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Discrete control systems

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Quantised robust ℋ∞ output feedback control of discrete-time systems with random communication delays
Author(s): F. Rasool, S.K. Nguang
Source: IET Control Theory & Applications, Volume 4, Issue 11, 2010 , p. 2252 - 2262
Type: Article
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In this study, a stability criterion and robust ℋ∞ mode delay-dependent quantised dynamic output feedback controller design problem for discrete-time systems with random communication delays, packet dropouts and quantisation errors are investigated. Random communication delays from the sensor to controller network are modelled using a finite-state Markov chain with a special transition probability. A logarithmic quantiser is used to quantise the measured output. The Lyapunov–Krasovskii (L–K) functional approach is used to derive the stochastic stability criterion for the system with a given attenuation level. Sufficient conditions for the existence of an output feedback controller is formulated in terms of bilinear matrix inequalities (BMIs). Owing to the special transition probability matrix, a new slack matrix is added to BMIs to relax the sufficient conditions for the existence of an output feedback controller. Furthermore, an iterative algorithm is used to convert the BMIs into the quasi-convex optimisation problem which can be solved easily. An example is given to demonstrate the effectiveness of the proposed design.

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Robust mode delay-dependent ℋ∞ control of discrete-time systems with random communication delays
Author(s): S. Chae, F. Rasool, S.K. Nguang, A. Swain
Source: IET Control Theory & Applications, Volume 4, Issue 6, 2010 , p. 936 - 944
Type: Article
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This study considers stability and robust mode delay-dependent ℋ∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controllers are modelled by a finite state Markov process. Based on Lyapunov–Krasovskii functional, a novel methodology for designing a mode delay-dependent state feedback controller has been proposed. The authors also show that the existing delay-dependent approach is a special case of the mode delay-dependent approach proposed in this study. The mode delay-dependent controller is obtained by solving linear matrix inequality optimisation problems using the cone complementarity linearisation algorithm. The effectiveness of the proposed design methodology is verified by a numerical example.

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