A switched state feedback law for the stabilization of LTI systems

Inspired by prior work in the design of switched feedback controllers for second order systems, we develop a switched state feedback control law for the stabilization of LTI systems of arbitrary dimension. The control law operates by switching between two static gain vectors in such a way that the state trajectory is driven onto a stable n - 1 dimensional hyperplane (where n represents the system dimension). We begin by briefly examining relevant geometric properties of the phase portraits in the case of two-dimensional systems and show how these geometric properties can be expressed as algebraic constraints on the switched vector fields that are applicable to LTI systems of arbitrary dimension. We then describe an explicit procedure for designing stabilizing controllers and illustrate the closed-loop transient performance via two examples.