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I tried it in Octave, there's definitely a glitch like you said. I tried it with "Tustin" instead of "zoh", same result. However I was puzzled by your high sampling frequency. Your lag controller has a pole at s = -0.01 and a zero at s = -0.1, they are both "slow" while your sampling frequency is really high. How to fix it : Change your sampling ...

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If you are given an input $x(t)$ with $x(t)=0$ for $t<t_0$, and you specify an initial condition $y(t_1)=0$ for $t_1>t_0$, then the resulting system is generally non-causal, because we already know the system's response at $t_1>t_0$, regardless of the input signal in the interval $[t_0,t_1]$. For a system to be linear (in the sense used by ...

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Filter types other than low pass (high pass, band pass, band stop) are obtained from a low pass prototype filter by frequency transformations (such as $s\rightarrow 1/s$ for a low pass / high pass transformation). These transformation destroy the optimality of the phase response. Nevertheless, filters obtained from a Bessel low pass prototype filter usually ...

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