The Experts below are selected from a list of 15819 Experts worldwide ranked by ideXlab platform
Chunjiang Qian - One of the best experts on this subject based on the ideXlab platform.
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local asymptotic stabilization for a class of uncertain Upper Triangular systems
2020Co-Authors: Jiandong Zhu, Chunjiang QianAbstract:Abstract This paper considers local asymptotic stabilization of a class of uncertain Upper-Triangular systems. It shows that, by appropriately increasing the powers of the states in a linear controller, an uncertain Upper-Triangular system can be locally asymptotically stabilized. A nested nonlinear controller is designed by introducing the notion of homogeneity with strictly decreasing degrees. For the stability analysis, a common Lyapunov/Chetaev function is constructed and a necessary and sufficient condition for the local asymptotic stability is established.
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a generalised homogeneous solution for global stabilisation of a class of non smooth Upper Triangular systems
2014Co-Authors: Weisong Tian, Chunjiang QianAbstract:This paper investigates the problem of using small controls to globally stabilise a class of Upper-Triangular systems, including non-smooth systems. A generalised definition of homogeneity with new weights is employed to relax the existing restrictions imposed on the nonlinearities and enable the design of non-smooth stabilisers. By developing a more delicate design approach, small state feedback controllers are recursively constructed in a bottom-to-top fashion to globally stabilise the Upper-Triangular systems. In addition, a number of typical examples are discussed in order to illustrate that the proposed result not only encompasses several existing works under the same topic, but also solves the global stabilisation problem of more general Upper-Triangular systems using simpler controller structures.
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global sampled data output feedback stabilisation of a class of Upper Triangular systems with input delay
2013Co-Authors: Chunjiang Qian, Yingying ChengAbstract:This study investigates the problem of designing a sampled-data output feedback controller to globally stabilise a class of Upper-Triangular systems with delay in the input. By using a linear observer, a linear dynamic sampled-data output feedback control law is explicitly constructed. To dominate the unknown non-linear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of an appropriate Lyapunov-Krasoveskii functional and the technique of sampled-data output-feedback domination, it is shown that the considered Upper-Triangular non-linear system with any bounded input delay can be globally stabilised by the proposed controller with appropriate gains. Finally, an example is given to verify the efficiency of the proposed method.
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homogeneity with incremental degrees and global stabilisation of a class of high order Upper Triangular systems
2012Co-Authors: Chunjiang Qian, Wei LinAbstract:The problem of global asymptotic stabilisation is investigated for a class of Upper-Triangular systems with uncontrollable linearisation. A notion of generalised homogeneity is introduced in this article, providing a new insight and a deeper perspective on how to categorise nonlinear terms into the higher-order and equal-order terms in a non-traditional way. The delicate analysis and new categorisation of the vector field make it possible to encompass more general nonlinearities. A globally stabilising controller is recursively constructed by a bottom-up, step-by-step procedure, containing the equal-order terms as its indispensable components. It is illustrated that the results obtained in this article incorporate and extend existing results for the global stabilisation of Upper-Triangular systems.
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global output feedback stabilization of a class of Upper Triangular systems with input delay
2012Co-Authors: Chunjiang Qian, Michael T FryeAbstract:This paper addresses the problem of global output feedback stabilization for a class of Upper-Triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that Upper-Triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.
Yu Wang - One of the best experts on this subject based on the ideXlab platform.
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the image of polynomials on 2 2 Upper Triangular matrix algebras
2021Co-Authors: Yu Wang, Jia Zhou, Yingyu LuoAbstract:Abstract The goal of the paper is to give a complete description of the image of polynomials with zero constant term on 2 × 2 Upper Triangular matrix algebras over an algebraically closed field.
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the images of completely homogeneous polynomials on 2 2 Upper Triangular matrix algebras
2020Co-Authors: Jia Zhou, Yu WangAbstract:The purpose of this paper is to initiate the study of the images of non-multilinear polynomials on Upper Triangular matrix algebras. We shall give a complete description of the images of completely homogenous polynomials on 2 × 2 Upper Triangular matrix algebras. As a consequence, we show that the image of some special completely homogenous polynomials on 2 × 2 Upper Triangular matrix algebras are not vector spaces.
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the images of multilinear polynomials on 2 2 Upper Triangular matrix algebras
2019Co-Authors: Yu WangAbstract:ABSTRACTThe purpose of this paper is to give a correct proof of a result on the images of non-commutative multilinear polynomials on 2×2 Upper Triangular matrix algebra.
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Functional identities in Upper Triangular matrix rings revisited
2017Co-Authors: Yu WangAbstract:AbstractThe aim of this paper is to give an improvement of a result on functional identities in Upper Triangular matrix rings obtained by Eremita, which presents a short proof of Eremita’s result.
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Jordan homomorphisms of Upper Triangular matrix rings over a prime ring
2014Co-Authors: Yiqiu Du, Yu WangAbstract:Abstract The aim of the paper is to prove that under a mild assumption every Jordan homomorphism from an Upper Triangular matrix ring over a unital ring onto another Upper Triangular matrix ring over a unital prime ring of characteristic not 2 is either a homomorphism or an anti-homomorphism. This result is an extension of a classical theorem of Herstein.
Qingrong Liu - One of the best experts on this subject based on the ideXlab platform.
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design of stabilizing controllers of Upper Triangular nonlinear time delay systems
2015Co-Authors: Zhishan Liang, Qingrong LiuAbstract:Abstract In this paper, it is considered the state feedback controller design for a class of Upper Triangular nonlinear systems with simultaneous input and state delays. By using the state transformation of nonlinear systems, the problem of designing controller can be converted into that of designing a dynamic parameter, which is dynamically regulated by a dynamic equation. Then, by appraising the nonlinear terms of the given systems, a dynamic equation can be delicately constructed. At last, with the help of Lyapunov stability theorem, it is provided the stability analysis for the closed-loop system consisting of the designed controller and the given systems. Both discrete delays and continuous delays with integral form are considered here. Different from many existing control designs for Upper Triangular nonlinear systems, neither forwarding recursive nor saturation computation is utilized here, and thus our design procedure is simpler. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
Mark Kambites - One of the best experts on this subject based on the ideXlab platform.
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identities in Upper Triangular tropical matrix semigroups and the bicyclic monoid
2018Co-Authors: Laure Daviaud, Marianne Johnson, Mark KambitesAbstract:Abstract We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n × n Upper Triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for checking whether such an identity holds, in time polynomial in the length of the identity and size of the alphabet. It also allows us to answer a question of Izhakian and Margolis, by showing that the identities which hold in the monoid of 2 × 2 Upper Triangular tropical matrices are exactly the same as those which hold in the bicyclic monoid. Our results extend to a broader class of “chain structured tropical matrix semigroups”; we exhibit a faithful representation of the free monogenic inverse semigroup within such a semigroup, which leads also to a representation by 3 × 3 Upper Triangular tropical matrices.
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identities in Upper Triangular tropical matrix semigroups and the bicyclic monoid
2016Co-Authors: Laure Daviaud, Marianne Johnson, Mark KambitesAbstract:We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of $n\times n$ Upper Triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for checking whether such an identity holds, in time polynomial in the length of the identity and size of the alphabet. It also allows us to answer a question of Izhakian and Margolis, by showing that the identities which hold in the monoid of $2\times 2$ Upper Triangular tropical matrices are exactly the same as those which hold in the bicyclic monoid. Our results extend to a broader class of "chain structured tropical matrix semigroups"; we exhibit a faithful representation of the free monogenic inverse semigroup within such a semigroup, which leads also to a representation by $3\times 3$ Upper Triangular matrix semigroups, and a new proof of the fact that this semigroup satisfies the same identities as the bicyclic monoid.
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on the krohn rhodes complexity of semigroups of Upper Triangular matrices
2007Co-Authors: Mark KambitesAbstract:We consider the Krohn–Rhodes complexity of certain semigroups of Upper Triangular matrices over finite fields. We show that for any n > 1 and finite field k, the semigroups of all n × n Upper Triangular matrices over k and of all n × n uniTriangular matrices over k have complexity n - 1. A consequence is that the complexity c > 1 of a finite semigroup places a lower bound of c + 1 on the dimension of any faithful Triangular representation of that semigroup over a finite field.
Jan Okninski - One of the best experts on this subject based on the ideXlab platform.
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a note on identities in plactic monoids and monoids of Upper Triangular tropical matrices
2017Co-Authors: Lukasz Kubat, Alan J Cain, Georg Klein, Antonio Malheiro, Jan OkninskiAbstract:This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank $n$ cannot satisfy a non-trivial identity of length less than or equal to $n$. A new identity is then proven to hold for the monoid of $n \times n$ Upper-Triangular tropical matrices. Finally, a straightforward embedding is exhibited of the plactic monoid of rank $3$ into the direct product of two copies of the monoid of $3\times 3$ Upper-Triangular tropical matrices, giving a new proof that the plactic monoid of rank $3$ satisfies a non-trivial identity.
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identities of the semigroup of Upper Triangular tropical matrices
2015Co-Authors: Jan OkninskiAbstract:A new family of identities satisfied by the semigroups U n (𝕋) of n × n Upper Triangular tropical matrices is constructed and an elementary proof is given.
