Quadratic Stabilization and Transit Problems for Switched Linear Systems via State Feedback

In this paper, two transit problems which pass through the ε-neighborhood of some given objective states in turn from an arbitrary initial state will be studied for both continuous-time and discrete-time switched linear systems with constant input. At first the quadratic stabilization problem for continuous-time switched linear systems with constant input will be investigated. Next, the same problem for discrete-time switched linear systems with constant input will be studied. After that two ε-transit problems by using switched linear systems with constant input via state-dependent switching will be formulated, and then solvability conditions will be given. Further, two illustrative numerical examples will be shown.