Exponential stabilization of a constrained bilinear system

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.

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“…And there exist many results on stabilization of bilinear systems in the literature ( [1,4,3,5,8,13,14]). …”

Section: Introductionmentioning

confidence: 99%

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

Zheng

Zhang

2003

Asian Journal of Control

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“…This problem has been considered in the finite-dimensional case [i.e., H = R n and A, B ∈ R n 2 (see [4])], who showed that the condition B)), ∀k ∈ IN is sufficient for exponential stabilization of the system (1) controlled by the feedback p 2 (t). In [7,14], it has been shown that if the spectrum σ (A) of A can be decomposed into σ u (A) = {λ : Re(λ) ≥ −γ } and σ s (A) = {λ : Re(λ) < −γ }, (for some γ > 0), then the state space H can be decomposed according to…”

Section: Introductionmentioning

confidence: 99%

“…For finite-dimensional systems, the conditions (3) and (4) are equivalent (see [4,17]). However, in infinite-dimensional case, and if B is compact, then the condition (4) is impossible.…”

Section: Introductionmentioning

confidence: 99%

Polynomial decay rate estimate for bilinear parabolic systems under weak observability condition

Tsouli

Boutoulout

2015

Rend. Circ. Mat. Palermo

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In this paper, we shall study the stability for distributed bilinear systems on a Hilbert state space that can be decomposed in two subspaces: unstable finite-dimensional and stable infinite-dimensional with respect to the evolution generator. Then, we shall show under a weaker observability assumption that stabilizing such a system with a feedback control of the form p r (t) = − y(t) −r y(t), By(t) for r < 2, reduces stabilizing only its projection on the finite-dimension subspace which make the whole system stable. To this end, we shall propose a new family of continuous feedback controls that guarantee the uniform stabilizability with an explicit optimal decay rate estimate of the stabilized state.Two illustrating examples and simulations are provided.

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“…Our goal is to propose a constrained feedback control that guarantee exponential stabilization for the semilinear system (1). Following the analogous study concerned with infinite-dimensional bilinear systems [10] and looking at finite-dimensional case [6], a natural feedback law which comes in mind is given by…”

Section: Introductionmentioning

confidence: 99%