derivation and implementation of the boundary integral formula for the convective acoustic wave equation in time domain kirchhoff s formula for the convective wave equation is derived using the generalized function theory the generalized convective wave equation for a stationary surface is obtained and the integral formulation the convective kirchhoff s formula is derived the formula has a similar form to the classical kirchhoff s formula but an additional term appears due to a moving medium effect for convenience the additional term is manipulated to a final form as the classical kirchhoff s formula the frequency domain boundary integral can be obtained from the current time domain boundary integral form the derived formula is verified by comparison with the analytic solution of source in the uniform flow the formula is also utilized as a boundary integral equation time domain boundary element method bem analysis using the boundary integral equation is conducted and the results show good agreement with the analytical solution the formula derived here can be useful for sound radiation and scattering by arbitrary bodies in a moving medium in the time domain

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

classification and characteristics of floquet factorisations in linear continuous time periodic systems this article has two purposes firstly the article is devoted to collecting basic facts about the floquet theorem and various floquet factorisation algorithms claimed for finite dimensional linear continuous time periodic fdlcp systems secondly the article presents a unified representation framework for various floquet factorisations in fdlcp systems while structural and analytic characteristics about them are examined as well more precisely the following aspects are considered i algorithms for floquet factorisations ii characteristics of floquet factors iii relationships and properties among floquet factorisations most results are reported for the first time while the others are generalised versions of existing ones

an integral formulation for wave propagation on weakly non uniform potential flows abstract an integral formulation for acoustic radiation in moving flows is presented it is based on a potential formulation for acoustic radiation on weakly non uniform subsonic mean flows this work is motivated by the absence of suitable kernels for wave propagation on non uniform flow the integral solution is formulated using a green s function obtained by combining the taylor and lorentz transformations although most conventional approaches based on either transform solve the helmholtz problem in a transformed domain the current green s function and associated integral equation are derived in the physical space a dimensional error analysis is developed to identify the limitations of the current formulation numerical applications are performed to assess the accuracy of the integral solution it is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field and as a means of solving scattering problems by rigid surfaces in non uniform flows the results show that the error associated with the physical model deteriorates with increasing frequency and mean flow mach number however the error is generated only in the domain where mean flow non uniformities are significant and is constant in regions where the flow is uniform

polynomially parameter dependent lyapunov functions for robust stability of polytopic systems an lmi approach in this note robust stability of state space models with respect to real parametric uncertainty is considered specifically a new class of parameter dependent quadratic lyapunov functions for establishing stability of a polytope of matrices is introduced i e the homogeneous polynomially parameter dependent quadratic lyapunov functions hpd qlfs the choice of this class which contains parameter dependent quadratic lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form is motivated by the property that a polytope of matrices is stable if and only there exists an hpd qlf the main result of the note is a sufficient condition for determining the sought hpd qlf which amounts to solving linear matrix inequalities lmis derived via the complete square matricial representation csmr of homogeneous matricial forms and the lyapunov matrix equation numerical examples are provided to demonstrate the effectiveness of the proposed approach

output reachable set estimation for switched linear systems and its application in safety verification this paper addresses the output reachable set estimation problem for continuous time switched linear systems consisting of hurwtiz stable subsystems based on a common lyapunov function approach the output reachable set is estimated by a union of bounding ellipsoids then multiple lyapunov functions with time scheduled structure are employed to estimate the output reachable set for switched systems under dwell time constraint furthermore the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation first a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed then the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters numerical examples are provided to illustrate our results

on reachable sets for positive linear systems under constrained exogenous inputs this paper focuses on positive linear time invariant systems with constant coefficients and specific exogenous disturbance the problem of finding a hyper pyramid to bound the set of the states that are reachable from the origin in the euclidean space is addressed subject to inputs whose 1 1 norm or 1 norm is bounded by a prescribed constant the lyapunov approach is applied and a bounding hyper pyramid is obtained by solving a set of inequalities iterative procedures with an adjustable parameter for reducing the hyper volume of the bounding hyper pyramid for the reachable set are proposed

q admissibility of solvable groups abstract a finite group g is called q admissible if there exists a division algebra finite dimensional and central over the rationals q which is a crossed product for g it is proved that a finite solvable group is q admissible if and only if all its sylow subgroups are metacyclic

admissibility of groups over function fields of p adic curves let k be a field and g a finite group the question of admissibility of g over k was originally posed by schacher who gave partial results in the case k q in this paper we give necessary conditions for admissibility of a finite group g over function fields of curves over complete discretely valued fields using this criterion we give an example of a finite group which is not admissible over qp t we also prove a certain hasse principle for division algebras over such fields

tamely ramified subfields of division algebras for any number field k it is unknown which finite groups appear as galois groups of extensions l k such that l is a maximal subfield of a division algebra with center k a k division algebra for k q the answer is described by the long standing q admissibility conjecture we extend a theorem of neukirch on embedding problems with local constraints in order to determine for every number field k what finite solvable groups g appear as galois groups of tamely ramified maximal subfields of k division algebras generalizing liedahl s theorem for metacyclic g and sonn s solution of the q admissibility conjecture for solvable groups

stability stabilization and l 2 gain analysis of periodic piecewise linear systems in this paper the stability stabilization and l 2 gain problems are investigated for periodic piecewise linear systems in which not all subsystems are hurwitz first some sufficient and necessary conditions for the exponential stability are established by employing a discontinuous lyapunov function with time varying lyapunov matrix stabilization and l 2 gain conditions of periodic piecewise linear systems are proposed by allowing the corresponding lyapunov function to be possibly non monotonically decreasing over a period a state feedback periodic piecewise controller is developed to stabilize the system and the corresponding algorithm is proposed to compute the controller gain the l 2 gain criteria with continuous time varying lyapunov matrix and piecewise constant lyapunov matrices are studied as well numerical examples are given to show the validity of the proposed techniques

lower bound functions for polynomials relaxation techniques for solving nonlinear systems and global optimisation problems require bounding from below the nonconvexities that occur in the constraints or in the objective function by affine or convex functions in this paper we consider such lower bound functions in the case of problems involving multivariate polynomials they are constructed by using bernstein expansion an error bound exhibiting quadratic convergence in the univariate case and some numerical examples are given

calculation of the radiated sound field using an open kirchhoff surface means of improving the accuracy of kirchhoff surface integral evaluations for sound fields in cases where the surface may not be completely closed are investigated asymptotic analysis for large temporal wave number is used to analyze time harmonic integral forms applicability to the moderate temporal wave numbers of real problems is discussed stationary phase arguments are used to show geometrically where good results are expected from a kirchhoff integral on an open surface a similar asymptotic analysis is used to provide correction terms to account partially for the missing portion of the integral surface the present study is restricted to the case where the mean flow is parallel to the available portion of the surface the analysis is extended to time domain formulation of transient problems two and three dimensional numerical examples are given to demonstrate and evaluate the method it is found that the derived correction terms can reduce the error in an open surface calculation of the radiated sound field by more than an order of magnitude

periodic lyapunov equation based approaches to the stabilization of continuous time periodic linear systems this note is concerned with stabilization of continuous time periodic linear cpl systems with state feedback the design is based on solutions to a class of parametric periodic lyapunov differential equations pldes resulting from the problem of minimal energy control with guaranteed convergence rate by carefully studying the properties of the pldes and their solutions a continuous periodic state feedback is designed the plde based approach is effective in designing stabilizing controller for cpl systems as the designers need only to solve a linear differential equation whose solution can be obtained analytically if the system is relative simple and can be computed numerically by integration in general cases necessary and sufficient conditions on the free parameter in the plde are proposed to guarantee the stability of the closed loop system whose characteristic multiplier set can even be exactly computed accordingly a numerical example is worked out to show the effectiveness of the proposed approach

stability and l_2 synthesis of a class of periodic piecewise time varying systems in this paper the stability stabilization and l 2 gain problems are investigated for periodic piecewise systems with time varying subsystems continuous lyapunov function with time varying lyapunov matrix is adopted a condition guaranteeing the negative definiteness of a matrix polynomial deriving from the lyapunov derivative is first obtained based on such a condition an exponential stability condition is provided moreover a state feedback controller with time varying gain is developed to stabilize the unstable periodic piecewise time varying system the l 2 gain criterion for periodic piecewise time varying system is also studied numerical examples are given to show the validity of the proposed techniques

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

the sound field of a rotor in a stationary duct a method is developed for the prediction of noise from rotors in an axisymmetric duct at rest the technique combines a previously developed model for noise from disc sources with a boundary integral equation method for scattering from the duct surface recent developments in the theory of gaussian quadrature and generalized elliptic integrals are used to simplify the implementation of the formulation the sound field of a simplified model ducted rotor is then calculated and its structure examined in the framework of known features of the field around rotating sources it is found that as for an open rotor the sonic radius plays an important role in the structure of the field

division algebras with psl 2 q galois maximal subfields abstract if g is a finite group and k is a field then g is k admissible if there exists a g galois extension l k such that l is a maximal subfield of a k division algebra we prove that psl 2 7 is k admissible for any number field which either fails to contain 1 or which has two primes lying over the dyadic prime in addition psl 2 11 is shown to be admissible over q or any number field k with at least two extensions of the dyadic prime indeed there exist infinitely many linearly disjoint admissible extensions for these groups

integral input to state stability for hybrid delayed systems with unstable continuous dynamics this paper considers integral input to state stability iiss for a class of hybrid time delay systems discrete dynamics includes impulsive and switching signals and continuous dynamics is not necessarily stable based on multiple lyapunov krasovskii functionals a dwell time bound is explicitly given to guarantee iiss of the hybrid delayed system compared with existing results on related problems the obtained stability criteria can be applied to a larger class of hybrid delayed systems moreover the obtained dwell time bound is less conservative than existing ones at last an example related to networked control systems ncss is provided to illustrate the effectiveness of the proposed result

lmi techniques for optimization over polynomials in control a survey numerous tasks in control systems involve optimization problems over polynomials and unfortunately these problems are in general nonconvex in order to cope with this difficulty linear matrix inequality lmi techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems this survey aims to provide the reader with a significant overview of the lmi techniques that are used in control systems for tackling optimization problems over polynomials describing approaches such as decomposition in sum of squares positivstellensatz theory of moments polya s theorem and matrix dilation moreover it aims to provide a collection of the essential problems in control systems where these lmi techniques are used such as stability and performance investigations in nonlinear systems uncertain systems time delay systems and genetic regulatory networks it is expected that this survey may be a concise useful reference for all readers

patching subfields of division algebras given a field f one may ask which finite groups are galois groups of field extensions e f such that e is a maximal subfield of a division algebra with center f this question was originally posed by schacher who gave partial results in the case f using patching we give a complete characterization of such groups in the case that f is the function field of a curve over a complete discretely valued field with algebraically closed residue field of characteristic zero as well as results in related cases

a bem fmm approach applied to the combined convected helmholtz integral formulation for the solution of aeroacoustic problems abstract exterior and interior acoustic calculations often exploit the advantages of boundary element method bem numerical scheme due to the large dimension of dense matrices arising in real case applications direct matrix vector products become prohibitive since the computational cost of standard methods increases quadratically in this work the black box fast multipole method bbfmm based on the chebyshev interpolation is extended to the integral solution of the convective helmholtz equation stabilized using the combined helmholtz integral equation formulation chief the chief approach relies on the solution of an over determined linear system achieved by adding a set of points internal to the scattering body in order to handle the distribution of the chief points within the body volume a robust stochastic approach has been also developed moreover an adaptive bbfmm abbfmm is presented for handling the oscillating kernels such as those arising in the solution of the convective helmholtz equation the proposed approach which has a complexity of o n l o g n is interesting for industrial applications especially in the aeroacoustic field

on the theory of acoustic flow measurement the motivation for this paper arises from problems frequently encountered in acoustic flow measurement of primary concern is that acoustic flow meters rather than directly measuring the volume flow rate measure some biased average of fluid velocity in a duct that is the average is usually not equal to the volume flow rate divided by the duct cross sectional area and is influenced by alterations in the flow profile in this paper perturbation analysis is used to characterize nontrivial situations under which a sound field may be convected to first order by the unbiased cross sectionally averaged flow perturbation analysis previous to this paper has considered only the plane wave approach to the problem this paper will examine the use of higher order duct modes it will be shown that under certain circumstances these modes are less prone to distortion by the flow field than the plane wave and will still average the flow to an approximation which improves with mode order the study is restricted to the consideration of rectangular section ducts and cylindrical ducts with axisymmetric flow fields as an aside the two dimensional viscous convective wave equation by mungur and gladwell j sound vib 9 28 48 1969 has been extended to three dimensions in this paper in deriving this form it was noticed that an error existed in the original equation this error has been corrected in the present three dimensional version of the equation

a direct boundary integral formulation for acoustic radiation in a subsonic uniform flow abstract in this paper a new boundary integral formulation is proposed for acoustic radiation in a subsonic flow this new boundary integral formulation uses the green s function derived from the adjoint operator of the original governing differential equation unlike the conventional formulation that uses the helmholtz integral equation in a transformed domain the new boundary integral formulation requires no co ordinate transformation the variables in the integral equation can be expressed explicitly in terms of the velocity potential as well as its normal and tangential derivatives this will facilitate a direct coupling of the boundary element method with other numerical techniques such as the finite element method for radiation and scattering in a non uniform flow region