Input-to-State Dynamical Analysis For Several Classes Of Differential Systems

With the vigorous development of control science and advanced control technology, the inter-disciplines between the control and the other subjects such as computer networks, electronic infor-mation, electric automation and so on become the focus of attention, and the control theories have been extensively utilized in the other subjects. In fact, many engineering problems involved can be characterized by differential systems in mathematics. However, the differential systems in practical applications are affected inevitably by a number of uncertainties, for example, parameter perturba-tions, nonlinear external interferences, measurement errors, etc. Thus, the analysis of the robustness for systems plays an important role in the control field.The stability of systems is the most basic question in the control theory. However, for the practical control system, quantitative analysis is always required for the effects from the errors of the measuring element or the actuators and the external input to the system. Based on the above discussions, this thesis mainly focuses on the input-to-state synchronization problems for the delayed driver-response systems with stochastic disturbances, the input-to-state robust stability problem for a class of differential systems with uncertain parameters and the uncertain external input and the robustly asymptotic stability problem for the load difference system. The main results of this thesis are summarized as follows.Firstly, the input-to-state synchronization problem is considered for a class of delayed drive-response systems with stochastic disturbances. In the network-based signal transmission system, the signals of the drive system and the response system suffer inevitably from disturbances when transmitted through the network, which are processed firstly by the data processor to generate an error signal and then transmitted to the controller, where control instructions are issued such that the response system can track the drive system so as to realize the synchronization. At the same time, the response system often suffers from the external attacks which can be regarded as the external disturbance signals which are irrelevant to the drive-response signals. In chapter 2, the synchronization problem is investigated for the drive-response systems affected by the stochastic disturbance and the external input perturbations. The controller gain matrix is obtained from the solution of linear matrix inequality (LMI) such that the signal of the error system is limited in a set given in advance, and the drive-response system achieves the input-to-state synchronization.Secondly, the input-to-state robust stability problem is concerned for a class of differential system with uncertain parameters which is disturbed by external inputs whose parameters are also uncertain. In chapter 3. such a case is discussed such that the input-to-state stability is satisfied for this class of differential system. A controller is designed, where the controller gain matrix can be derived by the solution of an LMI, and the states of the system can be constrained in a certain area even though the parameters of the external disturbance are uncertain. Numerical simulations have also verified the feasibility of the controller design scheme.Thirdly, based on the theoretical research in front part of the article and two lines’bus load data of Xinjiekou, Nanjing, In Chapter 4, we establish load difference models based on the actual simulation and discuss the robustly stability problem of price response systems such that, the load difference system with uncertain parameters is robustly asymptotic stable under the price control scheme.