By Xiaoming Chen
This thesis introduces novel and important effects concerning the research and synthesis of optimistic platforms, specifically below l1 and L1 functionality. It describes balance research, controller synthesis, and bounding positivity-preserving observer and filtering layout for various either discrete and non-stop confident systems.
It for this reason derives computationally effective options in accordance with linear programming by way of matrix inequalities, in addition to a few analytical ideas bought for specified situations. The thesis applies a variety of novel techniques and basic ideas to the extra examine of optimistic platforms, therefore contributing considerably to the speculation of optimistic structures, a “hot subject” within the box of keep an eye on.
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Extra resources for Analysis and Synthesis of Positive Systems Under ℓ1 and L1 Performance
I∗ < ε2 , where ε2 is a prescribed bound, then K opt = K i , If γi∗ − γi−1 p = pi . STOP. 4. Set i = i + 1 and K i = K i−1 , then go to Step 2. 36) C z + D z LC ≥≥ 0. 37) Under the condition, an output-feedback stabilizing control law can be obtained as K1 = −1 L. 37), but omitted here for brevity . 4 The parameter γ is optimized iteratively. Notice that γi+1 ≤ γi∗ since the corresponding parameters obtained in Step 4 will be utilized as the initial conditions to derive a smaller γ . Therefore, the convergence of the iterative process is naturally guaranteed.
A method has been derived to compute the exact value of 1 -induced norm for positive systems. A characterization has been proposed to ensure the asymptotic stability of the controlled system with a prescribed 1 -induced performance level. A necessary and sufficient condition for the existence of a desired controller has been established accordingly. Then, an iterative convex optimization algorithm has been developed to solve the design conditions. In addition, an analytical design approach has been put forward to investigate the synthesis of the state-feedback controller for SIMO positive systems.
Problem L1SOFCD: Given SI positive. 3) under x(0) = 0. 3, we present a condition for the existence of a solution to Problem L1SOFCD. 4 Given SI positive and suppose K ≤≤ 0. 23) 0. 20) is a positive system. 20) is robustly stable and satisfies z L 1 < γ w L 1 . The necessity can be obtained by reversing the above procedure and the proof is omitted here. 15). The non-positiveness of K facilitates the controller synthesis problem. It is noted that for a special case when B, C and Dz are known constant matrices, the constraint K ≤≤ 0 can be removed.
Analysis and Synthesis of Positive Systems Under ℓ1 and L1 Performance by Xiaoming Chen
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