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1.
The commenter argues that the result of the above-titled work (see ibid., vol.37, no.10, p.1558-1561, Oct. 1992) is incorrect. It is pointed out that when sampling a continuous-time system G (s ) using zero-order hold, the zeros of the resulting discrete-time system H (z ) become complicated functions of the sampling interval T . The system G (s ) has unstable continuous-time zeros, s =0.1±i . The zeros of the corresponding sampled system start for small T from a double zero at z =1 as exp(T (0.1±i )), i.e., on the unstable side. For T >1.067 . . . the zeros become stable. The criterion function of the above-titled work, F (T )=G *(j ωs/2)= H (-1)T /2, is, however, positive for all T , indicating only stable zeros. The zero-locus crosses the unit circle at complex values 相似文献
2.
The minimal realization of a given arbitrary transfer function matrix G (s ) is obtained by applying one orthogonal similarity transformation to the controllable realization of G ( s ). The similarity transformation is derived by computing the QR or the singular value decomposition of a matrix constructed from the coefficients of G (s ). It is emphasized that the procedure has not been proved to be numerically stable. Moreover, the matrix to be decomposed is larger than the matrices factorized during the step-by-step procedures given 相似文献
3.
Let a family of polynomials be P (s )=t 0s n+t 1s n±1 + . . . + t n where 0<a j⩽t j⩽b j. V.L. Kharitonov (1978) derived a necessary and sufficient condition for the above equation to have only zeros in the open left-half plane. The present authors derive some similar results for the equation to be strictly aperiodic (distinct real roots) 相似文献
4.
The problem of absolute stability in a vibrational feedback controller is introduced and discussed. It is shown that for any rational G (s )=n (s )/d (s ) with d (s ) Hurwitz and deg d (s ) -deg n (s )=1 there exists a linear dynamic periodic controller that ensures, in a certain sense, the infinite sector of absolute stability. This implies that an additional dynamical element, inserted in the feedback loop, may lead to improvements in the robustness of nonlinear systems 相似文献
5.
Let φ(s ,a )=φ0(s ,a )+ a 1φ1(s )+a 2 φ2(s )+ . . .+a kφ k(s )=φ0(s )-q(s , a ) be a family of real polynomials in s , with coefficients that depend linearly on parameters a i which are confined in a k -dimensional hypercube Ωa . Let φ0(s ) be stable of degree n and the φi(s ) polynomials (i ⩾1) of degree less than n . A Nyquist argument shows that the family φ(s ) is stable if and only if the complex number φ0(j ω) lies outside the set of complex points -q (j ω,Ωa) for every real ω. In a previous paper (Automat. Contr. Conf., Atlanta, GA, 1988) the authors have shown that -q (j ω,Ωa ), the so-called `-q locus', is a 2k convex parpolygon. The regularity of this figure simplifies the stability test. In the present paper they again exploit this shape and show that to test for stability only a finite number of frequency checks need to be done; this number is polynomial in k , 0(k 3), and these critical frequencies correspond to the real nonnegative roots of some polynomials 相似文献
6.
Considers the polynomial P (s )=t 0 S n+t 1 S n-1 +···+t n where 0<a j⩽t j⩽b j. Recently, V.L. Kharitonov (1978) derived a necessary and sufficient condition for this polynomial to have only zeros in the open left-half plane. Two lemmas are derived to investigate the existence of theorems similar to the theorem of Kharitonov. Using these lemmas, the theorem of Kharitonov is generalized for P(s) to have only zeros within a sector in the complex plane. The aperiodic case is also considered 相似文献
7.
The problem of tightly bounding and shaping the frequency responses of two objective functions T i(s )( i =1,2) associated with a closed-loop system is considered. It is proposed that an effective way of doing this is to minimize (or bound) the function max {∥T 1(s )∥ ∞, ∥T 2(s)∥∞} subject to internal stability of the closed-loop system. The problem is formulated as an H ∞ control problem, and an iterative solution is given 相似文献
8.
Cheetham R.P. Oommen B.J. Ng D.T.H. 《Knowledge and Data Engineering, IEEE Transactions on》1993,5(4):695-704
Consider a set A ={A 1,A 2 ,. . ., A n} of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S =[s 1,s 2 ,. . ., s N] and are to be arranged lexicographically using a binary search tree (BST). If S is known a priori, it is well known that an optimal BST may be constructed using A and S . The case when S is not known a priori is considered. A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme, the restructuring is performed only if it decreases the weighted path length (WPL) of the overall resultant tree. An optimized version of the latter method, which requires only one extra integer field per record has, is presented. Initial simulation results comparing this algorithm with various other static and dynamic schemes indicates that this scheme asymptotically produces trees which are an order of magnitude closer to the optimal one than those produced by many of the other BST schemes reported in the literature 相似文献
9.
A network-theoretic approach to the design of a dynamic precompensator C (s ) for a multiinput, multioutput plant T (s ) is considered. The design is based on the relative degree of each element of T (s ). Specifically, an efficient algorithm is presented for determining whether a given plant T (s ) has a diagonal precompensator C ( s ) such that, for almost all cases, T (s )C (s ) has a diagonal interactor. The algorithm also finds any optimal precompensator, in the sense that the total relative degree is minimal. The algorithm can be easily modified to work even when a T (s ) represented by a nonsquare matrix is given 相似文献
10.
In a general algebraic framework, starting with a bicoprime factorization P =N prD -1 N pl, a right-coprime factorization N p D p-1, a left-coprime factorization D -1pN p, and the generalized Bezout identities associated with the pairs (N p, D p) and (D ˜ p, N ˜p) are obtained. The set of all H -stabilizing compensators for P in the unity-feedback configuration S (P , C ) are expressed in terms of (N pr, D , N pt) and the elements of the Bezout identity. The state-space representation P =C (sI -A )-1B is included as an example 相似文献
11.
Let a family of polynomials be P (s )=t 0S n+t 1s n-1 . . .+t n where O <α j⩽t j⩽β. Recently, C.B. Soh and C.S. Berger have shown that a necessary and sufficient condition for this equation to have a damping ratio of φ is that the 2n+1 polynomials in it which have t k=αk or t k=βk have a damping ratio of φ. The authors derive a more powerful result requiring only eight polynomials to be Hurwitz for the equation to have a damping ratio of φ using Kharitonov's theorem for complex polynomials 相似文献
12.
A frame approach to the H ∞ superoptimal solution which offers computational improvements over existing algorithms is given. The approach is based on interpreting s numbers as the largest gains between appropriately defined spaces. Some useful bounds on Hankel singular values and s numbers are derived 相似文献
13.
Out-of-roundness problem revisited 总被引:4,自引:0,他引:4
Le V.-B. Lee D.T. 《IEEE transactions on pattern analysis and machine intelligence》1991,13(3):217-223
The properties and computation of the minimum radial separation (MRS) standard for out-of-roundness are discussed. Another standard out-of-roundness measurement called the minimum area difference (MAD) center is introduced. Although the two centers have different characteristics, the approach to finding both centers shares many commonalities. An O (n log n +k ) time algorithm which is used to compute the MRS center is presented. It also computes the MAD center of a simple polygon G , where n is the number of vertices of G , and k is the number of intersection points of the medial axis and the farthest-neighbor Voronoi diagram of G . The relationship between MRS and MAD is discussed 相似文献
14.
A necessary and sufficient condition is presented for the solution of the row-by-row decoupling problem (known as Morgan's problem) in the general case, that is, without any restrictive assumption added to the system to the feedback law u =Fx +Gy (G may be noninvertible). This is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system. These integers are the infinite zero orders (Morse's list I 4) and the essential orders of the system, which only depend on the input-output behavior, and Morse's list I 2 of the system, which depends on the choice of a particular state realization 相似文献
15.
The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to δP or not; (2) allowing the observation of the output of δP or not. The plant perturbation δP is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations δP for which the perturbed system remain stable 相似文献
16.
For discrete systems, the set of all state covariances X which can be assigned to the closed-loop system via a dynamic controller is characterized explicitly. For any assignable state covariance X , the set of all controllers that assign this X to the closed-loop system is parameterized with an arbitrary orthonormal matrix U of proper dimension 相似文献
17.
Considers the monic polynomial f (z ):=z n+a n-1z n-1+. . .+a 0 in the complex variable z with complex coefficients. Under the assumption that the nonleading coefficients of f lie in the disk |z |⩽A the authors give an estimate for the smallest disk |z |⩽R containing all zeros of f . The estimate has a guaranteed precision of a few percent. They proceed similarly to obtain a zero-free disk |z |⩽r 相似文献
18.
An algorithm intended for software implementation on a programmable systolic/wavefront computer is presented for the computation of a complex-valued frequency-response matrix G . Typically, real-valued state-space model matrices are given and the calculation of G must be performed for a very large number of values of the scalar frequency parameter. The algorithm is an orthogonal version of an algorithm described previously by A.J. Laub (ibid., vol.26, no.4, p.407-8, 1981). The system matrix A is reduced initially to an upper Hessenberg form which is preserved as the frequency varies subsequently. A systolic QR factorization of a certain complex-valued matrix is then implemented for effecting the necessary linear system solution (inversion). The critical computational component is the back solve. This computational component's process dependency graph is embedded optimally in space and time through the use of a nonlinear spacetime transformation. The computational period of the algorithm is O(n ) where n is the order of the matrix A 相似文献
19.
The condition under which it is possible to find a single controller that stabilizes k single-input single-output linear time-invariant systems p i(s ) (i =1,. . .,k ) is investigated. The concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable. A method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example 相似文献
20.
Simple formulas are presented to compute the internally balanced minimal realization and the singular decomposition of the Hankel operator of a given continuous-time p ×m stable transfer function matrix E(s )/d (s ). The proposed formulas involve the Schwarz numbers of d (s ) and the singular eigenvalues-eigenmatrices of a suitable finite matrix. Similar results are also obtained for a given discrete-time transfer function matrix 相似文献