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

Abstract

This paper is concerned with the and 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 and 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.