Abstract:
The work is devoted to the study of the sensibility of the eigenvalues of dynamic systems models in state space and the stability of dynamic systems models. The problem of finding state estimates of dynamic systems is quite common in the design of optimal continuous and discrete control systems in their stochastic and deterministic form. The possibility of solving individual problems of finding estimates and optimal controls by projecting multidimensional spaces onto their own subspaces in order of increasing difficulty of solved problems has been considered.
The possibility to estimate the sensitivity of the parameters of linear dynamic system models using projection methods was accomplished. The study of dynamic systems models for sensitivity allowed us to identify critical changes in the eigenvalues of the system operator and predict unstable system operation modes. The solution of the stability problem of the dynamic system model is determined by the structure of the dynamic system model matrix, its rank, type, and multiplicity of the roots of the characteristic polynomial, and is solved by the theory of multiple roots of eigenvalues and eigenvectors based on Hershhorin's theorems. The stability of the dynamic system model is determined by the location of the eigenvalues on the complex plane.
