Robust mode delay-dependent ℋ∞ control of discrete-time systems with random communication delays

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Robust mode delay-dependent ℋ∞ control of discrete-time systems with random communication delays

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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.

Inspec keywords: delays; control system synthesis; H∞ control; linear matrix inequalities; discrete time systems; linearisation techniques; state feedback; Lyapunov methods; Markov processes; optimisation; robust control

Other keywords: Lyapunov-Krasovskii functional; finite state Markov process; random communication delays; cone complementarity linearisation algorithm; mode delay-dependent state feedback controller; robust mode delay-dependent H∞ controller design; discrete-time systems; linear matrix inequality optimisation problems

Subjects: Stability in control theory; Discrete control systems; Distributed parameter control systems; Optimal control; Markov processes; Linear algebra (numerical analysis); Optimisation techniques; Control system analysis and synthesis methods

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