Quantised robust ℋ∞ output feedback control of discrete-time systems with random communication delays

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Quantised robust ℋ∞ output feedback control of discrete-time systems with random communication delays

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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.

Inspec keywords: feedback; discrete time systems; control system synthesis; iterative methods; Markov processes; delays; linear matrix inequalities; H∞ control; convex programming; robust control

Other keywords: bilinear matrix inequalities; quantised robust H∞ output feedback control; quasi-convex optimisation problem; random communication delays; stochastic stability criterion; logarithmic quantiser; special transition probability; finite-state Markov chain; iterative algorithm; discrete-time systems; Lyapunov-Krasovskii functional approach

Subjects: Interpolation and function approximation (numerical analysis); Distributed parameter control systems; Algebra; Optimal control; Optimisation techniques; Discrete control systems; Stability in control theory; Markov processes

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