Robust Finite Settling Time Stabilization for Multivariable Discrete Time Plants with Structured Uncertainties

Junhua CHANG

Robust Finite Settling Time Stabilization for Multivariable Discrete Time Plants with Structured Uncertainties

Junhua CHANG

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The robust finite settling time stabilization problem is considered for a multivariable discrete time plant with structured uncertainties. Finite settling time (FST) stability of a feedback system is a notion introduced recently for discrete time systems as a generalization of the dead-beat response. The uncertain plant treated in this paper is described by (E₀+Σ^K_i=1q_iE_i)x(t+1)(A₀+Σ^K_i=1q_iA_i)x(t)+(B₀+Σ^K_i=1q_iB_i)u(t), and y(t)=(C₀+Σ^K_i=1q_iC_i)x(t) where E_i, A_i, B_i and C_i (0iK) are prescribed real matrices and q_i (1iK) are uncertain parameters restricted to prescribed intervals [q_i, _i]. It is shown in this paper that a controller robustly FST stabilizes such an uncertain plant, if, the uncertain plant satisfies some conditions, and the controller simultaneously FST stabilizes a finite set of plants. The result leads to a testable necessary and sufficient condition of the existence of a solution to the robust FST stabilization problem, and a systematic method of designing a robust FST stable feedback system, in the case where the plant contains only one uncertain parameter.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.2 pp.216-224

Publication Date: 1993/02/25

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Type of Manuscript: PAPER

Category: Control and Computing

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Junhua CHANG, "Robust Finite Settling Time Stabilization for Multivariable Discrete Time Plants with Structured Uncertainties" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 2, pp. 216-224, February 1993, doi: .
Abstract: The robust finite settling time stabilization problem is considered for a multivariable discrete time plant with structured uncertainties. Finite settling time (FST) stability of a feedback system is a notion introduced recently for discrete time systems as a generalization of the dead-beat response. The uncertain plant treated in this paper is described by (E₀+Σ^K_i=1q_iE_i)x(t+1)(A₀+Σ^K_i=1q_iA_i)x(t)+(B₀+Σ^K_i=1q_iB_i)u(t), and y(t)=(C₀+Σ^K_i=1q_iC_i)x(t) where E_i, A_i, B_i and C_i (0iK) are prescribed real matrices and q_i (1iK) are uncertain parameters restricted to prescribed intervals [q_i, _i]. It is shown in this paper that a controller robustly FST stabilizes such an uncertain plant, if, the uncertain plant satisfies some conditions, and the controller simultaneously FST stabilizes a finite set of plants. The result leads to a testable necessary and sufficient condition of the existence of a solution to the robust FST stabilization problem, and a systematic method of designing a robust FST stable feedback system, in the case where the plant contains only one uncertain parameter.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e76-a_2_216/_p

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@ARTICLE{e76-a_2_216,
author={Junhua CHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Robust Finite Settling Time Stabilization for Multivariable Discrete Time Plants with Structured Uncertainties},
year={1993},
volume={E76-A},
number={2},
pages={216-224},
abstract={The robust finite settling time stabilization problem is considered for a multivariable discrete time plant with structured uncertainties. Finite settling time (FST) stability of a feedback system is a notion introduced recently for discrete time systems as a generalization of the dead-beat response. The uncertain plant treated in this paper is described by (E₀+Σ^K_i=1q_iE_i)x(t+1)(A₀+Σ^K_i=1q_iA_i)x(t)+(B₀+Σ^K_i=1q_iB_i)u(t), and y(t)=(C₀+Σ^K_i=1q_iC_i)x(t) where E_i, A_i, B_i and C_i (0iK) are prescribed real matrices and q_i (1iK) are uncertain parameters restricted to prescribed intervals [q_i, _i]. It is shown in this paper that a controller robustly FST stabilizes such an uncertain plant, if, the uncertain plant satisfies some conditions, and the controller simultaneously FST stabilizes a finite set of plants. The result leads to a testable necessary and sufficient condition of the existence of a solution to the robust FST stabilization problem, and a systematic method of designing a robust FST stable feedback system, in the case where the plant contains only one uncertain parameter.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Robust Finite Settling Time Stabilization for Multivariable Discrete Time Plants with Structured Uncertainties
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 216
EP - 224
AU - Junhua CHANG
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 1993
AB - The robust finite settling time stabilization problem is considered for a multivariable discrete time plant with structured uncertainties. Finite settling time (FST) stability of a feedback system is a notion introduced recently for discrete time systems as a generalization of the dead-beat response. The uncertain plant treated in this paper is described by (E₀+Σ^K_i=1q_iE_i)x(t+1)(A₀+Σ^K_i=1q_iA_i)x(t)+(B₀+Σ^K_i=1q_iB_i)u(t), and y(t)=(C₀+Σ^K_i=1q_iC_i)x(t) where E_i, A_i, B_i and C_i (0iK) are prescribed real matrices and q_i (1iK) are uncertain parameters restricted to prescribed intervals [q_i, _i]. It is shown in this paper that a controller robustly FST stabilizes such an uncertain plant, if, the uncertain plant satisfies some conditions, and the controller simultaneously FST stabilizes a finite set of plants. The result leads to a testable necessary and sufficient condition of the existence of a solution to the robust FST stabilization problem, and a systematic method of designing a robust FST stable feedback system, in the case where the plant contains only one uncertain parameter.
ER -