Robust pole placement under structural constraints

Santos, João Fábio S. dos; Pellanda, Paulo César; Simões, Alberto M.

doi:10.1016/j.sysconle.2018.03.008

Cited by 21 publications

(15 citation statements)

References 27 publications

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“…Confining the closed-loop poles to this region ensures that the damping ratio lies in [cos 1], the decay rate lies in [ab]. The region (14) can be characterized as the following corollary.…”

Section: Corollary 2 the Linear Stochastic Systemmentioning

confidence: 99%

Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized ‐representation method

Zhang

Xia

Shen

et al. 2020

Intl J Robust & Nonlinear

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This paper investigates pth moment regional stability, stabilization, and generalized pole assignment of stochastic systems, which are most useful in many specific systems and applications. With the help of the generalized -representation method, the necessary and sufficient conditions of pth moment regional stability and stabilization of stochastic systems are addressed.Meanwhile, the generalized pole assignment of stochastic systems is also considered. Finally, two examples are presented to show the effectiveness of the proposed methods. K E Y W O R D Spth moment -stability, generalized -representation, generalized pole assignment, power vector 1 3234 /journal/rnc Int J Robust Nonlinear Control. 2020;30:3234-3249.ZHANG et al. 3235control system. Frequently used pole assignment regions are generally including negative semi-plane, sector, disk, vertical stripe, and the intersection of them. Regional pole assignment of the linear deterministic system has been investigated in various aspects, such as robustness bounds of pole clustering, 12 robust pole placement, 13,14 and H 2 or H ∞ performance with pole placement constraints. 15,16 Recently, the -representation has been explicitly presented in Reference 17. As the most advantage of this method, many classical results of linear systems could be directly applied to the stochastic systems. [17][18][19][20][21][22] For example, Reference 17 proposed the concept of -representation method, and discussed the problem of generalized -stability/stabilization for linear stochastic systems. The stabilization with state-multiplicative noise was investigated, and the infinite horizon stochastic H 2 ∕H ∞ control with state-dependent and control-dependent noise were studied in Reference 20. Moment stability theorems for the systems with the stability properties were considered in Reference 22. However, it should be pointed out that the -representation method will be no longer valid for the corresponding cases in the meaning of pth moment stability/stabilization although it effectively solves the mean square stability and other related issues for the stochastic linear systems.Motivated by the pole placement, the -representation method and Itô formula, we will generalize the state matrix of the linear stochastic system to the extended state matrix by using the generalized -representation technique. The quadratic terms of the state vector in -representation could be extend to pth terms using the lexicographical order of the monomials. Then, the problems of pth moment regional stability, stabilization, and the generalized pole assignment of linear stochastic systems could be handled effectively as the means of the deterministic system. The main advantages of the proposed approach can be summarized as follows.First, the linear stochastic systems can be transformed into deterministic systems with the state matrixÂ n⋅p and the state vector x {p} by the generalized -representation method, which is the generalization of -representation in Reference 17. Then, the problems of p...

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Section: Corollary 2 the Linear Stochastic Systemmentioning

confidence: 99%

Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized ‐representation method

Zhang

Xia

Shen

et al. 2020

Intl J Robust & Nonlinear

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“…In practice, there are also requirements other than stability on the closed loop system's overall performance. The closed loop dynamic behaviour is determined by system poles (eigenvalues of a system matrix), therefore pole placement belongs to widely used controller design methods also studied in the robust control framework [5][6][7][8][9]. The corresponding controller then guarantees that the closed loop system poles have the predetermined values, thus shaping the closed loop system dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Though a vast amount of literature has been devoted to robust control and control algorithm design, e.g., References [1][2][3][4][5][6][7][8][9][10][11], and various approaches have been developed both in frequency domain and in state space, there still remain open questions in this field. The important issue is computational tractability which also motivated linear matrix inequality (LMI) problem formulation and the use of the corresponding computationally efficient techniques that enable solving a large set of convex problems in a polynomial time (see, e.g., Reference [1]).…”

Section: Introductionmentioning

confidence: 99%

“…Determination of the required closed loop system (CLS) pole position depends on performance requirements. When the continuous-time system is considered, the pole regions related to the prescribed stability degree and relative damping (which belong to the basic performance indices closely connected, e.g., with overshoot, rise time, settling time, and decay rate) are convex and can be formulated by LMI or D R regions [4][5][6]9]. However, this is not the case for the discrete-time counterpart, where the prescribed relative damping corresponds to the non-convex pole region.…”

Section: Introductionmentioning

confidence: 99%

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LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Rosinová

Hypiusova

2019

Algorithms

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Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called "D regions" where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system.

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“…Nota-se, que uma desvantagem das técnicas de controlé otimo com alocação de autovaloresé a não consideração de incertezas nos modelos obtidos, fazendo com que o critério multiobjetivo não seja satisfeito. Uma solução para esse problema são as técnicas de alocação robusta de autovalores, podendo-se destacar Le and Wang (2014) e dos Santos et al (2018). Estas técnicas apresentam grande vantagem combinadas com controleótimo, pois o critério multiobjetivoé satisfeito mesmo na presença de incertezas.…”

Section: Introductionunclassified

Controle Fuzzy Evolutivo com Alocação Ótima Robusta de Autoestruturas

Noronha

Serra

2019

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

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Robust pole placement under structural constraints

Cited by 21 publications

References 27 publications

Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized ‐representation method

Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized ‐representation method

LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Controle Fuzzy Evolutivo com Alocação Ótima Robusta de Autoestruturas

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