1. R. MASAROVA, M. JUHAS, B. JUHASOVA, Z. SUTOVA FACULTY OF MATERIALS SCIENCE AND TECHNOLOGY IN TRNAVA SLOVAK UNIVERSITY OF TECHNOLOGY IN BRATISLAVA TRNAVA SLOVAKIA COPENHAGEN, JUNE 12TH 2015 Inverse Matrix in the Theory of Dynamic Systems

2. Inverse matrix Mathematical model is often used for describing the properties of the dynamic system Inverse matrix (using different algorithms)  Transfer matrix of a dynamic system Definition: Let A be a regular matrix (a square matrix with a determinant different from 0). Matrix A -1 is an inverse matrix to matrix A if A. A -1 = A -1. A = I, where I is an identity matrix. Masarova, R., Juhasova, B., Juhas, M., Sutova, Z. Inverse Matrix in the Theory of Dynamic Systems

3. Calculating inverse matrix Adjusting the matrix (A | I) using either column or line equivalent operations to get a resulting matrix (I | A). Using the formula 1. Calculating the characteristic polynomial 2. Auxiliary matrices 3. Inverse matrix

4. Dynamic system State equations of a continuous linear system with the initial condition x( 0 ) = 0: Transfer matrix of a system: An inverse dynamic system exists when there exist an inverse matrix to G(s) -1, i.e. G(s) is regular (|G(s)|≠0). Masarova, R., Juhasova, B., Juhas, M., Sutova, Z. Inverse Matrix in the Theory of Dynamic Systems

5. Existence of inverse matrix Matrices A, B, C, D are number matrices: Let us create a matrix., and. As, an inverse dynamic system does not exist. Both classic and MATLAB calculations confirm the results: function deter(n, A, B, C, D) syms('s'); I=eye(n); M=[A B; C D] invmat=inv(s*I-A); G=C*invmat*B+D; det(G) end det(G) = 0 Masarova, R., Juhasova, B., Juhas, M., Sutova, Z. Inverse Matrix in the Theory of Dynamic Systems

6. Conclusion The problem of finding an inverse matrix in dynamic system theory is much vaster, as the inverse matrix can be found, e.g. by inverting graphs or using dynamic algorithms, etc. This paper is a part of the VEGA project 1/0463/13. Masarova, R., Juhasova, B., Juhas, M., Sutova, Z.: Inverse Matrix in the Theory of Dynamic Systems