Practical Control Method for Time Delay Systems

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The purpose of this research is to study design methods of linear quadratic (LQ) regulators for systems with time-delay of retarded and neutral type, to investigate their properties as control systems, to consider the robust stability, and to propose new practical control system design methods. Generally, to construct an LQ regulator for systems with time-delay, the infinite dimensional Riccati equation has to be solved, and to implement it, the feedback law with real-time integral operation is needed, This point is a difficulty to apply this regulator. Recently it was shown that a class of LQ regulators could be constructed by a memoryless feedback law with a solution of a set of linear matrix inequalities. This method was called the optimal memoryless regulator. In this research, this method was extended to apply the wider class of systems with time-delay. The uncertainty of the plant parameters was taken into account, and new design methods of control systems were proposed as follows :(1) LQ regulator design method for systems with mutually independent multiple time varying delays.(2) LQ regulator design method for systems with time varying delays with pre-assigned exponential stability.(3) LQ regulator design method for systems with multiple time delays of neutral type.(4) LQ regulator design method for systems with uncertain parameters and mutually independent time varying delays.