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a class of signals can be defined as those signals v having a 2 norm bounded by 1 ju)*y(ju)du≤1 (3.12) By filtering u, a new class of signals v can be est ablished, characteristic as input to the process either as dist urb an ces or as reference signals V={u(s)=W()b(s):‖l1l2≤1} (3.13) By designing the control system such that it minimizes the possible error given a certain class of normbounded input signals, all potential input s are treated equally. This can be an advant age, as it is rarely known in the design phase for cert ain, which reference changes or disturber dition Hence, the reference r and the disturb an ce d can be d erized by prepending input filters to our st andard feedback loop, see Figure 3.2 d'(s Wa(s Wr(s) K(s G(s)Im( Figure 3.2: Control loop with unit norm bounded signals as inputs (a =le sup(In=12 =ecifica2ion) This example has been taken from/MZ8g. Assume that the reference is known only to change 7 step, and that only small disturbances are present such that d(s)0 and u(s=r(s). Then an inp ut weight W(s)must be chosen such that u(s)=s and u(s)EV. An obvious choice to be w(s=1/s and to introduce v(s)as an imp ulse (U()=1). Howev v(s)=l does not belong to the set V' since the integral in(3. 12) become infinite(an impulse does note have finite 2 norm). Hence, the weight W(s)=1/s does not provide the desired haracteristics for the reference r(s. Instead, the following weight can be used B>0 (3.14) With this filter, a step input is contained in V. For instance, assume that v(s) is given by 15) 8+a # , ,! < " " ! < ' " & " " " = " ' " , , !" # $ % $ # & ' ( ) &% ,! ' & ( ) % & *% + -! , % - % & $+ 7!