For linear time-invariant descriptor models, this dissertation studies the extended strictly positive real (ESPR) design of continuous-time systems and the strictly positive real (SPR) analysis and design of discrete-time systems, respectively, all in the LMI framework. For a continuous-time system, by the LMI-based ESPR Lemma, a controller is designed such that the closed-loop system has its transfer matrix being ESPR while admissibility of the compensated descriptor system is guaranteed. Three forms of synthesis are considered, i.e. the static state feedback synthesis, estimated state feedback synthesis, and the dynamic output feedback synthesis. Moreover, design criterion of a dynamic output feedback controller in the state-space model is also addressed. For a discrete-time system, an LMI-based SPR characterization is developed. After giving the definition of SPR, the Cayley transformation is used to establish formulas bridging the admissible realizations for SPR and strictly bounded real (SBR) transfer matrices. Based on them, an LMI-based necessary and sufficient condition for a descriptor system to be, simultaneously, admissible and SPR is derived. When the descriptor variables are transformed into the SVD coordinate, it is shown that such a condition will have solution in the block diagonal form. Based on this result, the problem of static state feedback design to make transfer matrix of the closed-loop systems SPR is tackled.
The problems of robust ESPR and SPR analysis and design when the considered systems have norm-bounded unstructured uncertainty are also addressed. Similarly, LMI-based conditions to guarantee robust admissibility with transfer matrices being ESPR for continuous systems or being SPR for discrete systems are proposed. Based on them, for continuous systems, a static state feedback controller and a dynamic output feedback controller are designed to make the entire family of uncertain closed-loop systems robustly admissible with transfer matrices being ESPR. While for discrete systems, only static state feedback controller is designed to achieve the robust admissibility and robust SPR property.
Finally, based on ESPR lemma (or SPR lemma), we propose a new LMI-based robust admissibility analysis for a class of LTI continuous-time (or discrete-time) descriptor systems with convex polytopic uncertainties appearing on all the system matrices. Moreover, the development of state feedback controllers stemmed from these analysis results is also investigated. It is shown that the provided method has the capability to tackle the problem of computing a required feedback gain matrix for systems with either constant or polytopically dependent derivative (or advanced) state matrix in a unified way. Besides, the application of SPR property to absolute stability problem involving an LTI discrete-time descriptor system and a memoryless time-varying nonlinearity is also addressed. Since all conditions are expressed in LMIs, the obtained results are numerically tractable. It is illustrated by several numerical examples.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0710103-152954 |
| Date | 10 July 2003 |
| Creators | Chen, Jian-Liung |
| Contributors | Chun-Hsiung Fang, Chee-Fai Yung, Tsu-Tian Lee, Bor-Sen Chen, none, I-Kong Fong, Li Lee |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0710103-152954 |
| Rights | withheld, Copyright information available at source archive |
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