The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k₁e ≤ f(e) ≤ k₂e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (–¹/k₁, –¹/k₂).
The paper presents an overview of linearization methods of the non-linear state equation. The linearization is developed from the point of view of the application in the theoretical electrotechnics. Some aspects of these considerations can be used in the control theory. In particular the main emphasis is laid on three methods of linearization, i.e.: Taylor’s series expansion, optimal linearization method and global linearization method. The theoretical investigations are illustrated using the non-linear circuit composed of a solar generator and a DC motor. Finally, the global linearization method is presented using several examples, i.e. the asynchronous slip-ring motor and non-linear diode. Furthermore the principal theorem concerning the BIBS stability (bounded-input bounded state) is introduced.