Analytical construction of a robust regulator by means of Lyapunov edge conditions

A method is considered allowing to synthesize analytically robust control laws depending on a phase locus. System paths are not to exceed the bounds of this phase locus. The synthesis is being realized according to the so-called Lyapunov boundary conditions. The expression for these conditions is exactly the same that for the Lyapunov inequalities at a constraint function level surface. Control laws of desired type (linear, in particular) are determined analytically for an arbitrary system. Limitations on a technical implementation complexity (an order of a controller, as well as a number of components of a state vector) are also taken into account.