A Study On Robust Control For Uncertain Discrete 2-D Time-Delay Systems

2-D systems which depend on two independent status exist widely in modern industrial areas. For example, the systems of gas absorbing, water heating and air drying can modeled as 2-D systems. Especially, discrete 2-D systems are widely used in digital signal filtering, image processing, signal processing, and have attracted much attention of many scholars. For the practical industrial process, as people always want to obtain the exact mathematic models. However, the model under which the controller is designed is usually different from the real plant because of the model reduction, linear approximation and the ignoring of the some dynamics difficulty for modeling. Usually, these differences can be described as the uncertainties in the model arguments with the uncertainties restricted in some range. Robust control theory is an effective way to deal with the control problems of these uncertain systems. On the other hand, transmission process and complicated on-line analyzer etc, are common in a number of industrial processes, which can cause delay phenomena in the systems. Such delays will be the main cause of bad performance or even instability for control systems. Therefore, the research on the time delay systems also attracts considerable attentions in the control theory field, hi view of these considerations, robust control for uncertain discrete 2-D time-delay systems will be discussed in this paper.Based on the concepts of quadratic stability, quadratic stabilizability, guaranteed cost control and H_∞ control, adopting Lyapunov inequality, Schur complement and linear matrix inequality approarches, robust control for uncertain discrete 2-D time-delay systems are discussed deeply in this paper. The main contents are as follows:1. For interval discrete 2-D time-delay systems, the definitions of quadratic stability and quadratic stabilizability are given. Based on these definitions and Schur complement, sufficient conditions for quadratic stability and quadratic stabilizability of the systems are then deduced. The quadratically stabilizing controller designing method is also proposed.2. For interval discrete 2-D time-delay systems, the quadratic performance indexand the definition of guaranteed cost controller are given. Based on Lyapunov theory, sufficient condition for existence of guaranteed cost controller is then deduced. The guaranteed cost controller designing method is also proposed.3. For interval discrete 2-D time-delay systems, the H^ performance index and the definition of Hx controller are given. Based on Lyapunov theory, sufficient condition for existence of H^ controller is then deduced. The H^ controller designing method is also proposed.4. For norm-bounded uncertain discrete 2-D time-delay systems, delay-dependent robust control is studied. Based on Lyapunov theory, sufficient conditions for delay-dependent stability of the systems are deduced. The problem of state-feedback control is then investigated upon the proposed stability condition, where the complementary linearization idea is employed to convert the controller design into a nonlinear programming problem with linear matrix inequality constrains.5. For norm-bounded uncertain discrete 2-D time-delay systems, delay-dependent guaranteed cost control is studied. The quadratic performance index and the definition of guaranteed cost controller are given. Based on Lyapunov theory, sufficient condition for existence of delay-dependent guaranteed cost controller is then deduced. Delay-dependent guaranteed cost controller designing method is also proposed, where the complementary linearization idea is employed to convert the controller design into a nonlinear programming problem with linear matrix inequality constrains.Finally, the conclusion and perspective are given in the end of the paper.