Stabilization of Linear Systems Over Networks With Limited Communication Capacity

In this paper, we discuss the modeling and control problem for networked systems with access constraints and packet dropouts. Due to the limitation of communication capacity, only the limited number of sensors and actuators are allowed to gain access to network medium according to a stochastic access protocol, and packet dropouts may happen in both backward and forward channels, which can be described by i.i.d Bernoulli processes. Under consideration of the access constraints and packet dropouts, the networked control system can be modelled as a Markov jump system. In such a framework, to solve the controller synthesis problem, the time-varying Kalman filter is first designed. Then, by using the theory of Markovian jump systems and dynamic programming, an optimal controller is designed such that the networked system is exponentially mean-square stable while minimizing the quadratic cost. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed results.