The Study On Determine Of The Domain Of Attraction For Three Classes Of Nonlinear Quadratic Systems

Quadratic systems play an important role in the modelling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). This paper mainly study the problems on deter-mine of the domain of attraction for three classes of nonlinear quadratic systems. For a given polytopic region in the state space, a method for the problems of checking whether an assigned region belongs to the domain of attraction of the zero equilibrium point. The main research works of this dissertation are summarized as follows:1. The problems of stability analysis and guaranteed cost control for nonlinear quadratic systems with time-delay are investigated. Firstly, by using Lyapunov function and Razumikhin stability theorem, a sufficient condition for guaranteeing that the assigned polytope belongs to the domain of attraction of the zero equilibrium point. Secondly, it is also show that this problem is related to the. problem of determining a guaranteed bound for a quadratic cost function. The proposed algorithm requires the solution of a suitable feasibility problem involving linear matrix inequalities constraints. Finally, two simulation examples are presented to show the effectiveness of the proposed approach.2. The problems of stability analysis and controller design for discrete-time nonlinear quadratic systems with time-delay are investigated. Firstly, by using Lyapunov function, a suffi-cient condition for guaranteeing that the assigned polytope belongs to the domain of attraction of the zero equilibrium point. Secondly, it is also show that this problem is related to the problem of finding a state feedback law and an admissible initial condition domain such that the resulting closed-loop system is asymptotic stability for every initial condition from the admissible domain. The design procedures can be converted into a set of linear matrix inequalities. Finally, two simulation examples are provided to show the effectiveness of the proposed approach.3. The problems of stability analysis and controller design for discrete-time periodic nonlin-ear quadratic systems are investigated. Firstly, a stability criterion in linear matrix inequalities form is stated by using a periodic Lyapunov function and the concept of periodic invariant set. Secondly, based on stability analysis, a new result on the existence of nonlinear state feedback controllers is derived, and the controller design method is presented. Moreover, some known results are generalized. Finally, two simulation examples are presented to show the effectiveness of the proposed approach.