147 Stability problem

Given a SISO system with rational transfer function $G$, can we find a rational controller $-K$ such that

is stable rational? i) When $G=p/q$ is strictly proper and stable, Nyquist’s criterion is useful, especially for $K=1$, the constant negative feedback loop.

ii) Next we consider $G(s)=p(s)/q(s)$ with $p(s),q(s)\in 𝐂[s]$, where $G$ is possibly unstable, and look for controllers of specific forms. When $K=0$, we talk about the open loop system.

iii) Later we work with $G(s)=P(s)/Q(s)$ where $P(s),Q(s)\in 𝒮$ to obtain the general result.