摘要:

A new unifying approach for the study of pole assignment by constant output feedback (CPAP) for strictly proper and proper linear systems is presented. The multilinear nature of CPAP is reduced to a linear problem and to the standard multilinear problem of decomposability of multivectors; the solvability of CPAP thus becomes a problem of finding real intersections of a linear variety with the Grassmann variety of a projective space. An alternative proof to the ml≥n(m, I, n are the numbers of outputs, inputs, states) necessary and sufficient condition for generic pole-assignability of strictly proper systems by complex output feedback is given; the above result is extended to the ml≥ n + 1 condition for the case of proper systems. Stronger necessary conditions for generic pole assignment by a real output feedback are obtained by using the recently introduced invariant, the Plücker matrix Pn such conditions are that Pn must have full rank and ml≥n (strictly proper case), or ml≥ n + 1 (proper case). It is shown that if min{m, /} = 1, then the full rank condition of Pn is necessary and sufficient for complete pole-assignability by a real output feedback. New sufficient conditions for generic pole-assignability of generic strictly proper and generic proper systems with min {m, /} ≠ 1 are obtained; for the strictly proper case, these conditions are ml> n and that a number gfα0, α1α1-1) is odd. For the proper case, these conditions become ml≥n+ 1 and that a number ǵ( α0α1,,α1,-1) is odd. For the case of strictly proper systems with ml = n, the above result is reduced to the Brockett and Byrnes (1981) sufficient condition. The approach presented in this paper is suitable for the computation of the feedback, whenever a solution exists, and this is illustrated by a number of numerical examples.

ISSN:0020-7179    

DOI:10.1080/00207178508933382

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

This paper examines when the coefficients of the closed-loop characteristic polynomial are linear in the elements of the feedback matrix. An error in previous work (Tarokh 1980) is pointed out. Necessary and sufficient conditions are given for all of the coefficients to be linear in the elements of the output feedback matrix.

ISSN:0020-7179    

DOI:10.1080/00207178508933383

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A necessary and sufficient stability criterion is proved for multivariable systems in the presence of element-by-element bounded perturbations. The result constitutes a solution to the problem of computing the μ function for this class of perturbations, and the paper also provides an explicit approximation to the exact criterion.

ISSN:0020-7179    

DOI:10.1080/00207178508933384

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this paper, finite-time output stabilization is investigated for a continuous-time system with a constant disturbance. A new feedback control law is presented which stabilizes the continuous-time system and regulates the output in finite time, using only piecewise constant controls.

ISSN:0020-7179    

DOI:10.1080/00207178508933385

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A new feedback system representation of the transient stability model of multi-machine. power systems with transfer conductances is proposed. Based on this representation, a Lur'e-type Lyapunov function is constructed. In this procedure, no approximation is made, and the function obtained is a Lyapunov function in the rigorous sense. Examples of four-machine systems are studied. The result will be useful for the transient stability analysis of power systems in which the effects of transfer conductances cannot be neglected.

ISSN:0020-7179    

DOI:10.1080/00207178508933386

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In the paper a comparison is made between two approximate methods of system analysis based on the use of the operational matrices of integration and differentiation. Both methods applied to model problems involving linear time-invariant differential equations yielded results of equal order of accuracy for the same number of orthogonal polynomial terms. However, the operational matrix of differentiation method is not limited to initial-value problems, but may easily be applied to boundary-value problems. In addition, due to the exact definition of this matrix, transformations from an orthogonal polynomial base to another may easily be performed with the use of the operational matrix of polynomial series transformation. The operational matrix of differentiation approach may be easily applied to the analysis of other types of systems such as time-varying and distributed parameter systems, and can be easily extended for other types of orthogonal differentiable base functions such as the Fourier trigonometric functions and the Bessel functions.

ISSN:0020-7179    

DOI:10.1080/00207178508933387

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A frequency-domain theory which is applicable to all linear systems and a class of non-linear systems is formulated in a Hilbert resolution space setting. Our approach is predicated on an ‘analytic’ characterization of certain non-selfadjoint operator algebras due to Arveson. Although originally used as an analytic tool, Arveson, in fact, formulated an operator-valued frequency response function for the elements of these algebras which, in particular, include the causal operators defined on a Hilbert resolution space. The resultant Arveson frequency response (AFR) is well defined for all linear and non-linear systems on a Hilbert resolution space and in the linear case it is characterized by an analyticity theory which is identical to that of the classical time-invariant frequency response concept. Moreover, it yields computationally viable formulae for the most widely studied classes of linear systems including the time-varying ABCD systems. Finally, the classical frequency response concepts and their time-varying extensions are all readily derived from the AFR with the corresponding computational simplification.

ISSN:0020-7179    

DOI:10.1080/00207178508933388

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In the automatic assembly of space stations or the automatic rendezvous and docking of a space-shuttle vehicle with a space station, it is of interest to determine suitable guidance laws for orbital rendezvous which are amenable to on-board implementation. In this paper, various forms of non-linear guidance laws for automatic orbital rendezvous of two bodies represented by point masses in a central newtonian gravitational field are derived. A basic requirement is that the approach be smooth and non-oscillatory. The global dynamic behaviour of each of the resulting feedback systems is determined analytically and/or by computer simulation.

ISSN:0020-7179    

DOI:10.1080/00207178508933389

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The performance of a non-linear model-reference adaptive control system and of a classical linear control system are compared. The problem of a speed control loop for a DC drive system with a variable moment of inertia load is considered for the comparison exercise. The characteristics of the two control schemes are compared when (a) the plant input saturates, (6) step changes in the load moment of inertia occur, (c) parameter variations exceed the design assumptions and (d) external disturbance signals are applied to the output.

ISSN:0020-7179    

DOI:10.1080/00207178508933390

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Deterministic ‘quantized control’ problems are investigated from a novel and often computationally feasible ‘matched processors’ (MPs) perspective. It is noted that a bank of independent MPs, each matched to an admissible decision sequence, can evaluate, given the state and remaining duration, the dynamic performance cost-to-go values corresponding to a suitably selected ‘small’ subset of all admissible decision sequences. By choosing the best admissible decision sequence in this subset and using its first decision at each stage a computationally feasible and generally sub-optimum MP control scheme is produced. This scheme is found to be ideally suited for very-large-scale integration. In particular, for processes that are linear in the state and performance criteria that are quadratic in the state, the cost-to-go reduces to a simple quadratic function of the given state which in turn results in an MP control scheme structure similar to offered VLSI-based digital computers. It is demonstrated that the proposed scheme performs quite well in two experimental examples.

ISSN:0020-7179    

DOI:10.1080/00207178508933391

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor