Observer based tracking of bilinear systems: A differential algebraic approach (Q1392809)

The author considers the following bilinear dynamic system. The state and output equations have the form \[ {dx\over dt}=\left(A_0+ \sum^m_{i =1} A_iu_i\right) x+Bu\tag{1} \] \[ y=Cx+Du\tag{2} \] where \(x\in R^n\), \(y\in R^1\) and \(u\in R^m\) are state, observation and control vectors, respectively; \(A_i\), \(0\leq i\leq m\); \(B\), \(C\) and \(D\) are real matrices of appropriate dimensions. To obtain a controller in the proposed form the exact linearization of the tracking error dynamics is applied. The author proves that it is necessary to use an observer for this dynamics in order to implement such a controller. He also derives sufficient conditions for the output feedback stabilizability of the system.