A geometric approach to dynamic feedback design

Let dimensions of a spaces states $n$, inputs $m$, and outputs $p$ of a generic linear control system and also integer $l>0$ satisfy the restriction $n<mp+l(m+p\operatorname{min}(m,p))$. An algorithm dynamic compensator design of degree $l$ is suggested. It is shown if $n<mp$ a minimal order $l_{\operatorname{min}}$ of the compensator being assumed the control system is determined by correlation $(1+(n,mp)/(m+p,1)>l_{\operatorname{min}}(n,mp)/(m+p,1)$ (in case $n<mp$, $l_{\operatorname{min}}=0$). Besides, for the control systems with two inputs or putputs, the procedure completely solving the compensators design problem of the first and, partially, the second powers is elaborated. An example is given.