Digital control and sampling period assignment of multiple plants in networked control systems

This study investigates the problem of sampling period assignment and design of digital state feedback controllers for systems subject to time-varying sampling periods and uncertain delays. The system is controlled through a communication network, where the sampling period and the network-induced delay are bounded in a known interval. The sampled system is described by a linear parameter-varying discrete-time model obtained by means of the Cayley-Hamilton theorem. The proposed discretisation procedure improves the current approaches in the literature and allows the design of controllers that are robust to the delay and depending on the sampling period defined by a scheduling policy in a scenario with concurrent access to the communication network by multiple plants. The gain-scheduled linear quadratic controller is designed by means of linear matrix inequalities. The policy to access the network is dynamic and formulated as an optimisation problem. Numerical experiments illustrate the efficiency and the validity of the proposed approach.