Motivation for the Laplace Transform(continued In many applications, we do need to deal with unstable systems, e. g Stabilizing an inverted pendulum Stabilizing an airplane or space shuttle Instability is desired in some applications, e.g. oscillators and asers How do we analyze such signals/systems? Recall from Lecture #5, eigenfunction property of lti systems h(s st H( h(te s dt(assuming this converges) est is an eigenfunction of any lti system s=o+jo can be complex in generalMotivation for the Laplace Transform (continued) • How do we analyze such signals/systems? Recall from Lecture #5, eigenfunction property of LTI systems: — est is an eigenfunction of any LTI system — s = σ + j ω can be complex in general • In many applications, we do need to deal with unstable systems, e.g. — Stabilizing an inverted pendulum — Stabilizing an airplane or space shuttle # — Instability is desired in some applications, e.g. oscillators and lasers