Abstract
We will consider the problem of fast sampling control for singularly perturbed systems subject to actuator saturation andL2disturbance. A sufficient condition for the existence of a state feedback controller is proposed. Under this controller, the boundedness of the trajectories in the presence ofL2disturbances is guaranteed for any singular perturbation parameter less than or equal to a predefined upper bound. To improve the capacity of disturbance tolerance and disturbance rejection, two convex optimization problems are formulated. Finally, a numerical example is presented to demonstrate the effectiveness of the main results of this paper.
Highlights
Many practical physical systems consist of subsystems operating on different time scales
To overcome the numerical problem, singular perturbation theory was introduced to the field of control system and widely used in practice [1]
This paper focuses on fast sampling control of singularly perturbed system (SPS) subject to actuator saturation and L2 disturbance
Summary
Many practical physical systems consist of subsystems operating on different time scales. Many results have been proposed for estimating or enlarging the stability bound of the SPSs without actuator saturation [25,26,27,28,29,30,31,32]. In [33], continuoustime SPS with actuator saturation is considered and a state feedback controller is designed to achieve a desired stability. To the best knowledge of the authors, the fast sampling control problem of the SPSs with actuator saturation and disturbance has not been considered. This paper focuses on fast sampling control of SPSs subject to actuator saturation and L2 disturbance. A state feedback controller design method is proposed such that the trajectories of the closed-loop SPSs starting from a bounded set remain bounded for any allowable singular perturbation parameter and L2 disturbance. An ellipsoid Ω(Q, ρ) is defined as Ω(Q, ρ) ≜ {η ∈ Rn | ηTQη ≤ ρ}
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