ABSTRACT
We design control algorithms by minimizing performance functionals that quantitatively and qualitatively describe the system performance and capabilities. The following system variables are utilized: states x, outputs y, tracking errors e, and control u. Considering multi-input/multi-output systems, one has
x ∈ �n, y ∈ �b, e ∈ �b and u ∈ �m. The variables tuple (x,e,u) or quadruple (x,y,e,u) describe, specify, quantify,
and qualify the system performance and capabilities. The performance functional can be maximized or minimized.
