Synthesis and Properties of LQ Regulators for systems of Lumped-Parameter Part and Distributed-Parameter Part

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As particular classes of systems of a lumped-parameter part and a distributed-parameter part, neutral systems and retarded systems were chosen, and synthesis and properties of LQ regulators for them were investigated. Generally, LQ regulators for systems with time-delay was constructed with the state feedback, which was determined with a solution of an infinite dimensional Riccati equation. It was difficult to solve the equation and the state feedback was difficult to implement to the real plants. In this research, a method was developed to construct an LQ regulator with prescribed exponential stability using a memoryless feedback determined with a solution of LMTs. The solution could be calculated easily by a digital computer. The memoryless feedback did not require the memory of the internal variables and the real-time integral operation, so it was easy to implement. In these senses, the proposed regulator was easy to design and easy to implement. In the finite dimensional case, LQ regulators have many desirable properties. In this research, properties of above mentioned regulator of neutral systems were investigated, and some facts were found, such that, it had at least 50 percent of gain reduction tolerance and at least 60 degree of phase margin, and it had insensitivity against the parameter variation. Additionally, it was shown that the guaranteed cost control of neutral systems could be constructed.