Research progress

1. week 1 (10/1): Reconsider the stability analysis problem of the LPV system using the descriptor system approach. Iwasaki pointed out that the LPV system can modeled as a descriptor system.
2. week 2 (10/8): Compare the well-posedness approach with the descriptor system approach when dealing with the stability analysis problem of the LPV system.
3. week 3 (10/15): Found a mistake in the previous week's comparsion and discovered that the number of state variables used in the descriptor system model had a important impact on the stability analysis result of the LPV system.
4. week 4 (10/22): Propose a procedure for constructing the descriptor system from a given LPV system.
5. week 5 (10/29): Give the definition of quadratic admissibility for a class of uncertain descriptor systems and derive a necessary and sufficient condition for the quadratic admissibility. I also discovered that the existence of a parameter dependent Lyapunov function for the LPV system is equivalent to the quadratic admissibility of the uncertain descriptor system associated with the given LPV system.
6. week 6 (11/5): Found a better descriptor system model from the LPV system.
7. week 7 (11/12): Found my better descriptor system model in the previous week makes no sense, and there was not much progress in this week.
8. week 8 (11/19): A descriptor system approach for Fu and Dasgupta's result. Give the defintion of robust D_R-admissibility.
9. week 9 (11/26): A sufficient condition is proposed to ensure the robust D_R-admissibility based on the concept of multiconvexity.
10. week 10 (12/3): Starting to rewrite my previous notes. Lemma 1 is rewritten in such a way that the admissibility of a descriptor system is related to the detectability of a pair of matrices associated with the descriptor system.
    
11. week 11 (12/10): The concept of D_R-admissibility is introduced. Theorem 1 is outlined.
12. (12/17): Busying NSC project.
13. (12/24): Busying NSC project.
14. week 12 (12/31): Modify Lemma 1 and Theorem 1. Proposition 1 and Corollary 1 are added.
15. week 13 (1/7): Section 2: ``Stability analysis of LPV systems", is added.
16. week 14 (1/14): Theorem 2 uses a frequency domain approach to derive a necessary and sufficient condition for D_R-admissibility.
17. week 15 (1/21): An attempt is made to develop a new proof for the generalized KYP lemma based on techniques used in Theorem 1 and 2.
    

ps. Last modified at Jan 23, 2006.