A Study On Analysis And Synthesis Of Interval 2-D Systems

The model under which the controller is designed is usually different to the real plant in practical industrial process control. There are two main reasons to cause the difference. One is the change of the operating environment and other unmeasurable disturbances. The other is that some simplifications such as model reduction and linear approximations are made during modeling due to the limitation of theory and technology. The difference is usually described as the uncertainties in control systems. Interval system is one land of uncertain systems whose partial or whole parameters vary within fixed intervals. Uncertainties will affect systems' stability and other performances directly. Therefore they shouldn't be ignored during controller design. Analysis and synthesis of uncertain systems are the main topics of this paper. 2-D systems are extensively used in process industry, digital filters, image and signal processing, etc.. Uncertainties also exist in 2-D systems. Interval 2-D systems will be discussed in detail in this paper.Based on definitions of quadratic stability, quadratic stabilizability and guaranteed cost control, Lyapunov inequality, Schur complement and linear matrix inequality are adopted in this paper. Stability, stabilization and guaranteed cost control for interval 2-D systems are discussed in this paper. The main contents are as follows:1. For discrete interval 2-D systems, based on definitions of quadratic stability and quadratic stabilizability, sufficient and necessary quadratically stable and stabilizable conditions are given in terms of linear matrix inequalities. Quadratically stabilizing controller designing method is also proposed in this paper. The illustrative examples show the results are effective and less conservative.2. Based on general continuous 2-D systems model and Rosser model which is widely used in discrete 2-D systems, a unified interval 2-D systems model is proposed. Considering this unified model, sufficient and necessary quadratically stable and stabilizable conditions are given in terms of linear matrix inequalities.Quadratically stabilizing controller designing method is also proposed.3. For continuous and discrete interval 2-D systems with given quadratic cost functions, sufficient conditions to check the existence of state feedback guaranteed cost controllers are derived and expressed in a set of linear matrix inequalities. Furthermore, an optimal problem is proposed in this paper. The optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system will be obtained by solving this optimal problem. The illustrative example shows effectiveness of the result.The conclusion and perspective are given in the end of the paper.