Abstract:
We consider the problem of stabilization of discrete-time bilinear control systems. Using the linear matrix inequality technique and quadratic Lyapunov functions, we formulate a method for the construction of the so-called stabilizability ellipsoid having the property that the trajectories of the closed-loop system emanating from the points in the ellipsoid asymptotically tend to the origin. The proposed approach allows for an efficient construction of nonconvex domains of stabilizability of discrete-time bilinear control systems. The results are extended to the robust statement of the problem where the system matrix is subjected to structured uncertainties.
Keywords:discrete-time bilinear system, quadratic Lyapunov function, linear feedback, stabilizability ellipsoid, domain of stabilizability, linear matrix inequalities.
Presented by the member of Editorial Board:L. B. Rapoport