Systematic observer design for bilinear systems

Observer design for bilinear systems using Ljapunov's methods leads to systems of matrix equations and matrix inequalities to be satisfied. So far, no systematic approach has been implemented in order to attack this problem. The solution presented consists of two major steps. First the matrix equations and matrix inequalities are reduced to polynomial inequalities. Then Collins' algorithm is applied to settle the solvability of the problem and to compute an observer. The efficiency of the new observer design is demonstrated for a continuous furnace process.<<ETX>>

[1]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[2]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[3]  J. Gauthier,et al.  Observability for any of a class of nonlinear systems , 1981 .

[4]  S. Hara,et al.  Minimal order state observers for bilinear systems , 1976 .

[5]  M. Zeitz.  Observability canonical (phase-variable) form for non-linear time-variable systems , 1984 .

[6]  Y. Funahashi.  Stable state estimator for bilinear systems , 1979 .

[7]  N. Bose.  Applied multidimensional systems theory , 1982 .

[8]  B. Tibken,et al.  A Novel Computer Approach to Optimal Feedback Control of Bilinear Systems , 1989 .

[9]  B. Anderson,et al.  Output feedback stabilization—Solution by algebraic geometry methods , 1977, Proceedings of the IEEE.

[10]  David G. Luenberger,et al.  State space analysis of control systems , 1967 .

[11]  H. Keller.  Entwurf nichtlinearer, zeitvarianter Beobachter durch Polvorgabe mit Hilfe einer Zwei-Schritt-Transformation / Design of nonlinear time-variant observers by pole-assignment via two-step-transformation , 1986 .

[12]  I. Derese,et al.  Nonlinear control of bilinear systems , 1980 .

[13]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[14]  G. Bornard,et al.  Observability for any u(t) of a class of nonlinear systems , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.