution of the periodic riccati differential equation to a periodic equilibrium solution is also investigated the results are extensions of existing time invariant systems results to the case of periodic systems

optimal periodic control implemented as a generalized sampled data hold output feedback control a method for converting analog linear quadratic regulation control to a generalized sampled data hold output feedback control for a linear periodic system or a linear time variant system is presented it is shown that by using such a conversion one can implement the optimal periodic control scheme in the presence of incomplete and delayed state measurements

limit cycle stability reversal near a hopf bifurcation with aeroelastic applications abstract the objective of this paper is to present an analytical numerical analysis of the phenomenon of limit cycle stability reversal from unstable to stable and vice versa a singular perturbation technique the method of the normal form in the asymptotic expansion version is utilized the number of equations is then reduced to a minimal set for which the results are in good agreement with those from the original equations this minimal set is determined by the amplitude of the points a concept closely related to the small divisors in the kam theory this set is larger than that corresponding to the zero real part eigenvalues center manifold theorem the method is applied to a specific problem an aeroelastic section with cubic free play non linearities where the parameter is the flight speed numerical studies have been performed to show the dependence of the hopf bifurcation characteristics upon the structural and geometric properties of the wing section plots depicting amplitudes and frequency versus flight speed are presented

bifurcation analysis of airfoils in incompressible flow abstract bifurcations of airfoils with non linear pitching stiffness in incompressible flow are investigated the harmonic balance method which is more practical is adopted for the analysis and numerical integration results are used as standards of checking analytical solutions calculated by asymptotic expansion method and averaging method with the aid of computer algebra have confirmed the feasibility of the harmonic balance method

analysis of limit cycle flutter of an airfoil in incompressible flow both experimental and theoretical analyses are perfomed to investigate several types of self excited oscillations of a two dimensional wing model with non linear pitching stiffiness free play non linearity receives especial attention in the low speed wind tunnel test of the wing model with free play in pitch an interesting case of double limit cycle flutter is found subsequent harmonic balance analyses ascertain not only these two sustained oscillations but also two other unstable limit cycles a digital simulation method is also used for flutter analysis the theoretical results agree well with the experimental data

brief paper the extended periodic lyapunov lemma in this paper the so called lyapunov lemma for linear systems with periodically time varying coefficients is dealt with by this lemma the asymptotic stability of a given periodic system is linked with the existence of a periodic positive definite solution of the associated lyapunov equation under the assumption on the system being observable by relaxing the observability assumption to detectability an extended version of the lemma is obtained where the system stability is linked with the existence of a periodic positive semidefinite solution of the lyapunov equation

subharmonic bifurcation analysis of wing with store flutter abstract an approximate method is developed to analyze the subharmonic bifurcation of a wing with a store aeroelastic system of which the junction stiffness is piecewise linear the key point is to treat the store as a forced oscillator under harmonic excitation exerted through the junction from the wing in limit cycle flutter states then the criteria with respect to excitation frequency can be applied to predict subharmonic bifurcation both numerical integration and wind tunnel tests show that the approximate approach is feasible

an lmi approach to periodic discrete time unbiased filtering the problem of unbiased filtering for a discrete time linear periodic system is faced by means of linear matrix inequality techniques as leading case we derive the synthesis conditions to obtain an unbiased filter and an unbiased fixed lag smoother enforcing a bound on the h performance on the error dynamics

brief the periodic optimality of lq controllers satisfying strong stabilization an lq strong stabilization problem is proposed to determine when a controller with periodic gains is locally superior to a linear time invariant compensator for this problem a p test is presented for systems with strictly proper transfer functions it is proven that the frequency range where stable periodic controllers based on weak variations about the lti case can give better performance than stable lti compensators is finite in the development a means to evaluate the second partials of functions with respect to matrix valued parameters is introduced for those systems where periodic control is warranted techniques for designing optimal periodic strongly stabilizing controllers are presented two examples detailing the application of the p test are provided as well as an optimal periodic controller design example

hopf and two multiple semi stable limit cycle bifurcations of a restrained plate subjected to subsonic flow abstract this paper is mainly about the stabilities and bifurcations of a cantilevered plate with nonlinear motion constraints in an axial subsonic flow the galerkin method is employed to discretize the governing partial differential equation the fixed points and their stabilities are presented in a parameter space based on qualitative analysis and numerical studies the system loses stability by flutter and undergoes limit cycle oscillations after instability due to the nonlinearity the stabilities of the limit cycle oscillations are addressed on the basis of the equivalent linearized method the type of hopf bifurcation subcritical or supercritical is dependent on the location of the nonlinear motion constraints interestingly for some certain states the hopf bifurcations are both subcritical and supercritical the two multiple semi stable limit cycle bifurcation which is due to the extreme point of the flutter curve is also determined results of the numerical integration method sufficiently support the analytical method presented in this paper

robust h2 performance analysis and synthesis of linear polytopic discrete time periodic systems via lmis a particular class of uncertain linear discrete time periodic systems is considered the problem of robust stabilization of real polytopic linear discrete time periodic systems via a periodic state feedback control law is tackled here along with h2 performance optimization using additional slack variables and the periodic lyapunov lemma an extended sufficient condition of robust h2 stabilization is proposed based on periodic parameter dependent lyapunov functions this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework this is illustrated on a numerical example from the literature

transonic limit cycle oscillation analysis using aerodynamic describing functions and superposition principle limit cycle oscillation for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied transonic nonlinear aerodynamic forces are calculated by solving euler equations or navier stokes equations with respect to harmonic airfoil plunging pitching motion and then the aerodynamic describing functions and the superposition principle are used to build an equivalent linearized aerodynamic model in the frequency domain hence the transonic limit cycle oscillation solutions can be obtained by the frequency domain flutter analysis method the procedures for building the aerodynamic describing function and obtaining the limit cycle oscillation solution are described in detail four examples are adopted to verify the accuracy of the present method the isogai wing model with naca 64a010 airfoil is used as the first example to verify the accuracy of the transonic linear flutter solution of the present method another naca 64a010 airfoil model with different structural parameters is then adopt

the integrability criterion in su 2 chern simons gauge theory we prove that the multiplicity spaces appearing in chern simons theory as defioned by segal vanish unless they are associated to integrable representations this and other links with conformal field theory are examined

accurate numerical integration of state space models for aeroelastic systems with free play results show the importance of accurately locating the switching point between linear subdomains when numerically integrating a piecewise linear system of equations henon s method locates the switching point to a high degree of accuracy in one integration step while eliminating the need for a specified tolerance

groupe de picard des varietes de modules de fibres semi stables sur les courbes algebriques soient x une courbe algebrique projective lisse de genre g 2 sur r d des entiers avec r 2 on note u r d la variete de modules des fibres algebriques semi stables sur x de rang r et de degre d us r d l ouvert de u r d correspondant aux fibres stables on sait que u r d est une variete algebrique projective irreductible et normale si r et d ne sont pas premiers entre eux u r d n est pas lisse sauf dans une exception le cas ou g 2 r 2 et d est pair on supposera dans cet article qu on n est pas dans ce cas on a alors codimu r d u r d us r d 2 et u r d us r d est le lieu des points singuliers de u r d si l est un fibre en droites de degre d sur x on note u r l la sous variete fermee de u r d correspondant aux fibres vectoriels de determinant isomorphe a l on etudie dans cet article les groupes de picard pic u r d et pic u r l on montre d abord que les varietes u r d et u r l sont localement factorielles on calcule ensuite pic u r d et pic u r l qui sont decrits au moyen des diviseurs thetas generalises

parametric flutter margin method for aeroservoelastic stability analysis a new parametric flutter margin method for linear and nonlinear stability analysis of aeroservoelastic systems is presented the method is based on frequency response calculations with the system s

graph lyapunov function for switching stabilization and distributed computation abstract this paper studies stabilization of discrete time switched linear systems slss using the notion of graph control lyapunov functions gclfs a gclf is a set of lyapunov functions defined on a weighted digraph where each lyapunov function is represented by a node in the digraph and there is a lyapunov inequality associated with each subgraph consisting of a node and its out neighbors the weight of a directed edge indicates the decay or growth rate of the lyapunov functions it is proved that an sls is switching stabilizable if and only if there exists a gclf the main benefits of gclfs are reduced computational cost and conservatism for stabilizability tests besides we show that the proposed gclf framework unifies several control lyapunov functions and the related stabilization theorems moreover we propose a distributed algorithm to evaluate the stabilizability with reduced computational costs by taking benefits of the graph structure of gclfs several examples are given to demonstrate the efficiency of the algorithm

inertia theorems for the periodic liapunov equation and periodic riccati equation the inertia theorems for the time invariant liapunov equation and time invariant riccati equation are generalized to the case were the coefficient matrices are periodically time varying

h filtering for linear periodic systems with parameter uncertainty abstract this paper focuses on h filtering for a class of linear periodic systems with a certain type of norm bounded time varying parameter uncertainty which appears in both the state and output matrices the problem addressed is the design of a linear periodic estimator that guarantees both the quadratic stability and and prescribed h performance on infinite horizon for the estimation error for all admissible parameter uncertainties a solution to this problem is obtained via a riccati equation approach

stabilizability of discrete time controlled switched linear systems the goal of this paper is to study the stabilizability of controlled discrete time switched linear systems cslss where the discrete switching control input and the continuous control input coexist for a given positive integer h we propose a quantitative metric of stabilizability called h contraction rate h cr and prove that it serves as an indicator of the stabilizability in the following sense the h cr is less than one for sufficiently large h if and only if the switched linear system is stabilizable in addition we develop computational tools to estimate upper and lower bounds of the h cr in particular the upper bound estimation is expressed as a semidefinite programming problem we derive its lagrangian dual problem and prove that the dual problem with an additional rank constraint gives an exact characterization of the h cr an algorithm is developed to solve the dual problem with the rank constraint

structural non linearities and the nature of the classic flutter instability abstract the paper presents an investigation of the subcritical supercritical nature of the flutter hopf bifurcation of a two degree of freedom with linear quadratic and cubic restoring forces under certain conditions the instability gives rise to stable limit cycle oscillations whereas unstable periodic orbits appear for other conditions providing a potentially dangerous non linear instability mechanism in regimes for which linear analyses predict stability the analytic approach employed herein allows for a more thorough investigation of the high dimensional parameter space than that afforded by others experimental and computational efforts counterexamples to previously held conjectures are readily found favorable comparisons are made to predictions based on less rigorous describing function or harmonic balance techniques

deflection of rectangular orthotropic plates under uniform load an experiment was performed to determine the deflected shape of symmetrically supported orthotropic plates under uniform load the experimental results were then compared with the mathematical model for shape and deflection a symmetric clamped simply supported boundary condition case was selected because it has a larger difference in peak to overall plate deflection compared with a plate that is simply supported on all sides

some comments on chern simons gauge theory following m f atiyah and r bott ab and e witten w we consider the space of flat connections on the trivialsu 2 bundle over a surfacem modulo the space of gauge transformations we describe on this quotient space a natural hermitian line bundle with connection and prove that if the surfacem is now endowed with a complex structure this line bundle is isomorphic to the determinant bundle we show heuristically how path integral quantisation of the chern simons action yields holomorphic sections of this bundle

a note on the maximal solution of the periodic riccati equation the periodic symmetric solutions of the periodic riccati differential equation associated with the filtering problem are considered by the authors it is proven that under the sole assumption of detectability there exists a maximal solution moreover such a solution turns out to be strong i e the characteristic multipliers of the associated closed loop system belong to the closed unit disk the proof relies on an iterative linearization technique which calls for a sequence of periodic lyapunov equations similar results are given for the minimal solution

on a general optimal algorithm for multirate output feedback controllers for linear stochastic periodic systems a modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed by combining the discrete time linear quadratic regulation lqr control problem and the discrete time stochastic linear quadratic regulation slqr control problem to obtain an extended linear quadratic regulation elqr control problem one derives a general optimal algorithm to balance the advantages of the optimal transient response of the lqr control problem and the optimal steady state regulation of the slqr control problem in general the solution of this algorithm is obtained by solving a set of coupled matrix equations special cases for which the coupled matrix equations can be reduced to a discrete time algebraic riccati equation are discussed a reducable case is the optimal algorithm derived by h m al rahmani and g f franklin 1990 where the system has complete state information and the discrete time quadratic performance index is transformed from a continuous time one

maximal solution of a certain class of periodic riccati differential equations this paper deals with a generalized version of the well known periodic riccati differential equation which arises in certain optimal filtering problems for linear periodic systems a monotonicity property for symmetric periodic equilibrium solutions is established and it is proved that there exists a maximal symmetric periodic equilibrium solution

non linear dynamics of a two dimensional airfoil by incremental harmonic balance method periodic oscillations and bifurcations of a two dimensional airfoil in plunge and pitching motions with cubic pitching stiffness in incompressible flow is investigated using the incremental harmonic balance ihb method the bifurcations are obtained with the parametric continuation technique and the stability of the periodic motions is investigated using the floquet theory the autonomous non linear system of the airfoil undergoes initial hopf bifurcation leading to limit cycle oscillation as the airspeed parameter is increased further increase in the airspeed causes symmetry breaking saddle node and period doubling bifurcations leading to chaos the frequency of the limit cycle oscillation is also determined in the ihb method

toric structures on the moduli space of flat connections on a riemann surface volumes and the moment map abstract in earlier papers we constructed a hamiltonian torus action on an open dense set in the moduli space of flat su 2 connections on a compact riemann surface where the dimension of the torus is half the dimension of the moduli space this torus action shows that this set can be viewed symplectically as a noncompact toric variety the number of integral points of the moment map for the torus action turns out to be identical to the verlinde dimension d g k as an application we furnish a new proof of the relation between the large k limit of d g k and the volume of the moduli space from our point of view this relation follows from the equality between the symplectic volume of a toric variety and the euclidean volume of the image of the moment map similar considerations are shown to give rise to the volumes of moduli spaces of parabolic bundles on a riemann surface knowledge of these volumes has been shown to allow a proof of the verlinde formula for the dimension of the space of holomorphic sections of line bundles on this space

bifurcation analysis of a two degree of freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation incremental method abstract a perturbation incremental pi method is presented for the computation continuation and bifurcation analysis of limit cycle oscillations lco of a two degree of freedom aeroelastic system containing a freeplay structural nonlinearity both stable and unstable lcos can be calculated to any desired degree of accuracy and their stabilities are determined by the floquet theory thus the present method is capable of detecting complex aeroelastic responses such as periodic motion with harmonics period doubling pd saddle node bifurcation neimark sacker bifurcation and the coexistence of limit cycles emanating branch from a pd bifurcation can be constructed this method can also be applied to any piecewise linear systems

the difference periodic ricati equation for the periodic prediction problem gives a comprehensive treatment of several important aspects of the discrete time periodic riccati equation dpre arising from the prediction problem for linear discrete time periodic systems the authors analyze the symmetric periodic positive semidefinite spps solution of the dpre under appropriate assumptions of stabilizability and detectability of the periodic system among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the spps solution and the stability of the resulting closed loop system some of these results can be seen as extensions of the corresponding results for the time invariant case however a number of them contain contributions to the time invariant case as well the paper also gives a numerical algorithm based on an iterative linearization procedure for computing the spps solution the algorithm is a periodic version of kleinman s algorithm for the time invariant case

stabilizability and detectability of linear periodic systems abstract in this paper four characterizations of stabilizability and detectability of linear periodic systems are considered two of them look as natural extensions of the classical definitions given for time invariant systems the remaining two are modal characterizations which turn out to be useful in the analysis of the periodic lyapunov and riccati equations it is shown that all these notions of stabilizability and detectability are in fact equivalent to each other one of the various definitions calls for the existence of the kalman canonical decomposition of periodic systems this issue is addressed in the appendix

an iterative procedure for nonlinear flutter analysis an iterative procedure in the frequency domain is presented for flutter analysis of large dynamic systems with multiple structural nonlinearities the major components of the procedure are the describing function approach for system linearization a structural dynamics modification method for shifting system mode shapes and frequencies and a complex eigenvalue algorithm for solution of the flutter equation the purpose of the procedure is to achieve alignment of the oscillatory amplitude in each nonlinear spring with the describing function prediction of stiffness before computing the final stability characteristics the result is a system tuned to the flutter frequency at the time of instability to support the development and validation of the procedure several describing functions are formulated and a quantitative measure of the errors in each is presented validation of the iterative method is accomplished through examples involving dynamic systems of increasing complexity coupled with various representations of the unsteady aerodynamic forces both numerical simulations and experimental data are used to compare with the iterative predictions in the cases studied the agreement is good to excellent with the method accurately predicting the amplitude of a limit cycle flutter as well as the initial disturbance required to produce flutter

periodic solutions of periodic riccati equations for periodically time varying matrix riccati equations controllability and observability in the usual sense are shown to be sufficient for the existence of a unique positive definite periodic solution

h controllability and observability of linear periodic systems with reference to linear periodic systems the classical notion of controllability introduced by kalman k controllability is shown to be equivalent to the characterization of controllability h controllability first proposed by hewer as a natural extension to the periodic case of an eigenvalue eigenvector controllability condition independently introduced by several authors for time invariant systems only the proof of such an equivalence also leads to the conclusion that if a t periodic system s is k controllable and k is the degree of the minimal polynomial of the monodromy matrix associated with s then at any time t s is controllable over t t kt since k is lower than or equal to the system order a well known result due to brunovsky is slightly strengthened by duality the corresponding observability results follow

lyapunov and riccati equations periodic inertia theorems the lyapunov and riccati differential equations with periodically time varying coefficients are considered under the assumption of detectability of the underlying periodic system two inertia theorems are provided linking the inertia of the solution to the one of the so called monodromy matrix

estimates of asymptotic trajectory bounds in digital implementations of linear feedback control systems estimates are established for trajectory bounds which are easy to calculate applicable to general controller topologies and dependent on parameters i e eigenvalues and eigenvectors of the idealized linear system i e the control system model neglecting quantizers the approach utilizes the comparison principle in the lyapunov theory and the properties of minimal matrix norms the applicability of the results are demonstrated by means of a specific example

h sub infinity state estimation for linear periodic systems this note deals with the h sub infinity state estimation problem for linear periodic systems the question addressed is the design of an unbiased linear periodic and asymptotically stable estimator that achieves a prescribed h sub infinity performance on an infinite horizon necessary and sufficient conditions for the existence of a periodic estimator have been derived asymptotic properties of the finite horizon estimation problem when the time horizon tends to infinity are also investigated

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4