Solution of discrete regulation problems using linear algebraic equations†
N. Bergman, JAMES A. CADZOW · International Journal of Control · 1969
The solution of linear algebraic equations are used as a method of synthesizing linear, deterministic, multivariable, discrete systems for either stable or unstable open loop plants, Well-defined relationships are established between weights of a quadratic performance index and plant dynamics via the optimal system determinant. The discrete calculus of variations provides the necessary conditions for minimizing a quadratic cost functional. This gives closed form expressions for U°(z) and Y°(z) and generates the optimal system.