Passive Control of Singularly Perturbed Bilinear Systems with Input Saturation

doi:10.12068/j.issn.1005-3026.2022.12.002

Abstract

Abstract: For singularly perturbed bilinear systems with input constraints and time-varying delays， a design method of state feedback passive controller is proposed to eliminate the effects of delay factors and input saturation on the closed-loop system. Firstly， in the framework of Lyapunov stability theory and passivity theory， using linear matrix inequality technology and convex combination technology， the design of the system state feedback controller is reduced to solve a set of linear matrix inequalities independent of the upper bound of time delay. The obtained controller makes the closed-loop system asymptotically stable and passive， and constructs the estimation of the elliptic domain of attraction related to singular perturbation parameters. The above method is extended to the system without time delay and external input. Then， a convex optimization problem is proposed to obtain the maximum estimation of the domain of attraction of the closed-loop system， and the stability bound of singular perturbation parameter is also one of the design objectives. Finally， numerical simulation examples illustrate the effectiveness of the proposed theoretical method.

Key words: singularly perturbed bilinear systems; input saturation; passive control; linear matrix inequality; domain of attraction; singular perturbation parameter

CLC Number:

TP13

ZHANG Xiu-hua， REN Jia-xu. Passive Control of Singularly Perturbed Bilinear Systems with Input Saturation[J]. Journal of Northeastern University(Natural Science), 2022, 43(12): 1680-1687.

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