Hardy Space Robust Design

In Fig. 31.1 a single-input single-output system is given. A robust controller K(s) should be designed to guarantee sufficient closed-loop performance even in the presence of plant uncertainties. The actual plant transfer function is G_p = {1 + ΔN[u(t),t]}G where G denotes the nominal plant and ΔN[u(t), t] is a real-valued nonlinear time-varying function of the input signal u(t). The uncertainty ΔN is considered bounded by the sector gain γN 31.1$$\Delta N\left[ {u(t),t} \right] \le \gamma N\left| {u(t)} \right|{\rm{ }}\forall u(t){\rm{ where }}\Delta N\left[ {0,t} \right] = 0{\rm{ }}\forall t$$ The nonlinearity is not essential in this chapter but the derivations can easily be extended to several types of nonlinear uncertainty.