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

By Xiaoming Chen

This thesis introduces novel and demanding effects concerning the research and synthesis of optimistic platforms, in particular less than l1 and L1 functionality. It describes balance research, controller synthesis, and bounding positivity-preserving observer and filtering layout for a number of either discrete and non-stop confident systems.

It for this reason derives computationally effective suggestions according to linear programming by way of matrix inequalities, in addition to a few analytical suggestions acquired for unique situations. The thesis applies a variety of novel techniques and basic suggestions to the extra research of confident platforms, therefore contributing considerably to the speculation of confident platforms, a “hot subject” within the box of regulate.

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Springer Science+Business Media Singapore 2017 X. 1) where x(t) ∈ Rn , w(t) ∈ Rm and y(t) ∈ Rr are the system state, input and output, respectively. Now, we are in a position to give the definition of L 1 -induced norm. 2) L1 where : L 1 → L 1 denotes the convolution operator, that is, y(t) = ( ∗ w)(t). 3) (L 1 ,L 1 ) < γ , where γ > 0 is a given scalar. 1) can be computed directly. 1), the exact value of the L 1 -induced norm is given by (L 1 ,L 1 ) = Dw − C A−1 Bw 1 . 1), the impulse response G(t) is given by G(t) Next, let 0, t < 0, Ce At Bw + Dw δ(t), t ≥ 0.

Kaczorek T (1999) Stabilization of positive linear systems by state feedback. Pomiary, Automatyka, Kontrola 3:2–5 27. De Leenheer P, Aeyels D (2001) Stabilization of positive linear systems. Syst Control Lett 44(4):259–271 28. Liu X, Yu W, Wang L et al (2010) Stability analysis for continuous-time positive systems with time-varying delays. IEEE Trans Autom Control 55(4):1024–1028 29. Gurvits L, Shorten R, Mason O (2007) On the stability of switched positive linear systems. IEEE Trans Autom Control 52(6):1099–1103 30.

39) minimizes ρ(A + bK ) subject to A + bK ≥≥ 0. If ρ(A + bK ∗ ) < 1, then the closed-loop system achieves the minimal 1 -induced performance. 3 serves as a characterization of the existence of a state-feedback controller for general MIMO systems. Unfortunately, for multi-input systems, the problem of jointly minimizing all the elements of A + B K and C + D K is not generally well-posed. Under a structural constraint, we present a method to derive the minimal K for MIMO systems. 40) m×n ¯+ l1 l2 .

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