Upper bounds on the best achievable performance subject to SNR constraints in two-channel networked architectures

This paper studies control problems subject to signal-to-noise ratio (SNR) constraints for two-channel MIMO architectures. We first establish a second order moments equivalence between LTI feedback systems subject to SNR constraints and a class of Markov jump linear systems (MJLSs). This equivalence allows one to recast the original SNR constrained problem into an optimal mode-independent controller design problem for MJLSs. Exploiting this fact, and provided some linear matrix inequalities are feasible, we compute an upper bound on the best achievable performance subject to SNR constraints in two-channel architectures, when static state feedback controllers are employed. A numerical example is included to illustrate the results.