Ai-Guo Wu

Iterative algorithms for solving a class of complex conjugate and transpose matrix equations

This paper is concerned with iterative solutions to a class of complex matrix equations, which include some previously investigated matrix equations as special cases. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of matrix equations. A sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools. By using some properties of the real representation, a convergence condition that is easier to compute is also given in terms of original coefficient matrices. A numerical example is employed to illustrate the effectiveness of the proposed methods.

On closed-form solutions to the generalized Sylvester-conjugate matrix equation

Abstract In this paper, several explicit parametric solutions to the generalized Sylvester-conjugate matrix equation are given. The proposed solutions can provide all the degrees of freedom which are represented by a free parameter matrix. In addition, the approaches adopted in this paper do not require that the coefficient matrices are in any canonical forms.

Parametric solutions to Sylvester-conjugate matrix equations

By two recently proposed operations with respect to complex matrices, a simple explicit solution to the Sylvester-conjugate matrix equation is given in a finite series form. The obtained solution can also be equivalently expressed in terms of the so-called controllability-like matrix and observability-like matrix. The proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix. An illustrative example is employed to show the effectiveness of the proposed method.

Finite iterative algorithms for a common solution to a group of complex matrix equations

Abstract An iterative algorithm is constructed to give a common solution to a group of complex matrix equations. By using the proposed algorithm, the existence of a common solution can be determined automatically. When a common solution exists for this group of matrix equations, it is proven by using a real inner product in complex matrix spaces as a tool that a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a more general case. A numerical example is given to illustrate the effectiveness of the proposed method.

Implicit Iterative Algorithms for Continuous Markovian Jump Lyapunov Equations

In this technical note, implicit iterative algorithms with some tunable parameters are developed to solve the coupled Lyapunov matrix equations associated with continuous-time Markovian jump linear systems. A significant feature of the proposed algorithms is that the iterative sequences are updated by using not only the information in the last step, but also the information in the current step and the previous steps. Also the convergence rate of the proposed algorithms can be significantly improved by choosing appropriate parameters in the algorithms.

On j-conjugate product of quaternion polynomial matrices

In this paper, the concept of j-conjugate product over quaternion polynomial matrices is proposed. Further, some interesting properties of the proposed j-conjugate products are derived. By means of j-conjugate product, necessary and sufficient conditions for consimilarity over quaternion matrices are finally established.

Corrigendum: Corrigendum to Parametric solutions to Sylvester-conjugate matrix equations [Comput. Math. Appl. 62 (2011) 3317-3325]

Corrigendum Corrigendum to ‘‘Parametric solutions to Sylvester-conjugate matrix equations’’ [Comput. Math. Appl. 62 (2011) 3317–3325] Ai-Guo Wu a,∗, Lingling Lv b, Guang-Ren Duan c, Wanquan Liu d a Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China b Institute of Electric Power, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, PR China c Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China d Department of Computing, Curtin University, Perth, Australia

Robust energy-to-peak estimation for continuous-time polytopic uncertain time-delay systems

This paper is concerned with the problem of full-order robust L2-Linfin estimation for continuous-time polytopic uncertain time-delay systems. An improved L2-Linfin performance criterion is provided in terms of linear matrix inequalities. It exhibits a kind of decoupling between the Lyapunov matrices and the system dynamic matrices compared with the existing result. Then two sufficient conditions for the existence of the robust estimator are established based on the two performances respectively. At the same time, two admissible estimators are presented. A numerical example demonstrates the effectiveness of the two approaches and advantage of the second estimator design approach.