The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical signific...The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical significance of the result in is also analyzed. Thus, our work is of independent interest.展开更多
A new construction approach of the Bezout identity for singular systems with directcontrol feedthrough is developed here on the basis of a normal dynamic compensator design, and theparameterization of all Properly sta...A new construction approach of the Bezout identity for singular systems with directcontrol feedthrough is developed here on the basis of a normal dynamic compensator design, and theparameterization of all Properly stabilizing normal controllers is characterized and interpreted in astate-space form. Finally, an illustrative example is given.展开更多
In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decen...In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decentralized control systems is developed. What is more, the parametrization of all normal decentralized properly stabilizing controllers is characterized and interpreted on the basis of the decentralized Bezout identity presented here. In fact, the work done in this paper is an extension of which was derived for normal decentralized control systems in the references by Date (1991) and Date and Chow (1994).展开更多
In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime elements in a mai...In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime elements in a main ring. A ring that satisfies the property of the theorem is called a Bezout ring. We have given some geometry theorems that can be proved algebraically, although the methods of geometry and, in particular, of projective geometry are by far the most beautiful. Most geometric problems actually involve polynomial equations and can be translated into the language of polynomial ideals. We have given a few examples of a different nature without pretending to make a general theory.展开更多
文摘The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical significance of the result in is also analyzed. Thus, our work is of independent interest.
文摘A new construction approach of the Bezout identity for singular systems with directcontrol feedthrough is developed here on the basis of a normal dynamic compensator design, and theparameterization of all Properly stabilizing normal controllers is characterized and interpreted in astate-space form. Finally, an illustrative example is given.
基金This work was supported by National Natural Science Foundation of China!( 69874 0 2 7) Hong Kong Research Grant Council! 71
文摘In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decentralized control systems is developed. What is more, the parametrization of all normal decentralized properly stabilizing controllers is characterized and interpreted on the basis of the decentralized Bezout identity presented here. In fact, the work done in this paper is an extension of which was derived for normal decentralized control systems in the references by Date (1991) and Date and Chow (1994).
文摘In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime elements in a main ring. A ring that satisfies the property of the theorem is called a Bezout ring. We have given some geometry theorems that can be proved algebraically, although the methods of geometry and, in particular, of projective geometry are by far the most beautiful. Most geometric problems actually involve polynomial equations and can be translated into the language of polynomial ideals. We have given a few examples of a different nature without pretending to make a general theory.
