Quasi-Time-Optimal Feedback Control of Some Fifth-Order Systems

A quasi-time-optimal feedback control approach is proposed for certain fifth-order systems with a single saturable control input. A pure integrator system is treated initially and the suboptimal feedback control, which achieves finite-time transition to the state origin, is shown to be piecewise constant with at most seven switches in sign; the analysis is also valid for a system with negative real eigenvalues in simple ratio. The effectiveness of the approach is demonstrated by numerical example. An extension of the control, via a linear state transformation, to more general systems with real nonpositive eigenvalues is indicated.