Stable Direct Adaptive Control of Time-Varying Discrete-Time Systems: Detailed Analysis for a First-Order Plant

This paper considers the model reference adaptive control of a linear time-varying first-order discrete-time system. The principal result is a quantitative bound on the time-variations of the unknown parameter which ensures the boundedness of all the signals in the system. Since the quantitative bound provides a sufficient condition only, an example is also constructed to illustrate possible conditions for instability. A rigorous proof is provided for this instability result.