Delay Dependent Stability And Feedback Control Of Delay Systems

Time delays are frequently encountered in a variety of dynamic systems. For example chemical process, metallurgy, aviation, spaceflight, electric power, electronic, economic management and traffic system arise time-delay. So the studies of time-delay systems have widely pratical background. Because the existence of time-delay is often the reason of instability and deteriorates the control performance, the studies on time-delay systems stability and control have important theoretical and practical values. In particular, delay-dependent criteria, which employ information about the delay is less conservative than delay-independent criteria.In this dissertation, the main methods used to handle delay-dependent stability problems and their limitations are first examined, especially those involving a fixed model transformation. Secondly, this dissertation presents a refined method, called the integral inequality approach (IIA). The new method does not employ any model transformation technique, according to an improved integral inequality, transformates the integral terms, which contain the information of time delay, so that a solution can be obtained by solving linear matrix inequalities (LMIs), which make the method less conservative than those employing model transformationsThe new Integral inequalities are employed to analyze the delay-dependent stability of systems with a time-varying delay, three types of time-varying delay are discussed: continuous but not differential; continuous and differential and continuous in [h₁,,h]. Somedelay-dependent stability conditions are obtained based on LMIs. On this basis, the criteria are extended to systems with time-varying structured uncertainties. Furthermore, integral inequalities are employed to deal the problem of delay and its time-derivative dependent stability criteria for linear system with nonlinear perturbations. In the process of proof, we did not employ any model transformation technique.For a system with multiple time varying delays, delays and delays derivative dependent criteria are derived by Lyapunov and integral inequalities method. In addition, for a system with two time delays, delay-dependent criteria are derived by chosing Lyapunov function, which one special double integral term is about the relationship between the delaysÏ„₁ andÏ„₂. Numerical examples demonstrate that these results are not only simple but also superior conservative. In addition, this idea is extended to the derivation of delay-dependent stability criteria for a system with multiple time delays.The delay-dependent stability of linear neutral systems is also discussed. By employing the IIA and constructing a new Lyapuno-Krasovskii functional, delays dependent and delays derivative (if it exists) dependent criteria are derived about the system with time-varying neutral delay and time-varying state delay. The criteria are also extended to systems with time-varying structured uncertainties. In addition, this idea is extended to the derivation of all delays and their derivative dependent and delay-dependent stability criteria for systems with multiple time-varying state delays and multiple time-varying neutral delays.For linear systems with both input and state delays, based on integral inequality, a method of designing a delay-dependent memoryless state feedback controller is derived, the asymptotical stablility criteria of closed-loop system are obtained based on LMIs, provided that the given linear matrix inequality is feasible. The designing of memoryless controller based on only LMIs not on any parameter tuning and iterative algorithm is.derived.Lurie system is a class of typical nonlinear system. The delay-dependent absolute stability criteria of neutral type Lurie system; time-varying delays Lurie systems with two nonlinearities delays and Lurie systems with multiple nonlinearities are obtained. All conditions are then extended to above Lurie systems time-varying structured uncertainties. For a Lurie neutral system, the integral inequalities method and the free-weighting-matrix method are compared, though the two methods almost have the equal results, integral inequalities method not only has simply form but also is easily solved.Finally, the results of the dissertation are summarized and further research problems are point out.