Download e-book for kindle: Analysis and Synthesis of Positive Systems Under ℓ1 and L1 by Xiaoming Chen

By Xiaoming Chen

ISBN-10: 9811022267

ISBN-13: 9789811022265

ISBN-10: 9811022275

ISBN-13: 9789811022272

This thesis introduces novel and critical effects in regards to the research and synthesis of confident structures, specifically less than l1 and L1 functionality. It describes balance research, controller synthesis, and bounding positivity-preserving observer and filtering layout for numerous either discrete and non-stop confident systems.

It hence derives computationally effective suggestions in accordance with linear programming when it comes to matrix inequalities, in addition to a couple of analytical options received for designated instances. The thesis applies a number novel techniques and primary ideas to the additional research of confident structures, hence 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

Sample text

The convergence rate is characterized by the spectral radius. Hence, the closedloop system with K ∗ has the fastest convergence rate. The proof is completed. 4 gives a complete solution for the minimal 1 -induced performance problem when ρ(A + bK ∗ ) < 1. 36) gives the fastest convergence rate when the closed-loop system is stable, but it does not minimize the spectral radius of A + bK due to the presence of the constraint C + d K ≥≥ 0. ,n bi with the corresponding term inside {·} disappears if bi = 0.

Briat C (2013) Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L 1 -gain and L ∞ -gain characterization. Int J Robust Nonlinear Control 23(17):1932–1954 42. David G (1971) An introduction to observers. IEEE Trans Autom Control 16(6):596–602 43. Gauthier JP, Hammouri H, Othman S (1992) A simple observer for nonlinear systems applications to bioreactors. IEEE Trans Autom Control 37(6):875–880 44. Wang Z, Huang B, Unbehauen H et al (1999) Robust H∞ observer design of linear state delayed systems with parametric uncertainty: the discrete-time case.

3) is positive and asymptotically stable. 3) is G¯ 1→ 1 = (C + D K )(I − (A + B K ))−1 Bw + Dw 1 . 33), we have y 1 < γ w 1 holds. The necessity can be obtained by reversing the above procedure and the details are omitted here. In the following, we present an analytic solution to the controller design problem. 32) holds, we have that −1 (I − (A + B K )) ∞ = (A + B K )i . 3) will also be small when all the elements of A + B K ≥≥ 0 and C + D K ≥≥ 0 are sufficiently small. For SIMO systems, the problem can be analytically solved.

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Analysis and Synthesis of Positive Systems Under ℓ1 and L1 Performance by Xiaoming Chen


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