Sliding mode observers for a class of linear parameter varying systems

• Published in: International journal of robust and nonlinear control Vol. 30; no. 8; pp. 3134 - 3148
• Main Authors: Chen, L., Edwards, C., Alwi, H.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.05.2020
• Subjects: Dynamic stability; Dynamic structural analysis; fault detection and diagnosis; Liapunov functions; Linear matrix inequalities; linear parameter varying; Observers; Parameters; Sliding mode control; sliding mode observer; Stability analysis; State estimation; Synthesis; Variable structure control
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4951

Summary In this paper, a new framework for the synthesis of a class of sliding mode observers for affine linear parameter varying (LPV) systems is proposed. The sliding mode observer is synthesized by selecting the design freedom via linear matrix inequalities (LMIs). Posing the problem from a small gain perspective allows existing numerical techniques from the literature to be used for the purpose of synthesizing the observer gains. In particular, the framework allows affine parameter‐dependent Lyapunov functions to be considered for analyzing the stability of the state estimation error dynamics, to help reduce design conservatism. Initially a variable structure observer formulation is proposed, but by imposing further constraints on the LMIs, a stable sliding mode is introduced, which can force and maintain the output estimation error to be zero in finite time. The efficacy of the scheme is demonstrated using an LPV model of the short period dynamics of an aircraft and demonstrates simultaneous asymptotic estimation of the states and disturbances.