Optimization of bilinear systems subjected to exogenous disturbances. I. Analysis

The results associated with analysis problem for bilinear systems subjected to arbitrary bounded exogenous disturbances is presented. An approach is proposed to the construction of the so-called stabilizability ellipsoid and stabilizability domain for quadratic dynamical systems in both the continuous and discrete time versions. The main tool of this approach is the linear matrix inequality technique. This simple yet versatile approach has high potential in extensions and generalizations; partially, it is equally applicable to robust versions of the problem.