TAILIEUCHUNG - Discrete Time Systems Part 12

Tham khảo tài liệu 'discrete time systems part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Uncertain Discrete-Time Systems with Delayed State Robust Stabilization with Performance Specification via LMI Formulations 319 providing an Hrv guaranteed cost Y yfifi between the output ek as defined by 93 and the input signal wk. Proof. The proof follows similar steps to those of the proof of the Theorem 4. Once 94 is verified then the regularity of F P - F - FT 11 F12 F22A F22 is assured by the block P11i - F11 - ft P12i - F12 - ATF22 1 k p22i - F22 - F22 0. Thus it is possible to define the congruence transformation Th given by 53 with T I3 OF T I3 o F11 F12 F22A F22 -T to get Ỹị ThTTH . In block 7 7 of Ti it always exist a real scalar K 6 0 2 such that for Ỡ 6 0 1 k k - 2 -Ỡ. Thus replacing this block by k k - 2 Ip the optimization variables w and Wd by KF22 and KdF22 respectively and using the definitions given by 91 - 93 it is possible to verify 36 by i replacing matrices Ai Adi Ci Cdi Bwi and Dwi by Ai Adi Ci Cdi Bwi and Dwi respectively given in 93 ii choosing G K Ip that leads block 7 7 to be rewritten as in 55 iii assuming and Pi Qi F11 F12 F22A F22 F11 F12 F22A F22 Xh T P11i P12i P22i T r Q11i Q12i Q22i F11 F12 F22A F22 0 0 0 0 -1 F11 F12 F22A F22 F11 F12 F22A F22 K p -1 0 0 0 0 1 which completes the proof. An important aspect of Theorem 7 is the choice of A 6 Rn tlm in 94 . This matrix plays an important role in this optimization problem once it is used to adjust the dimensions of block 2 1 of F that allows to use F22 to design both robust state feedback gains K and Kd. This kind choice made a priori also appears in some results found on the literature of filtering theory. Another possibility is to use an interactive algorithm to search for a better choice of A. This can be done by taking the following steps 1. Set max_itert maximum number of iterations j t 0 e precision 2. Choose an initial value of Aj t A such that 94 is feasible. a Set Pj y Ay Pj F22 j t f22 wj t w wd j t wd. 3. While Ay e AND j max_iter 320 Discrete Time Systems a Set j j 1 b If j

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