Feedback stabilization for a bilinear control system under weak observability inequalities

Abstract

In this paper, we discuss the feedback stabilization of bilinear systems under weak observation properties. In this case, the uniform stability is not guaranteed. Thus we provide an explicit weak decay rate for all regular initial data. Applications to Schrödinger and wave equations are provided.2010 Mathematics Subject Classification. 93D15.

Optimal control problem for unbounded bilinear systems and applications

“…It is worth noting that there are several works that are interested in the question U ad ̸ = ∅ (see for instance [3,4,14,24]).…”

Robust stabilization for affine control systems in Banach spaces

“…In the case where is a Hilbert space, the feedback stabilization problem of () has been studied by many authors (see previous research [8–13]). In Ball and Slemrod [9], the authors studied the weak stabilization of () with the control under the assumption: …”

Global feedback stabilization of discrete‐time bilinear systems

“…More recently, Zaitsev [23] considered discrete‐time bilinear systems with periodic coefficients and obtained sufficient conditions for uniform global asymptotic stabilization of the origin by state feedback. In infinite dimension, the stabilization of bilinear systems has been studied by many authors in the continuous‐time case, such as Ouzahra [24] and Ammari and Ouzahra [10]. However, in the discrete‐time case, the question has seldom been addressed.…”

“…Thus, in practice, they are used to model a large variety of real-world processes [1][2][3][4][5][6][7][8]. Stabilization of bilinear systems is a fundamental issue in control theory and has been well investigated over the last few decades by many authors especially in the continuous time case [9][10][11][12][13][14][15][16][17][18][19][20][21]. In practice, modeling errors, such as noise disturbance and parameter uncertainties, are unavoidable.…”