On the stabilizability of two-dimensional linear systems via switched output feedback

The problem of stabilizing a second order SISO LTI system of the form x = Ax + Bu, y = Cx with feedback of the form u(x) = v(x)Cx is considered, where v(x). is real-valued and has domain which is all of R. It is shown that, when stabilization is possible, v(x) can be chosen to take on no more than two values throughout the entire state space (i.e., v(x) is an element of {v(1),v(2)} for all x and for some v(1),v(2)), and an algorithm for finding a specific choice of v(x) is presented. It is also shown that the classical root locus of the corresponding transfer function C(sI - A)(-1) B has a strong connection to this stabilization problem, and its utility is demonstrated through several design examples.