Sensitivity and robustness of sampled-data control systems: a frequency domain viewpoint

Considers a frequency domain, input-output based approach to the analysis of hybrid sampled-data systems. Based on previous works, the authors expound a frequency-domain lifting technique as an alternative to the time-domain lifting framework for sampled-data systems. In some cases, the approach pursued here can provide considerably simpler, more intuitive methods than time-domain lifting techniques to the analysis of the same problems. As applications, the authors consider the induced L/sub 2/ norms of the hybrid sensitivity and complementary sensitivity operators and the stability robustness of the hybrid system to linear time-invariant perturbations. In particularly for the single-input single-output case, "closed form" expressions arise for the induced norms, which allow straightforward numerical implementation.

[1]  Gilead Tadmor.  Optimal H∞ sampled-data control in continuous time systems , 1991, 1991 American Control Conference.

[2]  John C. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[3]  Richard H. Middleton,et al.  Robustness of zero shifting via generalized sampled-data hold functions , 1997, IEEE Trans. Autom. Control..

[4]  Richard H. Middleton,et al.  Non-pathological sampling for high order generalised sampled-data hold functions , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[5]  G. Goodwin,et al.  Generalized sample hold functions-frequency domain analysis of robustness, sensitivity, and intersample difficulties , 1994, IEEE Trans. Autom. Control..

[6]  Geir E. Dullerud,et al.  Robust stabilization of sampled-data systems to structured LTI perturbations , 1993, IEEE Trans. Autom. Control..

[7]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[8]  Pramod P. Khargonekar,et al.  Robust stability and performance analysis of sampled-data systems , 1993, IEEE Trans. Autom. Control..

[9]  Yutaka Yamamoto,et al.  Frequency responses for sampled-data systems-Their equivalence and relationships , 1994 .

[10]  B. Francis,et al.  Input-output stability of sampled-data systems , 1991 .

[11]  Pramod P. Khargonekar,et al.  Frequency response of sampled-data systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  S. Hara,et al.  Worst-case analysis and design of sampled-data control systems , 1993, IEEE Trans. Autom. Control..

[13]  Bassam Bamieh,et al.  A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control , 1992 .

[14]  B. Francis,et al.  Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers , 1988 .

[15]  P. Kabamba.  Control of Linear Systems Using Generalized Sampled-Data Hold Functions , 1987, 1987 American Control Conference.

[16]  Richard H. Middleton,et al.  Inherent design limitations for linear sampled-data feedback systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[17]  P. Khargonekar,et al.  H∞ control and filtering for sampled-data systems , 1993, IEEE Trans. Autom. Control..

[18]  Hannu T. Toivonen,et al.  Sampled-data control of continuous-time systems with an H∞ optimality criterion , 1992, Autom..

[19]  Tomomichi Hagiwara,et al.  Frequency-response of Sampled-data Systems II: Closed-loop Consideration , 1993 .

[20]  Yutaka Yamamoto,et al.  A function space approach to sampled data control systems and tracking problems , 1994, IEEE Trans. Autom. Control..

[21]  Yutaka Yamamoto.  On the state space and frequency domain characterization of H ∞ -norm of sampled-data systems , 1993 .

[22]  Tomomichi Hagiwara,et al.  Frequency response gains and H/sub /spl infin//-norm of a sampled-data system , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[23]  G.M.H. Leung,et al.  Performance analysis of sampled-data control systems , 1991, Autom..

[24]  Graham C. Goodwin,et al.  Frequency domain sensitivity functions for continuous time systems under sampled data control , 1994, Autom..