The authors investigate a class of observer-based discrete-time networked control systems (NCSs) with multiple-packet transmission where random packet dropouts occur independently in both the sensor-to-controller (S/C) and controller-to-actuator (C/A) channels. The authors first propose and prove the separation principle for the NCSs where packet dropouts in the C/A and S/C channels are governed by two independent Markov chains, respectively. Secondly, the authors derive a sufficient condition, in terms of linear matrix inequalities (LMIs), for stabilisation control of the Markov chain-driven NCSs. The authors also derive the necessary and sufficient condition for stabilisation control of the memoryless process-driven NCSs as a special case. A numerical example is provided to illustrate the effectiveness of our method.

A tractable closed-loop stability-related measure for controller structures, realised using the δ operator and digitally implemented with `finite word length' (FWL), is derived. The optimal realisations of the general finite-precision controller are defined as those that maximise this measure and are shown to be the solutions of a constrained nonlinear optimisation problem. For the special case of digital PID controllers, the constrained problem can be decoupled into two simpler unconstrained optimisation problems. A global optimisation strategy based on the adaptive simulated annealing (ASA) is adopted to provide an efficient method for solving this complex optimal realisation problem. Two numerical examples are presented to illustrate the design procedure, and the simulation results confirm that the optimal FWL realizations of the δ-operator based controller have better closed-loop stability margins than those of the usual shift-operator based controller, especially under fast sampling conditions.