# Robust Control of Linear Descriptor Systems by Yu Feng, Mohamed Yagoubi

By Yu Feng, Mohamed Yagoubi

This e-book develops unique effects concerning singular dynamic structures following diversified paths. the 1st contains generalizing effects from classical state-space circumstances to linear descriptor structures, reminiscent of dilated linear matrix inequality (LMI) characterizations for descriptor platforms and function keep an eye on less than rules constraints. the second one is a brand new course, which considers descriptor structures as a strong instrument for conceiving new keep watch over legislation, knowing and interpreting a few controller’s structure or even homogenizing different—existing—ways of acquiring a few new and/or identified effects for state-space platforms. The booklet additionally highlights the excellent regulate challenge for descriptor platforms for instance of utilizing the descriptor framework as a way to remodel a non-standard regulate challenge right into a vintage stabilization keep watch over challenge. In one other part, a correct answer is derived for the sensitivity limited linear optimum regulate additionally utilizing the descriptor framework. The publication is meant for graduate and postgraduate scholars, in addition to researchers within the box of platforms and regulate conception.

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**Extra info for Robust Control of Linear Descriptor Systems**

**Example text**

The matrix C is full row rank, ⎤ ⎡ −A B ⎥ ⎢ E −A B ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ . E B C=⎢ ⎥ ⎢ .. ⎥ ⎣ . −A . ⎦ E B (2) The following statements are equivalent. (2i) (2ii) (2iii) (2iv) (2v) θs is controllable. 40) is R-controllable. A, B1 = Rn 1 . rank ([s E − A B]) = n, for a finite s ∈ R. Im(λE − A) ⊕ Im(B) = Rn . (3) The following statements are equivalent. θ f is controllable. N , B2 = Rn 2 . rank ([E B]) = n. Im(E) ⊕ Im(B) = Rn . Im(N ) ⊕ Im(B2 ) = Rn 2 . The rows of B2 corresponding to the bottom rows of all Jordan blocks of N are linearly independent.

Dilated LMIs are appealed to address this problem. However, as it is shown previously, Characterization IV that contains only one single auxiliary matrix and is suitable for controller synthesis is impossible to derive. While the use of Characterizations I, II, and III that contain more than one auxiliary matrices indicates to impose certain structure on auxiliary matrices. This treatment of course gives a numerically tractable solution, but the resulting design process is conservative and no general conclusion can be found for the induced conservatism.

2 into an unconstrained control problem. 14). 17) is admissible and strictly dissipative. Proof Straightforward. 2, the following standard assumption is made [Mas07]. 14), S22 ≥ 0 and [S12 S22 ] has full column rank. 20) . 14). 25) where No 0 ϒ(T, , P, U ) = 0 I ⎡ He{A P} P Bd + A U + Cz (T, ) S12 Cz (T, ) ⎣ ∗ He{U Bd + S12 Dzd } − S11 Dzd ∗ ∗ −I ⎤ ⎦ No 0 , 0 I Nc 0 (Q, V ) = 0 I ⎡ ⎤ He{QA} (Bd + AV ) 1 + Q C z (Bd + AV ) 2 N 0 ⎣ ∗ He{(C z V + Dzd ) 1 } + H11 (C z V + Dzd ) 2 + H12 ⎦ c , 0 I ∗ ∗ H22 M= I ET I −T , N= , No = C D yd 0 I 0 I Q= I 0 Q ⊥ , Nc = B Dzu ⊥ , I I , V=V .