We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.
We describe precisely, under generic conditions, the contact of the accessibility set at time with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-riemannian system of rank 2. As a consequence we obtain in sub-riemannian geometry a new splitting-up of the sphere near an abnormal minimizer into two sectors, bordered by the first Pontryagin’s cone along , called the -sector and the -sector. Moreover we...
We describe precisely, under generic conditions, the contact of the accessibility set at time T with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer γ into two sectors, bordered by the first Pontryagin's cone along γ, called the L∞-sector and the L2-sector. Moreover...