Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

• Published in: Optimal control applications & methods Vol. 41; no. 5; pp. 1439 - 1450
• Main Authors: Ku, Cheung‐Chieh, Chang, Wen‐Jer, Yen, Chih‐Yu, Chen, Guan‐Wei
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.09.2020; Wiley Subscription Services, Inc
• Subjects: Control stability; Control systems design; Controllers; Design parameters; gain‐scheduled control; Liapunov functions; Linear matrix inequalities; Linear systems; LMI; LPV systems; Lyapunov function; pole assignment; Pole placement; Weighting functions
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2606

Summary This paper addresses a pole‐assignment control problem for discrete‐time linear parameter varying (LPV) systems. Based on LPV modeling approach, time‐varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain‐scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole‐assignment constraint. Moreover, two cases of Lyapunov function are respectively employed to derive some sufficient conditions which belong to linear matrix inequality (LMI) problems. Solving those derived conditions, the corresponding GS scheduled controller can be designed such that the asymptotical stability and pole assignment of LPV systems are guaranteed. Finally, a controller problem of truck‐trailer system is used to demonstrate the applicability and effectiveness of the proposed design methods.