SNR limitation for feedback control systems with amplitude-bounded noise

Abstract

This paper presents an SNR limitation in control under amplitude-bounded noise. The SNR of feedback link in control system is evaluated with respect to amplitude and minimized over all causal control laws. The minimum SNR is represented by the absolute value of the product of unstable poles of the plant. This index is known to describe performance limitations in various control problems. The optimal control law minimizing the SNR is simply constructed as a combination of scaling factor and the state feedback gain for minimum energy control. This control law overcomes the drawback of computational complexity of the encoding scheme minimizing bit-rate, which is employed to minimize an amplitude-base SNR in our preceding work. This simplification is accomplished by relaxing the requirement of stability to the convergence of the state to near the origin and introducing a new criterion for evaluating SNR.