The minimal signal-to-noise ratio required for stability of control systems over a noisy channel in the presence of packet dropouts

Abstract

The achievable performance of networked control systems (NCSs) are often constrained to the communication channel characteristics. This paper investigates the minimal signal-to-noise ratio (SNR) for stabilization of the single-input single-output (SISO), linear time-invariant systems whose output feedback is subjected to the additive white Gaussian noise (AWGN), and the effect of the packet dropouts which is modeled as a binary stochastic process. The authors considered both cases, with and without the input stochastic disturbance. With the parameterization of all stabilizing controllers, the results showed that signal-to-noise ratio performance is strongly dependent on the plant’s nonminimum phase zeros and unstable poles locations. It was also proven that the packet dropouts and the input stochastic disturbance might degenerate the signal-to-noise ratio performance. Lastly, simulations are provided in order to verify the obtained theoretical analysis results.