Abstract
The authors propose a state representation suited for describing uncertain single-input single-output systems and stabilizing method of that systems.
It is shown that any transfer function with uncertain fixed parameters is realized by a state equation consisting of an unknown system matrix and a known driving vector. With respect to that specific state representation, the stabilization problem is considered for uncertain systems with parameter variations of the system matrix and disturbances. Namely, the states are transformed by a diagonal matrix T=diag [1, α-1, …, α-n+1] where α is the positive design parameter and construct the state feedback control system by using observer. Then it is shown that the control system is practical stable when the observer gains and feedback gains are settled by using the solutions of some Riccati equations. Moreover, in order to estimate the capability of the control system, the relation between the design parameter α and the output norm is derived. And it is shown that the output norm converges to any vicinity of the origin at the any rate of stability by increasing α. Though, it is assumed that the numerator polynomial is asymptotically stable, this design method can be applied for the systems in which parameters of the numerator polynomial vary.
