Stability of the RC Circuit with Two Capacitors

Question

I want to find poles and zeros of the circuit shown below. So I can determine stability of the system.

$$ V_{C1} + V_{C2} + V_R = 0 $$ where $I$ is current of the loop, $$ V_{C1} + V_{C2} + RI = 0 $$ where $I = C\dot{V}_{C2}$, $$ V_{C1} + V_{C2} + R(C\dot{V}_{C2}) = 0 $$

I thought that I could determine the stability of the system with using Lyapunov's theorem but as can be seen, there are two unknown variables to be solved. How should I approach this problem to determine stability?

Answer 1

Your first equation has a problem

$$ -V_{C2} + V_{C1} + V_{R1} = \color{red}{0} \tag{1} $$

Since $C2$ and the source are in parallel

$$ V_{C2} = 0.8 \tag{2} $$