Dissipative Control Of Uncertain Time-delay Systems

The essential content of dissipative system is that a nonnegative energy function exists, which makes the energy consumption of the system is less than the energy provision. A kind of design and analytic idea is put forward in the dissipative theory, from the point of view of energy, and energy is described by input and output. The main study aim of the thesis is to study the dissipation and to give the sufficient conditions of the static or dynamic feedback control for uncertain delay systems with a full supply rate and the linear matrix inequality (LMI) technique.For the uncertain time-delay systems, the major contributions of this dissertation are as follows:(1) The robust dissipation control for uncertain delay differential system is discussed. The sufficient conditions for the existence of the dissipative controller is given via using a LMI, which ensures the closed loop system is strickly dissipative.(2) Delay-dependent dissipative control of linear systems with nonlinear perturbation is considered. Designing a state feedback controller which guarantees the closed loop system is robust stable by using linear matrix inequlity. The sufficient condition is presented for the existence of controller which depends on the maximum and minimum value of derivation of time-delay.(3) A new definition of disispativity for neural networks is presented. By constructing Lyapunov functions and using some analytic techniques, sufficient conditions are given to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties and the integro-differential neural networks in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the obtained results.(4) The problem of output feedback dissipative control for discrete-time systems with time-delay is analyzed.The systems are subject to time-varying normbounded parameter uncertainties. The problem aims at designing a state and a feedback controller such that the closed-loop is strictly dissipative. The solution to the problem, which is dependent on the size of the delay is given in terms of a linear matrix.