Design of distributed ℋ∞-optimized controllers considering stochastic communication link failures

This paper proposes an approach for the design of distributed state-feedback controllers for interconnected discrete-time LTI systems with uncertain communication links. These links may be subject to intermittent or persistent failure. In particular, we assume that the availability of the communication links over time can be modeled by a Markov chain. For the control design, it is shown in a first step that the combination of the LTI system dynamics and the stochastic model of the time-varying communication topology is a special case of Jump Markov Linear Systems (JMLS). Next, constraints on the information structure are introduced, restricting the subsystems´ local knowledge about the global network state. This assumes that each subsystem can only detect the availability of incoming communication links. Finally, the synthesis of a stabilizing distributed feedback control law respecting the given information structure and a guaranteed bound on the expected ℋ_∞-performance is formulated and solved as a semidefinite program.