Computer algebra software was used to analyze different properties of a class of discrete-time polynomial (nonlinear) systems. In particular, the Groebner basis method and quantifier elimination by partial cylindrical decomposition (QEPCAD) were used in analysing controllability, observability, stabilizability and design of time-optimal and stabilizing controllers for this class of systems. Computer algebra software leads to algorithmic methods for testing if a certain property holds. The main issue here is the computational complexity of the algorithms that is often prohibitive in general. However, for important special classes of nonlinear systems one can obtain simpler to check conditions.
Prof. I.M.Y. Mareels
Prof. T. Glad
Dr. M. Jirstrand
D. Nesic, I. M. Y. Mareels, T. Glad and M. Jirstrand, "Software for control system analysis and design: symbol manipulation", Encyclopedia of Electrical and Electronics Engineering, J. Webster (Ed.), J. Wiley, 2001, available online, http://www.interscience.wiley.com:83/eeee/ [invited]
D. Nesic and I. M. Y. Mareels, "Dead beat controllability of polynomial systems: symbolic computation approaches", IEEE Trans. Automat. Contr., vol. 43, No. 2 (1998), pp. 162-175.
D. Nesic, I. M. Y. Mareels, G. Bastin and R. Mahony, "Output dead beat control for a class of planar polynomial systems", SIAM J. Contr. Optimiz., vol. 36, No. 1 (1998), pp. 253-272.
D. Nesic and I. M. Y. Mareels, "Stabilizability and stability for implicit and explicit polynomial systems: a symbolic computation approach", Europ. J. Contr., vol. 5 (1999), pp. 32-43.
D. Nesic and I. M. Y. Mareels, "Controllability of structured polynomial systems", IEEE Trans. Automat. Contr., vol. 44, No. 4 (1999), pp. 761-765.