Discrete Time Systems Part 1 pdf

... -1. 120 -0.690 -0.332 0 0.332 0.690 1. 120 1. 764 0.079 0 .10 6 0 .12 1 0 .12 9 0 .13 0 0 .12 9 0 .12 1 0 .10 6 0.079 10 -1. 818 -1. 199 -0.789 -0.453 -0 .14 8 0 .14 8 0.453 0.789 1. 199 1. 818 0.069 0.093 0 .10 6 0 .11 4 ... -1. 603 -0.908 -0.424 0.0 0.424 0.908 1. 603 0 .11 0 0 .14 5 0 .16 2 0 .16 6 0 .16 2 0 .14 5 0 .11 0 8 -1. 690 -1. 023 -0.569 -0 .18 4 0 .18 4 0.569 1. 023 1. 6...

Ngày tải lên: 20/06/2014, 01:20

... 10 -4 -10 -5 0 5 x 10 -4 0 0. 01 400 420 440 460 480 500 10 20 10 40 10 60 10 80 11 00 -0.02 -0. 01 0 0. 01 -0. 01 0 0. 01 0.02 0 0. 01 t A’ t A’ t A’ t A’ t B’ t B’ t B’ t B’ 0 .1 0.05 -0.05 0 0 .1 0.05 -0.05 0 0 .1 0.05 -0.02 x ... = =++ ∑∑ ∑∑ ∑∑ ∑ 11 11 11 ki ki ki ki Nk N k N TTT lil lil kd ikd ilkd ilk d i xQx xQx x Qx −− −− ==− ==+− = =+ ∑∑ ∑ ∑ ∑ Using this, 2...

Ngày tải lên: 20/06/2014, 01:20

... d 1 = 2, d 2 = 1. 9, and d 3 = 1. 8 d 3 −→ 1. 5 1. 6 1. 7 1. 8 1. 9 2 0.86 0.87 0.88 0.89 24 1 G 25 1 G 51 1 G 53 2 G 52 1 I 53 1 G 26 1 G 27 1 I 54 1 I 55 1 I k r −→ (b) d 1 = 2, d 2 = 1. 9, and φ ... as: 1 ˆˆ (1| 1) (1| 1) (1) N jj j xk k x k k k μ = + += + + + ∑ (30) 1 (1| 1) ˆˆ ˆˆ [(|)( (1| 1) (1| 1))( (1| 1) (1| 1))] (1) N T jj jj j Pk k Pkk...

Ngày tải lên: 20/06/2014, 01:20

... (H d i −K d i C) T    r i times  (52) Σ = B  H 11 ···H 1s 1 H 21 ···H qs q  (53) Σ d = B  H d 11 ···H d 1r 1 H 21 ···H qr q  (54) Υ = diag  β 11 I s 1 , , β 1s 1 I s 1 , β 21 I s 2 , , β qs q I s q  (55) Υ d = ... are −5 0 5 10 0 10 10 0 −50 0 50 10 0 x 1 x 2 x 3 Fig. 1. Phase plot of the system a 11 = 1, b 11 = 1, a d 21 = 1, b d 21 = 1 A...

Ngày tải lên: 20/06/2014, 01:20

... M (L,L) t ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ . Concerning  P t +1 ,wehave  P t +1 =  A 1 t +1  M t  A 1 t +1 T +  T t +1  J t Q t  J t T  T t +1 T +  H t +1 R t +1  H t +1 T = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ A 1 t +1 M (0,0) t A 1 t +1 T A 1 t +1 M (0,0) t A 1 t +1 M (0 ,1) t A 1 t +1 M (0,L 1) t M (0,0) t A 1 t +1 T M (0,0) t M (0 ,1) t M (0,L 1) t M (...

Ngày tải lên: 20/06/2014, 01:20

... P 11 ,k|k 1 M k P 11 ,k|k 1 , (59) P 12 c,k := P 12 ,k|k 1 + P 11 ,k|k 1 M k P 12 ,k|k 1 , (60) P 22c,k := P 22,k|k 1 + P T 12 ,k |k 1 M k P 12 ,k|k 1 , ( 61) S 1, k := P 11 c,k − P 12 c,k , (62) S 2,k := P 12 c,k − ... about 94 Discrete Time Systems 10 Discrete Time Systems where, using the definitions presented in Step 1 of Table 2, we obtain P 11 ,k +1|...

Ngày tải lên: 20/06/2014, 01:20

... above formulas, s zE A−  is described as [] [][] [] [] [] [] [] 1 3 211 11 11 111 112 222 11 1 3 1 111 11 12222 1 3 1 112 1 3 12 {}{} () { } { } () () . s zE A zI F zI F zI F I H zI F G zE A ... 11 () () () T s Vk z kPz k= . (49) Discrete Time Systems 13 8 The difference of ()Vk along the trajectories of system Eq.(42) is given by [][] 11 11 11 1 1...

Ngày tải lên: 20/06/2014, 01:20

... Q 11 K T B and BKCQ = BK [Q 11 Q 12 ], (6) is equivalent to (A[Q 11 Q 12 ] T + BK Q 11 )Q 1 11 (A[Q 11 Q 12 ] T + BK Q 11 ) T −A  Q 11 Q T 12  Q 1 11 [Q 11 Q 12 ]A T + AQ A T − Q < 0 ( 31) Using ... ∗ ( A[Q 11 Q 12 ]+BK Q 11 ) T −Q 11  < 0 (32) where ¯ Θ 0 =  00 0 Q 22 − Q T 12 Q 1 11 Q 12  Since (Q 12 −εQ 11 ) T Q 1 11 (Q 12...

Ngày tải lên: 20/06/2014, 01:20

... 12 11 ˆˆ ˆ ˆ ˆ () 0 TTTTTT KK AXA X AXBBXB R BX A EE CC Q δ ρ − ∞∞ ∞ ∞ ∞ − −++++= (30) Discrete Time Mixed LQR/H ∞ Control Problems 16 9 21 1 11 1 322 2 3 11 111 1 11 1 211 112 11 1 211 2 1 ˆˆ ... d k ≤ 1 [0 .1 0 .1 − 0 .1 0.5 0 .1] [ 1. 1209 −0 .11 74] 0 ≤ d k ≤ 2 [0 .1 0 .1 − 0 .1 0.5 0 .1] [−0.9429 −0.0839] 0 ≤ d k ≤ 3 [0 .1 0 .1 − 0 .1 0.5 0 .1] [−0.7950...

Ngày tải lên: 20/06/2014, 01:20

... satellite attitude control uncertain discrete- time system (1) with parameters as follows: [] 22 11 0 .1 10 10 , , 0.2 0.3 , , , , 0 .1, 0.2 . 24 01 0.5 01 01 ab − ⎡ ⎤ ⎡⎤ ⎡⎤ ⎡⎤ ⎡⎤ === ===== ⎢ ⎥ ... condition of φ (·) and (10 5), the following equality holds: l 1 ∑ i =1 Δ ˆ φ(k + l −i|k) −Δ φ(k + l − i)≤max{L j } 1 j≤l 1 l 1 ∑ i =1 | ˘ y (k + l − i|k)| (10 6) From (93), (1...

Ngày tải lên: 20/06/2014, 01:20