A complex projection scheme and applications

Huang, Chih-Peng; Juang, Yau-Tarng; Lin, Hui-Ling

doi:10.1016/j.camwa.2004.11.004

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…Thus, according to Corollary 8, if there exist a scalar > 0 and matriceŝ,̂,̂in (42), and̂in (37) satisfying (46), system (41) with the PDSF controller is admissible. In the sequel, we will deduce that once (40) is satisfied, it can consequently imply (46).…”

Section: Controller Designmentioning

confidence: 98%

“…Based on the result in Theorem 14, we can verify whether the uncertain descriptor system (1) is -admissible via searching a set of feasible solutions > 0 and matrices > 0 and satisfying (35). Observing on (35), these equations provided for specific -admissibility need to involve complex numbers, where the traditional LMI solver [40] cannot be applicable, and we can alternatively use a previous result [41], which suitably serves for solving these complex LMIs.…”

Section: (36)mentioning

confidence: 99%

“…When multiplying to the individual inequality in (40) with respect to and then summing all of them, the integrated one equation can attain (46) with the inner blocks (1, 1) and (2, 1) that are replaced by (47) and (48), respectively. Thus, the closed-loop descriptor system (41) with the PDSF controller (37) is admissible for all the allowable uncertainties (2) and (3).…”

Section: Controller Designmentioning

confidence: 99%

“…In addition, a PDSF control law is involved to normalize and stabilize the closed-loop descriptor models. Since all the proposed criteria are explicitly expressed by strict LMIs' forms, we can handily evaluate them via existing LMI tools [40,41] for verification. The remainder content is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

“…] satisfying 1 = 2 = 0, an admissibility criterion can be constructed by a set of LMIs from(35). When evaluating them via the previous result[41], a set of feasible solutions is obtained as…”

mentioning

confidence: 99%

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SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

Huang

2016

Mathematical Problems in Engineering

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Stability analysis issues and controller synthesis for descriptor systems with parametric uncertainty in the derivative matrix are discussed in this paper. The proposed descriptor system can extend the system's modeling extent of physical and engineering systems from the traditional state-space model. First, based on the extended -stability definitions for the descriptor model, necessary and sufficient admissibility and -admissibility conditions for the unforced nominal descriptor system are derived and formulated by compact forms with strict linear matrix inequality (LMI) manner. In contrast, existing results need to involve nonstrict LMIs, which cannot be evaluated by current LMI solvers and need some extra treatments. Deducing from the obtained distinct results, the roust admissibility and -admissibility of the descriptor system with uncertainties in both the derivative matrix and the system's matrices thus can be coped. Furthermore, by involving a proportional and derivative state feedback (PDSF) control law, we further address the controller design for the resulting closed-loop systems. Since all the proposed criteria are explicitly expressed in terms of the strict LMIs, we can use applicable LMI solvers for evaluating the feasible solutions. Finally, the efficiency and practicability of the proposed approach are demonstrated by two illustrative examples.

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Section: Controller Designmentioning

confidence: 98%