Practical stabilizability of a class of homogeneous bilinear systems

This note investigates stabilizability of a class of homogeneous bilinear systems in which the drift term (A matrix) is unstable and the B matrix is rank deficient. It considers feedback control laws in the form of variable structure. It is possible to drive the system to within a small ball which includes the origin. Such stability is called practical stability. Four specific systems in \(R^3\) $R^3$ , \(R^4\) $R^4$ , and \(R^5\) $R^5$ are considered. A number of numerical examples are used to study the performance of the system.