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We consider the problem of boundary stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. This term puts all the eigenvalues of the open-loop system in the right half of the complex plane. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate. For plants with constant...
How to control an unstable linear system with a long pure delay in the actuator path? This question was resolved using dasiapredictorpsila or dasiafinite spectrum assignmentpsila designs in the 1970s. Here we address a more challenging question: How to control an unstable linear system with a wave PDE in the actuation path? Physically one can think of this problem as having to stabilize a system to...
This paper studies some properties of the recently developed parametric Lyapunov equation based low gain feedback design method. As applications of these new properties, alternative and simpler solutions are proposed to the (global) stabilization problem for a class of linear systems with input delay and the semi-global stabilization problem when the systems are in addition subject to actuator saturation...
In this paper, we investigate the state preparation problem of quantum noiselsss subsystems for the quantum Markovian systems via quantum feedback control. The controlled dynamics we consider are given by the so-called stochastic master equation including the coupling terms with the environment. We formulate the problem as a stochastic stabilization problem of an invariant set. This formulation allows...
In this paper we consider the dynamical stability of a tree-shape networks of Timoshenko beams with time-delay terms in the boundary controls. The time-delay feedback controllers at the exterior vertices are designed to derive the beams back to its equilibrium position. We first get the wellposedness of the closed loop system. Under certain conditions, we show that this system is asymptotically stable...
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