In this paper, the finite spectrum assignment (FSA) control of open-loop unstable time delay processes consisting of a single unstable pole is considered. Astrom's relay autotuning is extended to this class of processes. The conditions for the existence of limit cycles are established using the point transformation method. From the relay-induced input−output signals, the parameters of the model are estimated based on which the FSA controller can be designed. There are only three closed-loop specification parameters necessary from the user, and these are both classical and intuitive. It is also shown that the so autotuned FSA system is practically stable in the face of perturbations in the process dynamics. Simulation examples are included for illustration.

System stability and stability bounds play an essential role in control theory. This note is concerned with the exponential stability of a class of second-order linear time-varying vector differential equations with real piecewise continuous coefficient matrices. A less conservative explicit condition for stability of such a system is derived using the matrix measure theory and a more accurate upper bound for the decay exponent of its stable solution is established. Examples are included for illustration.

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