Dynamical Output Feedback Stabilization Of Mimo Bilinear Systems With Undamped Natural Response

Abstract

This paper considers the globally asymptotic stabilization problem of multi-input multi-output bilinear systems with undamped natural response. Under the conditions for asymptotic stabilization by static state feedback control and system detectability, two output dynamic feedback controllers with saturation bounded control are constructed. The global asymptotic stability of the closed-loop system is verified by Lyapunov stability theory and LaSalle's Lemma. An example is given to demonstrate the obtained results.

Solution Existence and Stabilization for Bilinear Descriptor Systems with Time-delay

“…Remark 3.2: The result in this paper extends the main results in [5], [6], [8] for bilinear systems and delayed bilinear systems. In addition, Theorem 3.1 forms a fundamental framework for the development of output feedback controller design for the given DBDS.…”

“…Similar to the assumptions in [5], [6], [8], we suppose that all eigenvalues for equation det(λE − A) = 0 satisfy Re(λ) ≤ 0. For simplicity, we make an additional assumption for DBDS (1).…”

“…Under the given sufficient condition, state feedback controller can be constructed to guarantee the uniqueness and existence of solution for the closed loop systems and the global asymptotic stability at the same time. The proposed approach extends the results for bilinear systems and delayed bilinear systems in [5], [6], [8]. It is worth mentioning that the approach developed in this paper is different from those for nonlinear descriptor systems in [2], [10], [11].…”

“…In [12], robust stability and stabilization for singular systems with state delay and parameter uncertainty were discussed by the means of linear matrix approach. In addition, bilinear systems are not only a special set of nonlinear systems, but can also be regarded as a practical starting point for the study of other nonlinear systems, and has received some interests [5], [6], [7], [8], etc.…”

Study of a Class of Almost‐controllable Discrete‐time Bilinear Systems

“…Thus, it is necessary to clarify the fundamental properties of bilinear systems, say, stabilizability and controllability. Lu et al [8] and Chen et al [9,10] studied stabilization of bilinear systems. Some research on controllability for continuous time bilinear systems has been made [2,11], where Lie group and Lie algebra play a key role as the main mathematical tools [12].…”