Analysis And Controller Design For 2D Discrete State-Delayed Systems

Over the past several years,a considerable interest has been devoted to 2D(two-dimensional) systems because of their engineering background and theoretical significance. 2D systems and signals have been studied in relation to several modern engineering fields such as digital image and signal processing,seismic data processing,thermal power engineering. 2D system control theory is an important theoretical support for analysis and synthesis of systems with repetitive dynamics such as repetitive process,repetitive control system and iterative learning control system.As is well known,delay phenomena of signal transmissions are frequently encountered in engineering and biological systems.There are also delay phenomena in some 2D systems, such as material rolling process,thermal process,numerical computation time spent on signal processing.Lyapunov-Krasovskii approach is principally adopted in studying delay systems.Stability is one of primary importance problems of analysis and synthesis for delay systems.Depending on whether the stability result includes the delay size as a parameter,existing stability criteria of delay systems can be classified into two types,i.e. delay-independent stability criteria and delay-dependent stability criteria.In practice,it is usually difficult to characterize the dynamics of the controlled object exactly by a mathematical model,there are a variety of disturbances and noises that are not precisely known in advance.Therefore,it is indispensable that designed control systems are subject to some special robust performance.Both H_∞control and guaranteed cost control are more successful and practical in solving robust control problems.This dissertation addresses the stability,H_∞control and guaranteed cost control for 2D discrete state-delayed systems according to 2D Lyapunov stability theory and LMI(linear matrix inequality)approach.The main contents and results are as follows: 1.Delay-independent and delay-dependent asymptotic stability criterions for 2D discrete systems with FM LSS(Fornasini-Marchesini local state-space)model and Roesser model are respectively formulated in terms of a certain LMI.2.Delay-independent and delay-dependent sufficient conditions to have H_∞performanceγfor 2D discrete systems with FM LSS model and Roesser model are respectively provided in terms of a certain LMI.H_∞controller minimizing the upper bound of H_∞performanceγis obtained by solving the corresponding convex optimization problem ineluding LMI constraints.3.Considering a class of 2D discrete state-delayed systems with uncertainties described by FM LSS model,delay-independent and delay-dependent sufficient conditions for the existence of the guaranteed cost controller are respectively presented via LMI approach. Corresponding algorithm to obtain robust guaranteed cost controller minimizing the upper bound of the cost function is proposed by using LMI optimization techniques.4.Considering a class of 2D discrete state-delayed systems with uncertainties described by Roesser model,delay-independent and delay-dependent sufficient conditions for the existence of the guaranteed cost controller are respectively presented via LMI approach. Optimal robust guaranteed cost controller minimizing the upper bound of the cost function is obtained by solving the corresponding convex optimization problem including LMI constraints.5.Simulations for thermal processes and linear repetitive processes with state-delayed are given respectively by applying the the above research results on H_∞control and guaranteed cost control.