Pole placement LMI constraints for stability and transient performance of LPV systems with incomplete state measurement

• Published in: Journal of the Franklin Institute Vol. 359; no. 2; pp. 837 - 858
• Main Authors: Sereni, B., Beteto, M.A.L., Assunção, E., Teixeira, M.C.M.
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01-01-2022; Elsevier Science Ltd
• Subjects: Accelerometers; Algorithms; Control stability; Design; Feedback control systems; Gain scheduling; Linear matrix inequalities; Mathematical analysis; Matrix; Measurement; Nonlinear systems; Output feedback; Pole placement; Transient performance; Transient response
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.05.009

In this paper, new conditions for the stabilisation and transient performance improvement of linear parameter-varying (LPV) systems considering the gain-scheduling (GS) strategy are proposed. Our work is focused on dealing with LPV systems under the major practical constraint of incomplete state measurement. In that sense, we propose two new control design strategies based on linear matrix inequalities (LMI). First, for coping with the general case where only a subset of the state variables is measured, we propose a new static output feedback (SOF) strategy. Second, for dealing with the particular case where only accelerometers signals are available, we bring new synthesis conditions for the design of state derivative feedback (SDF) controllers. Further from stability, our proposed methods are able to induce better transient response by including pole placement LMI constraints in the control design. For illustrating our contribution efficacy, we present a couple of design examples.