Spectral radius bounds for positive matrices with applications to networked control systems over fading channels

Upper and lower bounds for spectral radius of positive matrices are derived, and are shown to be tight. These bounds are characterized by the determinant and trace of some related matrix, and they find applications in networked control systems (NCS) over fading channels. Results are obtained for the relation between mean-square (MS) stabilization and standard ℋ₂ optimal control, and for the MS stabilizability condition under state feedback control. An encoding and decoding matrix pair is introduced to help design the state feedback controllers, when the MS stabilizability condition holds true.