H2 and H∞ State-Feedback Control Through Multi-Hop Networks: Trade-Off Analysis Between the Network Load and Performance Degradation

This paper is concerned with the H2 and H∞ control problems in networked control framework, dealing specifically with cases where the communication between the components is made via a multi-hop network susceptible to packet loss, which is modeled by a Markov chain with Bernoulli distribution. The aim is to investigate the trade-off between the network resource saving and the closed-loop performance degradation in the context of state-feedback control. The performance of the control design is measured by means of the H2 and H∞ norms. Two main topics are evaluated: i) The influence of the initial probability distribution on the design of the controller; and ii) The relationship between the expected value of the output signal energy and the probability of successful transmissions (associated with the maximum allowable transmission per data packet) for a given transport scheme and a given performance criterion. The results are applied in a case study based on a linearized numerical model of the Furuta’s inverted pendulum.