Passivity-based sliding mode control of uncertain singular time-delay systems

• Published in: Automatica (Oxford) Vol. 45; no. 9; pp. 2120 - 2127
• Main Authors: Wu, Ligang, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2009; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Dynamical systems; Dynamics; Exact sciences and technology; Law; Mathematical analysis; Nonlinear dynamics; Passivity; Sheet molding compounds; Singular systems; Sliding mode control; Sliding mode control (SMC); Switching; Time-delay systems; Time-delay systems; Sliding mode control (SMC); Singular systems; Passivity; Singular matrix; Singularity; Variable structure control; Sliding mode; Switching function; Non linear control; Delay system; Passive system; Delay dependent system; Non linear system; Geometrical model; Uncertain system; Linear matrix inequality; Delay time; Solvability
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.05.014

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.