Discrete Time Systems Part 3 ppt

... In this case, the EC P is given by ( 13) . Now, 74 Discrete Time Systems Discrete Time Systems 50 This completes the proof of Theorem 2. Proof of Theorem 3 a., c. Equations (18) and (19) immediately ... Automatic Control, Vol. 39 , No. 6, pp. 133 8– 134 1 Hou, M. & R. J. Patton, R. J. (1998). Optimal filtering for systems with unknown inputs, IEEE Trans. Automatic Co...

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... be partitioned as P k+1|k =  P 11,k+1|k P 12,k+1|k P T 12,k +1|k P 22,k+1|k  , (50) 101 Kalman Filtering for Discrete Time Uncertain Systems Kalman Filtering for Discrete Time Uncertain Systems ... E  e (j) i,k  2 , (81) E  e (j) i,k  ≈ 1 N N ∑ j=1 e (j) i,k , (82) 104 Discrete Time Systems Kalman Filtering for Discrete Time Uncertain Systems 13 Step 0 (Initial...

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... 0.14297 0.19192 0.019 139 0.8656 0.28816 0.67152 0.01 136 0 .38 651 0.5 038 0.4 637 1 0.9712 0. 938 39 0.42246 0. 130 09 0.764 43 0.47657 0.54 837 0.4089 0 .34 529 0.61187 0.15809 0.46 639 0. 535 36 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ We ... obtain K =  −0 .39 14 −0 .36 03 −2 .36 04 −1.1 034  using ( 43) or K =  1.48 13 0.5720 3. 72 03 −1.86 93  using (44). Example 2. We randomly generate 5000 stabilizab...

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... − ˆ T 2 A d − ˆ ρ 2 (YA d − ˜ GC d ) 00000 T 3 ρ 3 Y −T 3 A −ρ 3 (YA − ˜ GC) −T 3 A d −ρ 3 (YA d − ˜ GC d ) 00000 ˆ T 3 ˆ ρ 3 Y − ˆ T 3 A − ˆ ρ 3 (YA − ˜ GC ) − ˆ T 3 A d − ˆ ρ 3 (YA d − ˜ GC d ) 00000 T 4 ρ 4 Y ... discrete- time Riccati equation (21) to get 18.5 238 3. 8295 0.1664 3. 8295 51 .32 12 23. 3226 0 0.1664 23. 3226 22. 735 4 X ∞ ⎡⎤ ⎢⎥ = > ⎢⎥ ⎢⎥ ⎣⎦...

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... 1)=Gz(t). (3. 34) Noting that G is a stochastic matrix, then, by Assumption 3. 2 and knowledge of the Markov chain, we have lim t→∞ G t = 1π T , (3. 35) 237 Decentralized Adaptive Control of Discrete- Time ... i.e., lim t→∞ ˆ γ i (t)=γ i . (3. 6) 234 Discrete Time Systems (2) The system can achieve synchronization in sense of mean, i.e., lim T→∞ 1 T T ∑ t=1 |e ij (t)| = 0, ∀i =...

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... 601–611, 19 83. [2] F. L. Lewis, “A survey of linear singular systems, ” Circuits Systems Signal Process,vol.5, no. 1, pp. 3 36 , 1986. 34 8 Discrete Time Systems 0 5 10 15 20 25 30 35 40 45 50 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0 ... , (4 .34 ) 34 5 Stability and L 2 Gain Analysis of Switched Linear Discrete- Time Descriptor Systems Stability Analysis of Grey Discrete...

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... of discrete- time singular systems: A matrix inequalities approach," Automatica, vol. 35 , no. 9, pp. 16 13 1617, 1999. 34 9 Stability and L 2 Gain Analysis of Switched Linear Discrete- Time ... 12 41 .33 98 8.7000 38 .1986 8.6 432 , 8.7000 86.6915 8.6 432 93. 8897 XX − − ⎡ ⎤⎡ ⎤ == ⎢ ⎥⎢ ⎥ −− ⎣ ⎦⎣ ⎦ 11 41 .34 15 8.6656 51.2846 ,, 8.7540 86.4219 26.5670 T GY −− ⎡ ⎤⎡ ⎤ == ⎢ ⎥...

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... h 1 1 h 1 2 h 1 3 h 1 2N h 2 1 h 2 2 h 2 3 h 2 2N h 3 1 h 3 2 h 3 3 h 3 2N h γ 1 h γ 2 h γ 3 h γ 2N o 2N i o 1 i o 2 i o 3 i X 1 i+1 X 2 i+1 X 3 i+1 X 2N i+1 X 1 i+2 X 2 i+2 X 3 i+2 X 2N i+2 X 1 i +3 X 2 i +3 X 3 i +3 X 2N ... robust in AWGN and NEXT channel as compared to the existing algorithm. 39 8 Discrete Time Systems Discrete Time Systems...

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... q 3 )A 1 (q 2 , q 3 ) T , b 1 =(q 1 , q 3 )A 2 ( q 1 , q 3 ) T , C 1 =(q 2 , q 3 )(q 2 A 11 + q 3 A 12 )(q 2 , q 3 ) T , C 2 =(q 1 , q 3 )(q 1 A 21 + q 3 A 22 )(q 1 , q 3 ) T , r 1 20 =(q 2 , q 3 )A 1 (w 2 20 , ... q 3 z n + q 3 z n + 1 2 w 3 20 z 2 n + w 3 11 z n z n + 1 2 w 3 02 z 2 n 492 Discrete Time Systems We have: Proposition 4 .3. (i) The solution...

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... -0 .35 5 0 .35 5 1.218 0.2 23 0.277 0.277 0.2 23 5 -1 .37 7 -0.592 0.0 0.592 1 .37 7 0.169 0.216 0. 230 0.216 0.169 6 -1.499 -0.768 -0.242 0.242 0.768 1.499 0. 134 0.175 0.191 0.191 0.175 0. 134 7 -1.6 03 -0.908 ... to x qj (k);in 10 Discrete Time Systems Part 1 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Part 2 Chapter 7 Chapter 8 Preface IX Discrete- Time...

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