Observer Construction Methods for a Class of Bilinear Systems

Abstract

This paper presents methods to construct an observer and an adaptive observer for the bilinear systems described as follows:
x(k+1)=u_i(k)Ax(k)+Bu(k)
y(k)=Cx(k),
where x(k) is an n×1 state vector, u(k) is an r×1 input vector, y(k) is an m×1 output vector, u_i(k) is the i-th element of the vector u(k), and A, B, C are real matrices of proper dimensions. An example of this type of bilinear systems appears, for instance, in a heatexchange process. In this paper, it is supposed that
rank [C^T, A^TC^T, …, (A^n-1)^TC^T]^T=n.
The observer proposed here has an advantage that the estimated value of the state vector agrees with a true one in a finite number of steps and the adaptive observer also has the same property for the input with sufficient generality.