Abstract
From the viewpoint of state estimation, we may regard bilinear systems as time-varying systems and apply to them the results with the observer of a linear time-varying system. However, since the input is in general not known a priori, it seems impossible to apply the theories of time-varying linear systems to bilinear systems. For the purpose of simple implementation, a new type of state observer is proposed in this paper.
The output of the bilinear system is one-time differentiable. Based on this fact and on the concept of Lyapunov stability, we propose a method for designing a state observer for bilinear systems, using information on the input, output and one-time deriverative of the output. This state observer has a specific feature of simple structure and the norm of the estimation error converges to zero asymptotically irrespective of the input. As a result, state observers are shown to be designed for a wider class of bilinear systems. Also the condition, under which a state observer without information on one-time derivative can be designed, is given obviously.
