Robust H_∞ Control Of Linear Disrete-time Systems

H∞ control is an optimizing control, which controls the H∞ norm of the transfer function matrix between some signals inside the controlled systems in order to take it as optimizing performance design level. It makes up some dificiency of the former control theory in practical utilization, and its model itself has wide-ranging application, hence it has been abroadly regarded since it emerged. After more than 20 years' development, H∞ control theory has been the most important theory and had the largest influence at present. Parameter uncertainty abroadly exists in practical controlled systems, because model error, linearization, condition change and date error etc. all can lead to uncertainties of systems matrices. In the wake of the development of H∞ control theory and the deepnees of robust control theory, the study of the problem for robust H∞ control has received many scholars' concern in recent years. Nowdays, the study of continuous systems has been perfected basically, but the discrete-time situation is involved a little.The problems for robust H∞ control of two kinds of systems-2-D Roessermodels and linear dicrete-time singular systems-are discussed and studied.Based on the bounded real lemma, solvability of the problems for robust H∞ control of the two systems are respectively summed up existence of constrained solution of the linear matrix inequality about the systems' parameter matrices or not. which largely simplifies the solvability judgement of the problems. The approaches to designning controller which meets the requirements are given. Compared with the reached conclusions of the problems, the judgements in the paper are more clear and much simpler than others either in criterion conditions which make the problems be solvable, or in design approaches of the controllers.The main conclusions in the paper are:(1) The problem for robust H∞ control of 2-D Roesser models with time-invariant norm-bounded parameter uncertainties is discussed. The purpose is the design of static state feedback controller such that the resulting closed-loop systems have prescribed H∞ performance level 7 for all admissible parameter uncertainties. Different versions of bounded real lemma of 2-D Roesser models are established in terms of linear matrix inequalities, which these conditions are equivallent. Based onthis, a sufficient condition for the solvability of the problem is solved, and a desired static state feedback controller can be constructed using the conditions by solving a set of linear matrix inequalities.(2) Based on the first problem, the problem for robust if oo control of 2-D Roesser models with generalized Frobenius norm-bounded parameter uncertainties is further discussed. A sufficient condition for the solvability of the problem is solved in terms of linear matrix inequalities, and Based on the condition, a desired static state feedback controller can be constructed using the conditions by solving a set of linear matrix inequalities.(3) The problem for robust Hoo control of linear dicrete-time singular systems with time-invariant norm-bounded parameter uncertainties is studied. Firstly, bounded real lemma of the systems is given. Based on the lemma, A sufficient condition for the solvability of the problem is solved. At last, a desired static state feedback controller can be constructed using the conditions, such that the resulting closed-loop systems are admissible and have prescribed Hoo performance level 7 for all admissible parameter uncertainties.