Oberseminar "Dynamische Systeme und Kontrolltheorie" - Prof. Dr. Vitaliy Slynko

"Solution Area for a Class of Linear Differential Equations with Hukuhara Derivative"

We will provide a definition and basic information about the Hukuhara derivative and differential equations with the Hukuhara derivative. A brief review of some results on the development of the direct Lyapunov method for these equations we will given. A formula for the solution area for a class of linear differential equations with Hukuhara derivative we will discussed. We will consider the Cauchy problem for the differential equation D H X(t) = AX(t), X(0) = X 0 (1) where D H is the Hukuhara derivative operator, X(t) ∈ conv R 2 , t ∈ [0, T ], T is a positive number, and A ∈ L(R 2 ) is a linear operator extended to the space conv R 2 in a natural way: AX = {Ax, x ∈ X} ⊂ conv R 2 The main idea of the research is to construct a countable comparison system and its solution in explicit form. An explicit formula is obtained for the area S[X(t)] of solutions X(t) of the Cauchy problem (1) under the assumption that | det A| = 1 and tr A < 2.

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