Uniform controllability of a class of linear time-varying systems

Linear controllers for exponential tracking of systems in chained-form

“…If u P (t) satis"es Assumption 2.12 it follows immediately from Theorem 2 in Reference [18] that the pair (A28) is UCO, which completes the proof. )…”

“…This is a direct consequence of Theorem 2 in Reference [18]. ) Theorem 2.14 Consider system (14) in closed loop with the controller…”

Tracking control of an underactuated ship

“…For basic concepts, the reader is referred to [16]. The result we need in this paper is a corollary of [17,Th. 2].…”

Time‐varying linear controllers for exponential tracking of non‐holonomic systems in chained form

“…An important technique used in the paper is a modified time-varying dilation used as the co-ordinate transformation, which was initially proposed by Astolfi [4] and then developed in [7,17] for the stabilization problem of non-holonomic systems. Using this technique and a cascade-design approach for nonlinear time-varying systems [18], we convert the tracking control problem for the chained-form system into some global exponential stabilization problems for linear time-varying systems. Afterwards, smooth time-varying controllers are constructed, which render the tracking-error dynamics globally K-exponentially stable.…”