On calculation of norms of 2D-systems

Application of the Lyapunov method to the stability analysis and search of the 2D-system norms gives rise to the algebraic problems interpretable as expansion of the nontrivial matrix polynomials into the sum of squares or as parameterized linear matrix inequalities to be satisfied for certain ranges of the parameter values. The paper demonstrated a mechanism for transformation of such problems arising seeking the $\mathcal H_2$-norm and a method for calculation of the $\mathcal H_2$-norm of the 2D-systems. Both computational schemes are simpler than the existing results. Numerical examples are presented.