Slow Sampling Control of Singularly Perturbed Systems Subject to Actuator Saturation and L₂ Disturbance

Abstract

This paper is concerned with the slow sampling control problem for singularly perturbed systems with actuator saturation and L2 disturbance. Convex hull is utilized to deal with the actuator saturation. A sufficient condition is proposed such that the boundedness of all the state trajectories will be guaranteed for any singular perturbation parameter less than or equal to a predefined upper bound in the presence of L2 disturbance. Then, two convex optimization problems are formulated to estimate the capability of disturbance tolerance/rejection based on this condition. Finally, an example is presented to demonstrate the effectiveness of the main results of this paper.

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

“…for k ≥ 0. Thus, the problem of estimating the domain of attraction can be formulated as the following optimization problem: (27), the constraint (a) is equivalent to:…”

“…which is obviously satisfied if conditions (21) hold. Now, to calculate the left term in inequality (b) of the optimization problem (27), we consider the closed-loop system composed by (2) and (10):…”

“…Especially, for discrete-time T-S fuzzy systems, results devoted to SOF control can be found in [5,12,18,19,21,23,24]; and especially, in [4] and [12], where a fuzzy weighting-dependent Lyapunov function (FWDLF) has been used. At last, some performances are generally to be added, H ∞ attenuation being one of the most widely used for T-S systems [8,[10][11][12][13]17,19,20,22,[25][26][27][28][29][30]. For real-time control, another important issue is the physical limitations of the actuators, such as input bounds and/or rate saturation constraints.…”

H∞ switching fuzzy control of solar power generation systems with asymmetric input constraint

“…Indeed, actuator saturation can seriously degrade the control performance or can cause instability of closed‐loop systems . Due to this reason, many results have been investigated in the literature for systems with actuator symmetric saturation . In this context, both methods (constrained and saturated) address the actuators saturation problem.…”

Output Tracking for One‐Dimensional Schrödinger Equation subject to Boundary Disturbance

“…However, the system does not consider the boundary disturbance, but many physical phenomena governed by ordinary differential equation and partial differential equation are inevitably subject to certain degrees of modeling uncertainties or exogenous disturbances in the interior domain or at the boundary, it often used the sliding mode control and active disturbance rejection control .…”