A Smooth, High-Gain Adaptive Stabilizer for Linear Systems with Known Relative Degree

Adaptive controllers and root loci of minimum-phase systems

“…a proof. see Ilchmann and Owens [7]. This shows that condition (6) is an extension of the well-known minimumphase dehnition for single-input, single-output systems given usually in the frequency domain.…”

“…), i(') e I2Q, o). Therefore (see, e.g., Ilchmann and Owens [7]), lim,--y(l) : lin1,-z(r) : 0. Since the system becomes constant after finite time, asymptotic decay of r(r) implies exponential decay, which proves part (i).…”

“…Although this inequality has been implicitly used in earlier works [8,19], or in a more general framework, including nonlinear disturbances [7] and Zo-functions [5] forp > 1, we would like to give a straightforward proof in the present simple situation. The inequality is a basic tool for the proof of stability of the universal adaptive stabilizer presented in section 4.…”

Robust Adaptive Control With Multiple Estimation Models for Stabilization of a Class of Non‐inversely Stable Time‐varying Plants

“…Finally, from (13) and the fact that w i ∈ L ∞ and w L ∞ ∈ , it follows that f i ∈ L ∞ . Finally, from (13) and the fact that w i ∈ L ∞ and w L ∞ ∈ , it follows that f i ∈ L ∞ .…”

“…These assumptions were then proved to be very restrictive and unnecessary for the convergence and stability proofs of adaptive control systems. Also, some researches which relaxed one or several of the aforementioned assumptions have been presented, [3,5,7,8,[10][11][12][13]. Adaptive control algorithms which ensured the robustness of the systems in the presence of disturbances have been designed [2].…”