On Avoiding the Effect of Non-Minimum Phase Zeros Over the Signal-to-Noise Ratio Limitation

Abstract

Fundamental limitations in networked control systems have been researched for the last years with many stability results, from channel transmission minimal rate based on information theory, to minimal signal-to-noise (SNR). For the latter, it has been confirmed early on that the usual culprits increase the minimal SNR for stability, such as unstable plant poles, non-minimum phase (NMP) zeros, time delay, together with new ones such as communication channel bandwidth and colored transmission noise. In this letter we specifically propose two approaches to completely avoid the effect of NMP zeros on the minimal SNR for stability in discrete-time. The first approach stems from the observation that the controller that achieves the minimal SNR for a minimum phase plant in discretetime, has all its zeros located outside the unit circle (NMP zeros). Such observation allow then to characterize this set of NMP zeros as candidate NMP zeros of alternative plant models with the same unstable poles, which in turn will not increase the minimal SNR for stability above the expression imposed only by the plant unstable poles. Our second approach extends the set of possible NMP zeros that do not increase the SNR limitation to any location, by proposing the synthesis of a two-degree of freedom linear time invariant controller solution that achieves the minimal SNR for stability imposed only by the plant unstable poles.