Abstract
In this paper we propose a stabilizing control method of uncertain single-input, single-output systems by using a state observer. The controlled objects contain uncertain but bounded parameters and disturbances, and the nominal systems are described by output form.
We consider the design method, in which the states are practical stable, on the coordinates transformed by a diagonal matrix T=diag[1, α-1, …, α-n+1] where α is positive and a design parameter. First, in the case where the driving vector of a nominal system is bTS=[0, …, 0, 1], it is shown that the control systems can be constructed in which the ultimate norm of the system output converges to any small region by increasing design parameter α. Next, in the case where the driving vector consists of some nonzero elements, it is shown that controlled object can be transformed to such a system as described in the first case by using a precompensator. Namely, the control system, having prescribed property, can be constructed. That precompensator is in proportion to the inverse function of the numerator polynomial. Therefore, the numerator polynomial must be asymptotically stable for guaranteeing internally stability of the control system.
Finally, computer simulation results are presented to illustrate the effectiveness of the proposed method.
