By Edited by Magdi S. Mahmoud

ISBN-10: 9535108751

ISBN-13: 9789535108757

This quantity brings in regards to the modern ends up in the sphere of discrete-time structures. It covers papers written at the issues of strong keep watch over, nonlinear structures and up to date functions. even though the technical perspectives are varied, all of them geared in the direction of concentrating on the updated wisdom achieve via the researchers and offering powerful advancements alongside the platforms and keep watch over enviornment. every one subject has a close discussions and recommendations for destiny perusal via investigators.

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This quantity brings in regards to the modern leads to the sphere of discrete-time structures. It covers papers written at the subject matters of strong keep watch over, nonlinear structures and up to date purposes. even though the technical perspectives are varied, all of them geared in the direction of targeting the up to date wisdom achieve by means of the researchers and offering potent advancements alongside the structures and regulate area.

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The descriptor system (19) is robustly admissible with H∞ disturbance attenuation γ if and only if there exist matrices P > 0, Q such that AT A T PA − E T PE + C T C A T PB + C T D + T SQ T + QS T A B < 0 B B T PA + D T C B T PB + D T D − γ2 I (20) where S ∈ ℜn×(n−r) is any matrix with full column rank and satisfies E T S = 0. (ii) Given a scalar γ > 0. The descriptor system (19) is robustly admissible with H∞ disturbance attenuation γ if and only if there exist matrix P such that E T PE ≥ 0, (21) A T PA − E T PE + C T C A T PB + C T D < 0.

To determine the mean value function, we take mathematical expectation of the both hand of the above two equations to get x¯ (k + 1) = (A + B2 K )x¯ (k ) + B1w(k ) z¯ (k ) = (C1 + D12 K )x¯ (k) 23 24 Advances in Discrete Time Systems 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 + 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 = .

The results in [10], [27], [33], [36] considered discrete-time systems with time-invariant delays. Gao and Chen [11], Hara and Yoneyama [12], [13] gave robust stability conditions. Fridman and Shaked [8] solved a guaranteed cost control problem. Fridman and Shaked [9], Zhang and Han [37] considered the H∞ disturbance attenuation. The results have been extended to a class of discrete-time descriptor delay systems in [2], [3], [24]. In general, control systems are designed not only for the stability, but also for robustness with respect to system parameters.

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ADVANCES IN DISCRETE TIME SYSTEMS by Edited by Magdi S. Mahmoud


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