Parametric solutions to the regulator-conjugate matrix equations

Zhang, Lei; Zhu, Aibin; Wu, Ai‐Guo; Lv, Lingling

doi:10.3934/jimo.2016036

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…One can see some related works in refs. [13][14][15][16][17][18][19][20] and the references therein. The linear periodic system with time-varying state and input dimensions has also attracted the research interest of scholars in the recent years.…”

Section: Introductionmentioning

confidence: 99%

Output feedback based poles configuration for LDP systems with varying state and input dimensions

Gao

Han²,

Zhao

et al. 2022

IET Control Theory & Appl

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The problem of pole configuration via periodic output feedback for linear discrete periodic systems with time-varying dimensions of states and input spaces is addressed. By some mathematical derivation, the considered problem can be reduced into solving a special Sylvester matrix equation from which the periodic output feedback gains can be separated and computed explicitly. Based on this, a detail parametric algorithm is presented, by which countless periodic output feedback gains can be generated by choosing different free parameter matrices. Furthermore, the proposed approach is used to achieve robustness performance and robust poles configuration algorithm is provided. Numerical examples are employed to illustrate the effectiveness of the proposed algorithms.

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Section: Introductionmentioning

confidence: 99%

Output feedback based poles configuration for LDP systems with varying state and input dimensions

Gao

Han²,

Zhao

et al. 2022

IET Control Theory & Appl

Self Cite

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“…By constructing an objective function and using the gradient search, a gradient-based iteration is established in [9] for solving the coupled matrix equations A i XB i = F i , i = 1, 2, ..., p. By using the hierarchical identification principle and introducing the convergence factor and the iterative matrix, a family of inversion-free iterative algorithms is proposed in [24] for solving nonlinear matrix equations X + A T X −1 A = I. M. Dehghan and M. Hajarian proposed some iterative algorithms based on the conjugate gradient (CG) method for solving the system of generalized Sylvester matrix equations( [5]), coupled Sylvester matrix equations( [6]) and the second-order Sylvester matrix equation EV F 2 − AV F 2 − CV = BW ( [7]), which are applications of CG in the area of solving time-invariant matrix equations. There are still many papers that are available for reference(one can see [25,15,1,2,3,17,18,20,21]).…”

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confidence: 99%

An iterative algorithm for periodic sylvester matrix equations

Lv¹,

Zhang²,

Zhang³

et al. 2018

Journal of Industrial &Amp; Management Optimization

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The problem of solving periodic Sylvester matrix equations is discussed in this paper. A new kind of iterative algorithm is proposed for constructing the least square solution for the equations. The basic idea is to develop the solution matrices in the least square sense. Two numerical examples are presented to illustrate the convergence and performance of the iterative method. 2010 Mathematics Subject Classification. 15A24.

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Explicit solutions of conjugate, periodic, time-varying Sylvester equations

Ma,

Chang,

Han

et al. 2023

J Inequal Appl

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Solutions of a group of conjugate time-varying matrix equations are discussed in this paper. Through mathematical derivation, the solutions to this group of equations are equivalent to the solutions to a class of conjugate time-invariant matrix equations. Further, the related conditions of solvability are obtained and the general explicit solutions are represented by using quasicontrollability and quasiobservability matrices. A detailed algorithm is presented to make the calculation process clear, and the effectiveness of the algorithm is verified by a concrete example. The proposed algorithm can provide complete solutions to the considered equation in explicit parametric form and its main computation includes solving an ordinary linear algebraic equation and some matrix multiplication operations.

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Parametric solutions to the regulator-conjugate matrix equations

Cited by 3 publications

References 13 publications

Output feedback based poles configuration for LDP systems with varying state and input dimensions

Output feedback based poles configuration for LDP systems with varying state and input dimensions

An iterative algorithm for periodic sylvester matrix equations

Explicit solutions of conjugate, periodic, time-varying Sylvester equations

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