摘要:

Hermite's stability criterion is expressed in a simpler form involving a suitably defined observability matrix, and the Hermite matrixHis represented in controllability-observability matrix form. These results are generalized to the ease when the polynomial is expressed in terms of an arbitrary orthogonal basis. The relationship between the Hermitian matrixHand an alternative real symmetric matrix is given, together with the appropriate criteria for root location with respect to the imaginary axis. Also discussed are the form of the inverse ofHand applications to Sylvester-form matrices, the reduced Hermite and Schur-Cohn matrices, and the Markov criterion.

ISSN:0020-7179    

DOI:10.1080/00207177908922728

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Popov-type stability criteria are given for two types of multivariable feedback systems. The systems are regarded as interconnections of several subsystems and the composite-system method is used to derive the criteria. The values of constants which are needed in the criteria are calculated and tabulated for first- and second-order subsystems. By using these values, we can immediately obtain a stability criterion for the system consisting of first- and/or second-order subsystems. Examples show that the criteria obtained are as sharp as or sharper than previously reported criteria.

ISSN:0020-7179    

DOI:10.1080/00207177908922729

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The ability to manipulate the release condition of the state vector from the input terminals of linear systems is of importance to a number of control applications. This problem has already received considerable attention for single-input single-output systems and suitable generalizations of the results to the multivariable case are discussed in this paper. A study of the geometric properties of the subspaces in the state space where the transferring of the state vector in minimum time is possible leads to the concept of controllability subspace in a manner that enables the unification of the existing physical, algebraic and geometric definitions of controllability subspace. A characterization of controllability subspace in terms of polynomial vectors is discussed together with possible applications for its computation.

ISSN:0020-7179    

DOI:10.1080/00207177908922730

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The Kronecker canonical form of the input-state pencil8N-NAis used in the derivation of the basis matrix description of the polynomial vectors p(8) lying in the kernel space of8N-NA; starting from that description of the vectors p(8), the basis matrix characterization of controllability subspaces (c.s.) (Vardulakis 1978) follows in a simple yet general way. The significance of the matrix characterization of c.s. extends beyond the computational aspects of c.s. ; using arguments based on the special structure of the basis matrix, simple proofs of the Warren and Eckberg (1975)results are given.

ISSN:0020-7179    

DOI:10.1080/00207177908922731

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Frame alignment, performed by the ALIGN algorithm, plays an important role in the characteristic locus design method. A number of extensions to ALIGN intended to enhance the effectiveness of the design technique are proposed. In particular, the application of ALIGN at a number of frequency points is considered while an alternative least squares approach to frame alignment is developed. The problem of scaling both the frames to be aligned as well as the resulting frame solutions is examined and procedures for optimizing the use of the approximate commutative controller technique are suggested.

ISSN:0020-7179    

DOI:10.1080/00207177908922732

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Lower and upper bounds for the quadratic cost functional of linear regulators are derived. These bounds are explicitly expressed in terms of some system parameters, arc independent of the initial conditions and are rather easy to compute. The results are based on a previous work by the authors concerning the lower bound. In this paper, the upper bound established is used to improve the lower bound, both being calculated by an iterative procedure to any degree of accuracy which is dependent on the number of iterations only.

ISSN:0020-7179    

DOI:10.1080/00207177908922733

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

We study the asymptotic tracking and disturbance rejection property of a general non-linear multi-input multi-output distributed servomechanism which consists of input as well as output channel non-linearity. We also explore the robustness of this property of such non-linear servomechanism. Our result shows that the design principle of the robust linear servomechanism (i.e. replicating the dynamics of the reference and disturbance signals) works well for a large class of non-linear servos provided that certain stability conditions are satisfied.

ISSN:0020-7179    

DOI:10.1080/00207177908922734

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

This paper presents an algorithm for the computation of optimal singular control. The trajectory is decomposed to singular and non-singular sub-arcs. Each sub-arc is optimized locally. The interactions between different sub-arcs are then determined by a second level controller. An illustrative example is included.

ISSN:0020-7179    

DOI:10.1080/00207177908922735

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Structural properties of a linear multivariable system have been defined as invariants under various transformation groups using the theory of singular pencils of matrices or using a geometric approach. In this paper it is shown that for a strictly proper system in state-space form, these structural properties can be identified by bringing the system matrix to a particular form under system similarity. This allows a structural analysis to be incorporated in existing computer-aided design methods for multivariable control systems. In relation to these structural properties, Rosenbrock's definition of system zeros is investigated and it is shown how this definition fits into the framework of pencil theory and of the geometric approach. This leads to a precise structural interpretation of the relation between Rosenbrock's system zeros and the invariant zeros defined in accordance with pencil theory. The structural analysis presented in this paper also allows us to identify the zeros at infinity and to characterize their nature irrespective of restrictive assumptions such as system invertibility or equal number of inputs and outputs

ISSN:0020-7179    

DOI:10.1080/00207177908922736

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Some results on the optimization of the geometric structure of zones of action connected with an optimal control problem are presented. These results represent an extension of a previous study (Amouroux and Babary 1978), and show by example, analogies between results for pointwise control and distributed control over zones.

ISSN:0020-7179    

DOI:10.1080/00207177908922737

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor