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This quantity brings in regards to the modern leads to the sphere of discrete-time platforms. It covers papers written at the themes of sturdy keep an eye on, nonlinear platforms and up to date functions. even if the technical perspectives are assorted, all of them geared in the direction of targeting the updated wisdom achieve via the researchers and offering powerful advancements alongside the platforms and regulate area. each one subject has an in depth discussions and recommendations for destiny perusal by means of investigators.

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22] Lu, G. C. Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation, IEEE Transactions on Automatic Control, 2006;51 818-823. 5772/ 51538 51 Robust Control Design of Uncertain Discrete-Time Descriptor Systems with Delays 23 [23] Lv, L. & Lin, Z. Analysis and design of singular linear systems under actuator saturation and disturbances, Systems and Control Letters, 2008;57 904-912. , Cheng, Z. & Zhang, C. Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays, IEE Proceedings on Control Theory and Applications, 2007;1 1086-1095.

6. Given K, the descriptor system (6) is robustly admissible if and only if there exist matrix P and scalar ε > 0 such that − E T PE + ε( G T G + K T K ) ( A + BK ) T P P( A + BK ) −P 0 HT P 0 αB T P E T PE ≥ 0, (10) 0 0 PH αPB < 0. 3. Robust control design In the previous section, we have obtained robust admissibility conditions of the closed-loop system (6). Based on those conditions, we now seek how to calculate a feedback gain K in the controller (4). 7. There exists a controller (4) that makes the descriptor system (2) robustly admissible if there exist matrices P > 0, Q and scalar ε > 0 such that Γ = P−1 − ε−1 Hc HcT > 0, QS T A + A T SQ T − E T PE + εG T G + ε−1 QS T Hc HcT SQ T + Θ T Γ−1 Θ − ΨΛ−1 Ψ T < 0 (12) (13) where S ∈ ℜn×(n−r) is any matrix with full column rank and satisfies E T S = 0, and Ψ = QS T B + Θ T Γ−1 B, Λ = B T Γ−1 B + εI, Θ = A + ε−1 Hc HcT SQ T .

Letw(k ) = γ −2U 1−1 B1T X ∞ (A + B2 K )x¯ (k), then the trajectories of mean values of states of result‐ ing closed-loop system with x¯ 0 = 3 2 T are given in Fig. 1. Figure 1. 1. 1. 0205. 3727. 0000 0 ,C1 + D12 F ∞ C2 = . 0174 Taking mathematical expectation of the both hand of the above two equations to get x¯ (k + 1) = (A + B2 F ∞ C2)x¯ (k ) + B1w(k ) z(k) = (C1 + D12 F ∞ C2)x¯ (k ) where, E { x(k )} = x¯ (k ), E {z(k )} = z¯ (k),E { x(0)} = x¯ 0. Letw(k ) = γ −2U 1−1 B1T X ∞ (A + B2F ∞ C2)x¯ (k ), then the trajectories of mean values of states of re‐ sulting closed-loop system with x¯ 0 = 1 2 T are given in Fig.