Stabilization And Model Reference Tracking Of Antilinear Systems

During the latest several decades of development in the field of system control theory, there have been many kinds of systems: from continuous systems to discrete systems, from simple linear systems to complex nonlinear systems,from deterministic systems to stochastic systems with variable parameters and so on. With the continuous expansion of theoretical research, recently, a new kind of system which is the so called antilinear systems attracts people’s attention. The concept of antilinear systems comes from the research in the field of quantum,which is different from the linear systems and has a unique structure and characteristics. Therefore, it is very significant to study antilinear systems whether in theory or in practice.Based on the discrete-time antilinear systems, this paper, firstly, studies the problem of stability of it. By analyzing the structural characteristics of antilinear systems and using the appropriate structural transformations and the stability conclusions of linear systems, one has established the necessary and sufficient conditions for stability. What’s more, this paper also considers getting another stability condition with the LMI form of antilinear systems by adopting the Lyapunov stability theory. Numerical example shows the effectiveness of stability conditions.Then, based on the stability conditions of antilinear systems above, this paper further discusses the state feedback stabilization problem of it. By constructing an appropriate Lyapunov functional, the existence condition of state feedback stabilization controller is built in the LMI form. In addition, this paper does further research on the stabilization problem of antilinear systems when the system states are not or not completely available. Based on the Lyapunov stability theory combined with the output feedback control methods, one establishes the state feedback stabilization condition by constructing a state observer.Numerical examples show the effectiveness of the proposed algorithms above.In the last, one also studies the model reference tracking control of antilinear systems, which is required to solve a complex conjugate matrix equations.In this paper, two methods which are analytic and numerical respectively are proposed to solve them and numerical example illustrates the effectiveness of them.