For a general dynamical system Σ and cascade compensation <m:math> <m:semantics> <m:mrow> <m:mover accent=’true’> <m:mi>Σ</m:mi> <m:mo stretchy=’true’>¯</m:mo> </m:mover> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$$\overline \Sigma$ conditions are developed for the existence of a state-feedback law F which when applied to Σ causes the result-ing closed-loop system ΣF to exhibit the same input-output behavior as the cascade connection of Σ with <m:math> <m:semantics> <m:mrow> <m:mover accent=’true’> <m:mi>Σ</m:mi> <m:mo stretchy=’true’>¯</m:mo> </m:mover> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\overline \Sigma$$ . For a controllable, observable linear system Σ with transfer matrix TΣ, it is shown that an invertible linear cascade compensator with transfer matrix <m:math> <m:semantics> <m:mrow> <m:mover accent=’true’> <m:mi>T</m:mi> <m:mo stretchy=’true’>¯</m:mo> </m:mover> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\overline \Sigma$$ . can be implemented with state feedback if and only if the McMillan Degree of TΣ equals the McMillan Degree of <m:math display=’block’> <m:semantics> <m:mrow> <m:mrow><m:mo>[</m:mo> <m:mtable columnalign=’left’> <m:mtr> <m:mtd> <m:msub> <m:mi>T</m:mi> <m:mi>Σ</m:mi> </m:msub> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mmultiscripts> <m:mo>−</m:mo> <m:mprescripts/> <m:mrow> <m:mover accent=’true’> <m:mi>T</m:mi> <m:mo stretchy=’true’>¯</m:mo> </m:mover> </m:mrow> <m:none/> </m:mmultiscripts> <m:mn>1</m:mn> </m:mtd> </m:mtr> </m:mtable> <m:mo>]</m:mo></m:mrow> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\left[ \matrix{ {T_\Sigma } \hfill \cr {}_{\overline T } - 1 \hfill \cr} \right]$$ .