L2-induced norms and frequency gains of sampled-data sensitivity operators

This paper develops exact, computable formulas for the frequency gain and L/sub 2/-induced norm of the sensitivity operator in a sampled-data control system. With sampled data, we refer to a system that combines both continuous-time and discrete time signals, which is studied in continuous time. The expressions are obtained using lifting techniques in the frequency domain and have application in performance and stability robustness analysis taking into account full intersample information.

[1]  A. Balakrishnan Applied Functional Analysis , 1976 .

[2]  C. Loan Computing integrals involving the matrix exponential , 1978 .

[3]  S. Marcus,et al.  Nonexistence of finite dimensional filters for conditional statistics of the cubic sensor problem , 1983 .

[4]  J. Doyle,et al.  New conic sectors for sampled-data feedback systems , 1986 .

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

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

[7]  B. Francis,et al.  On the L 2 -induced norm of a sampled-data system , 1990 .

[8]  Yutaka Yamamoto,et al.  New approach to sampled-data control systems-a function space method , 1990, 29th IEEE Conference on Decision and Control.

[9]  B. Francis,et al.  A lifting technique for linear periodic systems with applications to sampled-data control , 1991 .

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

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

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

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

[14]  Gilead Tadmor,et al.  H ∞ optimal sampled-data control in continuous time systems , 1992 .

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

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

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

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

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

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

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

[22]  Pierre T. Kabamba,et al.  Multi-channel output gain margin improvement using generalized sampled-data hold functions , 1994, IEEE Trans. Autom. Control..

[23]  Thomas W. Parks,et al.  Linear periodic systems and multirate filter design , 1994, IEEE Trans. Signal Process..

[24]  P. Khargonekar,et al.  Characterization of the ${\cal L}_2$-Induced Norm for Linear Systems with Jumps with Applications to Sampled-Data Systems , 1994 .

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

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

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

[28]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[29]  Tomomichi Hagiwara,et al.  Robust stability of sampled-data systems under possibly unstable additive/multiplicative perturbations , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[30]  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.

[31]  Gjerrit Meinsma,et al.  On a key sampling formula relating the Laplace and L transforms , 1997 .

[32]  R. Middleton,et al.  Inherent design limitations for linear sampled-data feedback systems , 1995 .

[33]  Tomomichi Hagiwara,et al.  Computation of the frequency response gains and H ∞ -norm of a sampled-data system , 1995 .

[34]  James S. Freudenberg,et al.  Non-pathological sampling for generalized sampled-data hold functions , 1995, Autom..

[35]  Tomomichi Hagiwara,et al.  Frequency response of sampled-data systems , 1996, Autom..

[36]  Tomomichi Hagiwara,et al.  Robust stability of sampled-data systems under possibly unstable additive/multiplicative perturbations , 1998, IEEE Trans. Autom. Control..

[37]  M. Athans,et al.  Conic sectors for sampled-data feedback systems * , .