Based on the well-known Leverrier algorithm, a simple explicit solution to right factorization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symm...Based on the well-known Leverrier algorithm, a simple explicit solution to right factorization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equatiorls and the problem of parametric eigenstructure assignment by state feedback are investigated,and general complete parametric solutions to these two problems are deduced. These new solutions are simple, and possess desirable structural properties which render the solutions readily implementable. An example demonstrates the effect of the proposed results.展开更多
In the process of formulating the General Provisions of the Civil Law of P. R. China, the attribute of virtual property rights has changed from real rights to non-real rights. Article No. 127 thereof does not clarify ...In the process of formulating the General Provisions of the Civil Law of P. R. China, the attribute of virtual property rights has changed from real rights to non-real rights. Article No. 127 thereof does not clarify the nature of virtual property rights after all, and the place where virtual property is put in the "Civil Rights" chapter of General Provisions of the Civil Law makes the concept even more complex and confusing. The "relationships paradigm" protection of virtual property does not have a definite classification criterion, nor stands opposite to the "rights paradigm." There are two different ways to justify the "theory of virtual property as a real right" under the "rights paradigm" protection, namely, essentialism and consequentialism. The former resulted from utilizing features in a demonstration and identifying disposal rights with real rights, while the latter resulted from adherence to the dichotomy system of property rights comprising real rights and creditor's rights. From the perspective of larceny in Criminal Law and virtual property insurance in The Social Insurance Law, the attribute of virtual property rights is irrelevant to creditor's rights. The attribute of virtual property rights shall be defined as virtual property rights so that it can be included in the system of civil rights. The uniqueness of virtual property is enough to become an object of emerging civil rights; intangible property rights as a superordinate theoretical concept cannot reflect the essence of virtual property rights. The legislative frame of virtual property rights shall be comprised of the subject, object, exercise, publication and change of the rights.展开更多
This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester ma...This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).展开更多
基金This work was supported bythe Chinese Outstanding Youth Foundation (No .69504002) .
文摘Based on the well-known Leverrier algorithm, a simple explicit solution to right factorization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equatiorls and the problem of parametric eigenstructure assignment by state feedback are investigated,and general complete parametric solutions to these two problems are deduced. These new solutions are simple, and possess desirable structural properties which render the solutions readily implementable. An example demonstrates the effect of the proposed results.
基金a phase achievement of Research on the Legal Problem of Third Party Infringing Contract Conclusion Interestsa general item under the national social sciences foundation(item number:16BFX1l0)Research on Expansion of Non-normative Provisions in Civil Legislation,one of the national subjects on rule of law and legal theory(item number:16SFB3031)
文摘In the process of formulating the General Provisions of the Civil Law of P. R. China, the attribute of virtual property rights has changed from real rights to non-real rights. Article No. 127 thereof does not clarify the nature of virtual property rights after all, and the place where virtual property is put in the "Civil Rights" chapter of General Provisions of the Civil Law makes the concept even more complex and confusing. The "relationships paradigm" protection of virtual property does not have a definite classification criterion, nor stands opposite to the "rights paradigm." There are two different ways to justify the "theory of virtual property as a real right" under the "rights paradigm" protection, namely, essentialism and consequentialism. The former resulted from utilizing features in a demonstration and identifying disposal rights with real rights, while the latter resulted from adherence to the dichotomy system of property rights comprising real rights and creditor's rights. From the perspective of larceny in Criminal Law and virtual property insurance in The Social Insurance Law, the attribute of virtual property rights is irrelevant to creditor's rights. The attribute of virtual property rights shall be defined as virtual property rights so that it can be included in the system of civil rights. The uniqueness of virtual property is enough to become an object of emerging civil rights; intangible property rights as a superordinate theoretical concept cannot reflect the essence of virtual property rights. The legislative frame of virtual property rights shall be comprised of the subject, object, exercise, publication and change of the rights.
文摘This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).
