By Cornelius T. Leondes
''This e-book might be an invaluable connection with keep an eye on engineers and researchers. The papers contained conceal good the hot advances within the box of contemporary regulate theory.''-IEEE team Correspondence''This booklet can assist all these researchers who valiantly try and maintain abreast of what's new within the thought and perform of optimum control.''-Control
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8. T. Kaczorek, "Pole Assignment for Linear Discrete-Time Systems by Periodic Output Feedbacks", System Control Letters 6, pp. 267-269 (1985). 9. T. Kaczorek, "Deadbeat Control of Linear Discrete-Time Systems by Periodic Output-Feedback", IEEE Transactions on Automatic Control AC-31, pp. 1153-1156 (1986). OPTIMALHOLDFUNCTIONS 35 10. J. D. Dissertation, Washington University, Saint Louis, MO, (1983). 11. X. D. Dissertation, Washington University, Saint Louis, MO, (1985). 12. J. Zavgren and T. Tarn, "Periodic Output Feedback Stabilization of InfiniteDimensional Systems", Proceedings of the 9th IFA C Triennial World Congress, Budapest, Hungary, (1984).
Next, we compare step function tracking using ZOH and GSHF. We show that under the "fixed monodromy constraint" defined in Section IV A, it may not be possible to improve tracking performance. However, using the fact that GSHF transforms the output feedback problem into a state feedback problem we show that it may still be possible to improve tracking performance using GSHF. 1. STEP FUNCTION TRACKING FOR A SECOND ORDER SYSTEM  The plant is a double integrator with position measurement of the form :~= 0x+ u, x(0)= (95) , y=[10lx.
1, we first need the following preliminary result: Define L(k) :: E[xa(k)xTa (k)]. I" If the closed loop system, Eq. (17), is stable, we have i) lim L(k)= L(oo)= L, k--~,,o (99) ii) lim 1 ~?. L(i) : L. I: Equation (17) represents a stable, linear, time- invariant, discrete-time system driven by white noise. Therefore, L(k) satisfies the following Lyapunov equation: L(k + 1 ) = V a L ( k ) V T + DaRvDT + Since the closed loop system is stable, we know that L(k) will converge with exponential rate.
Digital Control Systems Implementation and Computational Techniques by Cornelius T. Leondes