This paper deals with new finite-time estimation algorithms for Linear Parameter Varying (LPV) discrete-time systems and their application to output feedback stabilization. Two exact finite-time estimation schemes are proposed. The first scheme provides a direct and explicit estimation algorithm based on the use of delayed outputs, while the second scheme uses two combined asymptotic observers, connected by a condition of invertibility of a certain time-varying matrix, to recover solution of the LPV system in a finite-time. Furthermore, two stabilization strategies are proposed. The first strategy, called Delayed Inputs/Outputs Feedback (DIOF) stabilization method, is based on the use of the explicit estimation algorithm. The second technique, called Two Connected Observers Feedback (2-COF) stabilization method, is based on the use of two combined observers providing exact finite-time estimation. A numerical example is given to show the validity and effectiveness of the proposed algorithms by simulation.
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The authors would like to thank the anonymous reviewers for their constructive comments and helpful suggestions. This work was funded by the TechnOptiz start-up company founded by K. Chaib-Draa, and by King Abdullah University of Science and Technology (KAUST) baseline ( BAS/1/1627-0101 ). R. Rajamani thanks the Benjamin Y.H.Liu-TSI endowment fund for support. F. Bedouhene thanks the Direction Générale de la Recherche Scientientifique et du Développement Technologique DGRSDT/MESRS-Algeria for the financial support. A. Zemouche thanks the IUT Henri Poincaré of Longwy for the partial support of this work.
Rajesh Rajamani obtained his M.S. and Ph.D. degrees from the University of California at Berkeley in 1991 and 1993 respectively and his B.Tech degree from the Indian Institute of Technology at Madras in 1989. Dr. Rajamani is currently the Benjamin Y.H. Liu-TSI Endowed Professor of Mechanical Engineering at the University of Minnesota. His active research interests include sensing, estimation and control for smart/ autonomous systems. Dr. Rajamani has co-authored over 150 journal papers and is a co-inventor on 17 patent applications. He is the author of the popular book “Vehicle Dynamics and Control” published by Springer Verlag. Dr. Rajamani has served as Chair of the IEEE Technical Committee on Automotive Control and on the editorial boards of the IEEE Transactions on Control Systems Technology, the IEEE/ASME Transactions on Mechatronics, and the IEEE Control Systems Magazine. Dr. Rajamani is a Fellow of ASME and has been a recipient of the CAREER award from the National Science Foundation, the Ralph Teetor Award from SAE, the O. Hugo Schuck Award from the American Automatic Control Council, and a number of best paper awards from conferences and journals. Several inventions from his laboratory have been commercialized through start-up ventures co-founded by industry executives. One of these companies, Innotronics, was recently recognized among the 35 Best University Start-Ups of 2016 in a competition conducted by the US National Council of Entrepreneurial Tech Transfer.
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- LMI approach
- LPV systems
- Observer design
- Output feedback stabilization