二维线性系统一类渐近观测器的充要条件

本文对二维线性系统的渐近观测器进行了讨论，给出了关于二维线性系统的一个重要定理，并从这个定理出发得到了二维线性系统一类渐近观测器的充要条件．

Characteristic polynomial assignment in F-M model Ⅱ of 2-D systems

The problems of characteristic polynomial assignment in Fomasini-Marchesini (F-M) model Ⅱ of 2-D systems are investigated. The corresponding closed-loop systems described by F-M model II are obtained via the state feedback. Using the algebraic geometry method, the characteristic polynomial assignment in the dosed-loop systems is discussed. In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment is transferred to the one whether a rational mapping is onto. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in F-M model Ⅱ of 2-D systems via state feedback are derived, and they are available for multi-input cases. It also has been shown that this method can be applied to assign the characteristic polynomial with output feedback. The sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of multi-input 2-D systems described by F-M model Ⅱ with output feedback are established.

Symmetry Reduction of Two-Dimensional Damped Kuramoto-Sivashinsky Equation

In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.

Nonlinear Waves in Two-Dimensional (2D) Square Lattice Frenkel-Kontorova (FK) System

A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.

Design of observer-based discrete repetitive-control system based on 2D model

A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.

Nonautonomous Solitons in the(3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Sehr6dinger equation in the （3＋ 1 ）-dimensionM inhomogeneous cubic-quintic nonlinear medium. The gain parameter has no effects on the motion of the soliton＇s phase or their velocities, and it affects just the evolution of their peaks. As two examples, we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system. Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly, but also broadens their width.