Stabilization of Two-Dimensional Persistently Excited Linear Control Systems with Arbitrary Rate of Convergence
نویسندگان
چکیده
We consider the control system ẋ = Ax+α(t)bu, where the pair (A, b) is controllable, x ∈ R2, u is a scalar control, and the unknown signal α satisfies a persistent excitation condition. We study the stabilization of this system, and we prove that it is globally asymptotically stable with arbitrarily large exponential rate uniformly with respect to all signals satisfying a common persistent excitation condition and a common Lipschitz continuity bound.
منابع مشابه
A new switching strategy for exponential stabilization of uncertain discrete-time switched linear systems in guaranteed cost control problem
Uncertain switched linear systems are known as an important class of control systems. Performance of these systems is affected by uncertainties and its stabilization is a main concern of recent studies. Existing work on stabilization of these systems only provides asymptotical stabilization via designing switching strategy and state-feedback controller. In this paper, a new switching strate...
متن کاملOn the Stabilization of Persistently Excited Linear Systems
We consider control systems of the type ẋ = Ax+α(t)bu, where u ∈ R, (A, b) is a controllable pair and α is an unknown time-varying signal with values in [0, 1] satisfying a persistent excitation condition i.e., ∫ t+T t α(s)ds ≥ μ for every t ≥ 0, with 0 < μ ≤ T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T, μ) if the eigenvalu...
متن کاملStabilization of persistently excited linear systems by delayed feedback laws
This paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback, where we suppose that the feedback law is not applied instantaneously, but after a certain positive delay (not necessarily constant). The main result is that, under certain spectral hypotheses on the linear system, stabilization by means of a linear delayed feedback ...
متن کامل0 81 0 . 21 22 v 3 [ m at h . O C ] 1 8 M ay 2 00 9 On the stabilization of persistently excited linear systems ∗
We consider control systems of the type ẋ = Ax+α(t)bu, where u ∈ R, (A, b) is a controllable pair and α is an unknown time-varying signal with values in [0, 1] satisfying a persistent excitation condition i.e., ∫ t+T t α(s)ds ≥ μ for every t ≥ 0, with 0 < μ ≤ T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T, μ) if the eigenvalu...
متن کاملGrowth rates for persistently excited linear systems
We consider a family of linear control systems ẋ = Ax+αBu where α belongs to a given class of persistently exciting signals. We seek maximal α-uniform stabilisation and destabilisation by means of linear feedbacks u = Kx. We extend previous results obtained for bidimensional singleinput linear control systems to the general case as follows: if the pair (A,B) verifies a certain Lie bracket gener...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Control and Optimization
دوره 51 شماره
صفحات -
تاریخ انتشار 2013