On existence and construction of stabilizing switching laws between two unstable linear systems

Issues regarding the application of two equivalent sufficient conditions for the existence of stabilizing switching laws between two unstable linear systems are studied. One of the conditions is effective for theoretical derivation, while the other is easily implementable. To further understand the geometrical insight of the conditions, an equivalent condition involving the information of eigenvalues and eigenvectors of system dynamics is presented for planar cases. With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is also presented. The controllers and stabilizing switching laws are explicitly constructed through the use of an existed algorithm.