摘要:

For fixed degree monic polynomials with real coefficients, the direct and inverse problems of root inclusion are denned. The direct problem is to find the infimal region Γ1γof the C-plane that contains all roots of the bounded coefficient norm polynomials. The inverse problem is to define the maximal subregion Γ2γof Γ1γsuch that all polynomials with their roots in Γ2γare bounded norm coefficient polynomials. Those two problems are solved in the case of stable and totally unstable polynomials and the boundaries of Γ1γ,Γ2γ: regions are defined as branches of an algebraic function defined by the norm bound y. For general polynomials, the inverse problem is also solved for polynomials of any degree, whereas the direct problem is discussed in the case of third-order polynomials.

ISSN:0020-7179    

DOI:10.1080/00207179108953657

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

A simple and efficient method for the computation of root loci is proposed. The method solves characteristic equations by pivoting procedures. The algorithm is simple, and applicable to linear systems with time delay. Some theoretical results are given to validate the algorithm. The efficiency of the method is shown by several numerical examples.

ISSN:0020-7179    

DOI:10.1080/00207179108953658

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

For technical plants, a bounded continuum of parameter values describes admissible process models. A robust controller guarantees the observance of minimal requirements for all of the allowed process models. In this paper a frequency domain approach is proposed that permits the instability of a family of polynomials to be checked. This method can be extended in an easy manner to investigate the Instability of a closed loop. The plant is thereby described by a family of models with a polytopical region of uncertainty in the parameter space. As an important special case of the general D-stability, the Hurwitz stability of the closed loop is investigated and a minimal set of necessary and sufficient conditions for robust Hurwitz stability is given. A generalization for other stability domains is possible. Besides an algebraic criterion based on a zero inclusion check for a minimal set of exposed edges of the polytopical region, a graphic criterion of Nyquist type can also be used.

ISSN:0020-7179    

DOI:10.1080/00207179108953659

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

This paper addresses the design of sliding-mode controllers for singularly perturbed systems. The full-order system is separated into slow and fast subsystems and a sliding-mode controller is designed for each subsystem. A composite of these controls is then implemented on the full-order system. It is shown that if specific reaching conditions are satisfied for the reduced-order models and an additional condition is met, then the reaching conditions are also satisfied for the full-order model. Furthermore, sufficient conditions are derived which guarantee that the approximation error between the controlled reduced-order response and the controlled full-order model response is small. A numerical example is given which successfully demonstrates the techniques developed in this paper.

ISSN:0020-7179    

DOI:10.1080/00207179108953660

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor