Robust Control For A Class Of Uncertain Nonlinear Time-delay Systems

In practical dynamic systems, time delays are general, which often lead to instability and bad performance. At the same time, it is unavoidable to include uncertain parameters and disturbances in practical control systems due to modeling errors,measurement errors, linearity approximations, and so on. Thus, it is of great importance in theoretical and pratical application to study the robust control for the uncertain time-delay systems.In this thesis, based on the Lyapunov stability theory and linear matrix inequalities(LMIs),we main study the problems of robust stability analysis and robust controller design by making use of the delay partitioning approach for a class of uncertain nonlinear time-delay systems. At the same time, robust stability criterion of uncertain nonlinear time-delay system is derived by using the linear matrix inequality and robust controller based on state feedback is designed. The design is practical. but also, it is minimize the conservative on the basis of using time-delay information. The detailed contents are as follows:(1) In terms of the delay partitioning idea, the problem of delay-dependent robust stability is addressed for a class of uncertain nonlinear time-delay systems. These results are in standard form of linear matrix inequalities and can be solved by Matlab tools. Some examples are provided to prove the advantage of these theorems.(2) In terms of the delay partitioning idea, the problem of delay-dependent robust control is discussed for a class of uncertain nonlinear time-delay systems. First, a delay-dependent sufficient condition is established such that the nominal system can be stabilized. Based on this criterion, robust state-feedback controllers are designed for uncertain nonlinear time-delay systems such that the closed-loop systems have the characteristics of asymptotic stability. Then, it is extended to nonlinear time-delay systems with uncertain parameters. Finally, the results obtained are demonstrated to be applicable and less conservative via numerical examples.(3) In terms of the delay partitioning idea, the problem of delay-dependent robust H∞control is discussed for a class of uncertain nonlinear time-delay systems. First, a delay-dependent H∞sufficient condition is established such that the nominal system is asmptotically stable with H-infinity performance . Based on this criterion, robust H∞state-feedback controllers are designed for uncertain nonlinear time-delay systems such that the closed-loop systems have a given degree of H∞interference suppressionγ. Then . it is extended to nonlinear time-delay systems with uncertain parameters Finally, the results obtained are demonstrated to be applicable and less conservative via numerical examples.