Decentralized Bezout Identity and a Parametrization of Decentralized Controllers for Singular Systems

1　 IntroductionConsider a singular decentralized control system of the formEx(t) =Ax(t) ∑Ni=1Biui(t)yi =Cix(t) ,i∈ N ={ 1 ,2 ,… ,N}(1 )where x(t)∈ Rn is the state vector,ui(t)∈ Rmi and yi(t)∈ Rpi are respectively the localcontrol input and measure outputvectors of the ith control channel.The matrix E may besingular,i.e.,rank(E) 相似文献   

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.     

THE BERRY-ESSEEN BOUND AND LIL PP CM STATISTIC TESTING UNIFORM DISTRIBUTION ON SPHERE ABOUT DIMENSION AND SAMPLE SIZE

1. IntroductionXI, Xz,'' I Xu are i.i.d. p dimension random vectors with distribution function F(x).Cuilzldefined PP Cramer-Von Mises test statistic as follows:where F:(x) ~ (Z:=, I[a'Xi 5 x])/n is the empirical distribution function of a'XI, a'X2,' ', a'X.. F"(x) ~ P(a'X, 5 x) is distribution function of a'XI, p(.) is uniform measuxeon SP--1. Under null hypothesis HO: XI has uniform distribution on SP--1, F"(x) 2 G(x) =if, g(u)du, where g(u) ~ {r(p/2)(1 -- u')(P--')/'}/{(r(1/2…     

A CHARACTERIZATION OF REALCOMPACT STONIAN SPACES X AND EXTENDED RIESZ HOMOMORPHISMS ON C~∞(X)

1. IntroductionBy R(= [--co, co]) we denote the two-point compactification of the real line R. The rulesfor addition and multiplication are extended to boo in the usual wad, i.e., for ally af A E Rand A > 0, we define a (f co) ~ boo, (boo) (loo) = boo, A. (boo) = boo, (--A). (boo) =Too, (boo).(~oo) = co and (loo).(Too) = --co, where it is understood that the multiplicationobeys 0' (boo) ~ (loo)' 0 = 0. For any p) q E R, we say that p q makes sense whenever thecase of p ~ co and q…     

STRONGLY CONSISTENT ESTIMATION FOR A MULTIVARIATE LINEAR RELATIONSHIP MODEL WITH ESTIMATED COVARIANCES MATRIX

1 IntroductionSuppose that the true values Of a set of variables satisfy exact linear relationships, but theyare unobserved. We can Obtain the Observed values which are the sums of the true values anderrors of measurement. The model is described as follows. A set of rmdimensional vectors {xh}satisfyB'xk or = 0, k = 1,2,'' t (1.1)where B is an m x p parameter mains with rank p < m and o is a p x 1 parameter vector. Weobserved {Zk}, which are m x 1 random vectors and satisfyZk = ac ed, …     

GOODNESS-OF-FIT TEST ON TWO SAMPLES

1. IntroductionLet XI t X2,'', X. and YI, YZ,'', Ye be i.i.d. random variables with continuous distribu-tion functions F(x) and G(x) respectively. We want to test the hypothesisbased on (XI, X2,'' t X.; YI, Y2,'. I Ym).It is well know that this is called a two--sample problem. In 1930, Smirnov proposed astatistics, referred to ajs Smirnov Statistics (SM-statistics), to test hypothesis (1). But the powero' SM-statistics is lower. To improve the test power, some statisticians pro…     

QUATERNARY DELSARTE—GOETHALS AND GOETHALS—DELSARTE CODES

1 IlltroductionLet an be the ring of integers modulo 4 and m be the set of n-tuples over wi. A an-linearcode C of length n is a ffe-submodule of m. The type of C is defined to be the type of C asan abelian group. Define the dual code Cl of C byCl = {(x1,x2,'' 5 x.) e wr: x1y1 x2y2 '' xrty. = 0,V(y1,y2,'',y.) 6 C}.The Lee weights of 0, l, 2, 3 E Wi are defined to be 0, 1, 2, l, respectively, and the Lee weightWL(a) of a 6 W is the rational sum of the Lee weights of its cornponent…     

THE SPECTRAL COMPLETION OF A CLASS OF OPERATOR PARTIAL MATRICES

1. IntroductionLet Hi be complex Banach spaces, i = 1, 2,'' 5 n, and B(Hi, Hi) (B(Hi) if i = j) denotethe Banach space of all bounded linear operators from Hi to Hi. Let H ~ ffi:=IHi; thenA E B(H) may .be denoted by (Ail)... with Ail e B(Hj,Hi). Given a subset J C {(i,j)li,j = 1, 2,'',n} and Ail E B(Hj,Hi) for (i,i) e J, we get a partially specified n x n matriX(Xij)... with Xij ~ Ail if (i,i) e J and Xby (Ail)J If Q = (oil) E B(H) such that oil ~ Aijwhenever (i,i) e J, the…     

THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

1 Formulation of Dirichlet Problem and Neumann Problem fOrParabolic SystemsLet O be a bounded domain in Rn and the boundary On E C2. Denote Q = g x I,I =0 < t 5 T, 0 < T < ool 0Q = Sl U S2 is the parabolic boundary where S1 = a x {t = 0} is thebottom and S2 = an x I is the lateral boundary. We consider the nonlinear parabolic systemof second order equationsFh(t, xl ut D.u, D:u) -- Hukt = 0 in Q, k = 1, 2,'',m. (l.l)Under certain conditions, system (1.1) can be reduced to the fOrmw…     

APPLICATIONS OF INTEGRATED SEMIGROUPS TO HIGHER ORDER ABSTRACT CAUCHY PROBLEMS

This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:(ACP_n) x~(n)(t)=sum from i=0 to n-1 B_ix~(i)(t),x~(i)(0)=x_i,0(?)i(?)n-1where B_i (0(?)i(?)n-1) are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B_(n-1) is bounded andD(B_(n-2))(?)D(B_i)(0(?)i(?)n-3) are obtained.     

IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

Let x_1,…, x_n be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the timet=r, where r is a stopping time. The observed data set is Z_n=(x_(1),…, x_(k), r(x)),where x_(i)(i=1,…, n) is the order statistic of x_i, i=1,…, n and k=k(x) is the num-ber of the observed data. Suppose that the distribution family of x_i, i=1,…, n is i.i.d.exponential with life expectation θ>0. For testing the hypothesis H_0: θ≤θ_0 againstH_1: θ>θ_0, we use the total time of experiment S_r=sub from i=1 to k x_(i) +(n-k)r (x) as the teststatistic. We reject H_0 as large value of S_r is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement ofthe one, which is based on r, in the sense that the power functions of the two tests are thesame but the test based on r_0 is the one which has the minimnm total experiment time.     

Parallel Rosenbrock Methods for DifferentialAlgebraic Equations

1. INTRODUCTIONWe consider the system of dtherelltial-algebraic equations(DAE)where y is in some space E and z in EI. For convenience of notations we assume that y and z are scalarqualities. All subsequeDt formulas remain valid for vectors if the derivatives are interpreted as multilinearmappings. We suppose that the initial values are consistent, i.e. g(yo, to) = 0. Moreover j and g are assumedto be sufficiently differentiable. We also assume the DAE system to be of index one; it me…     

Error Analysis in Frequency Domain for Linear Multipass Algorithms

1. INTRoDUCTIONConsider the dyntalc systemdridt = Ax Bu (1)y = Cx Du (2)whre u is the inPut VaIable; y is the output wriab1e, and x = (x', x2,...,x")" is the state vahale. A, B, Cand D are n x n, n x r, l x n, l x r constant matrices, respectively The transfer function H(s) of equabo (1)and (2) is given bywhere H(s) and oi(i = 0, 1,..., n) are l x r matrices; pi, i = 0, 1,... 1 n are real nUIners. lt can be seen thathe sca1ar relation between every pair of input comPoneni ui and …     

SYSTEM MODELING AND OPTIMIZATION OF A PORT SYSTEM WITH DIFFERENT SHIP''''S KINDS

The analysis and evaluation of an actual port system containing R differentship's kinds and N subsystems each of which consists of M.(i=1, 2,…, N) ports arederived. The external arrivals of ships to the system come from R different Poisson sourcesand the interarrivals to the queue of each port of a subsystem are determined according tocondition probabilities. Each port has multiple berths whose service times are distributedaccording to Erlang probability distribution functions. Each port of a subsystem has Rinfinite capacity buffers for storing ships interarrived. This method provides a good approximation procedure for obtaining system perfor-mance measures such as waiting times of ships, average queue lengths, etc. Optimum portcapacity can thus be evaluated by using this analysis. A simulation is also presented totest this approximate analysis, and a good agreement is observed. This model shall be usedin the planning of several actual port systems. Through the application of this model, itis possible to analyze and evaluate performances of the systems.     

EXISTENCE OF CONSISTENT ESTIMATES OF LINEAR REGRESSION COEFFICIENTS WHEN THE ERROR VARIANCES ARE UNEQUAL

Consider the linear regression model Y_i=x_i′β+σ_ie_i,i=1,…,n,…,where E(e_i)=0,E(e_ie_j)=δ_(ij),0<σ_1~2(?)σ_2~2(?)…and {x_i} satisfies A_1(?)sum from i=1 to n x_ix_i′/n(?)A_2,for n large,A_1>0,A_2>0.This paper shows that (i) ifσ_i~2,i=1,2…,are known,then the necessary and sufficient condition for theconsistency of the best unbiased linear estimate of β is sum from i=1 to ∞σ_i~(-2)=∞;(ii)if{σ_i~2}is only known to belong to the set {(h_1,h_2,…)∶0相似文献   

LAWS OF THE ITERAFED LOGARITHM FOR TRIMMED SUM

1.IntroductionLetX,X1,X2,''beasequenceofn0n-degenerateindependelltidenticallydistributedra-n-domVarableswithcommondistributionfunctionF,andletXl,'',X2beanarrangementofXl,'Xnindecreasingorderofmagnitude,i.e.IX:l2''2IX2I.SetS;=Z:. ,X;.Forx>0,defineandforx=0,setG(O)=Q(O)=P(IXI>O),K(0)=0-DeAneLetrnbeanynon-decreasingsequenceofilltegerssuchthatwheref>0andwewritel2nforloglogn.By(1.1)and(l.2),forsufficientlylargentwecandeflneasequenceb.byP.S.Griffinl1Jobtainedthefollowingtheorem:R…     

A CLASS OF GENERALIZED MULTIPROCESSOR SCHEDULING PROBLEMS

1. IntroductionOne of the fundamental problems in the theory of scheduling is to sChedule n independent jobs non-preemptively on m 2 2 multiprocessors. It is well-known that PllCm.. andPI I Z:=, wiCi are strongly NP-hardll'2].In this paper, we consider a class of generalized multiprocessor scheduling problem. It canbe described as follows: There are m almost identical processors M = {MI, M2,'' 5 Mm}, andn independent jobs J = {JI, J2,'' 9 Jn}. The processing time of job Ji is pi. A…     

LOWER BOUNDS OF RAMSEY NUMBERS

The lower bounds for any R(l_1,…,l_q;r)are investigated.Let K_n~r be the completer-uniform hypergraph on n points.Define R(l_1,…,l_q;r)as the minimal natural number n sothat if the edges of K_n~r are q-colored,there is a set S of l_i(i∈{1,…,q})vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd(?)s and J.Spencer.In this paper,we shall give the lower bounds for any R(l_1,…,l_q;r).     

Subspace decomposition-based correlation matrix multiplication

The correlation matrix, which is widely used in eigenvalue decomposition （EVD） or singular value decomposition （SVD）, usually can be denoted by R = E[yiy＇i]. A novel method for constructing the correlation matrix R is proposed. The proposed algorithm can improve the resolving power of the signal eigenvalues and overcomes the shortcomings of the traditional subspace methods, which cannot be applied to low SNR. Then the proposed method is applied to the direct sequence spread spectrum （DSSS） signal＇s signature sequence estimation. The performance of the proposed algorithm is analyzed, and some illustrative simulation results are presented.     

EQUITABLE COLORINGS OF LINE GRAPHS AND COMPLETE r-PARTITE GRAPHS

1. IntroductionLet G be a graph with vertex set V(G), edge set E(G), maximum degree A(G), minimumdegree 8(G), vertex chromatic number X(G), and edge chromatic number X'(G). G is equitablyk-colorable if V(G) can be pajrtitioned icao k independent sets VI, V2,'', Vk such that llKI III 1 5 1 for all i and j. The such smallest integer k as above is called the equitable chromaticnumber of G, denoted by X= (G). Similaxly we can define the equitable edge chromatic numberof a graph G and d…