Synthesis of state descriptors in the problem of multiprogram stabilization of bilinear systems (Q1810221)

This paper deals with systems of the form \[ \dot x=\bigl(A(t)+ \sum^r_{i=1} B_i(t)u_i \bigr)x+F(t) \] with \(x\in\mathbb{R}^n\). It is assumed that a number of program controls \(u_1(t),\dots,u_N(t)\) are given, each of them realizing a certain objective described by some corresponding program motions \(x_1(t), \dots,x_N(t)\). The basic problem is to construct a control \(u=u(x,t)\) which realizes all the program motions by ensuring at the same time their Lyapunov stability. The present paper considers the case of a partial observation of the deviations from the given program motions. The problem is solved by the construction of suitable state estimators.