Stability Conditions Derived from Spectral Theory: Discrete Systems with Periodic Feedback

Davis, Jon H.

doi:10.1137/0310001

Cited by 61 publications

(10 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We therefore have the result that time-varying discrete-time systems of period 2 can be described by means of the 2 × 2 matrix-value Z-transform given above [14,15,16].…”

Section: O:f ~ (~M Ejm#f2m(1)' Eejm°f 2m+l ( -1) ) Mmentioning

confidence: 99%

See 1 more Smart Citation

Time-varying systems and crossed products

Murray

1984

Math. Systems Theory

View full text Add to dashboard Cite

Abstract. Crossed product algebras are proposed as a framework for the study of input-output properties of linear time-varying systems. It is shown that internally stable systems with bounded continuous coefficients have transfer operators in a crossed product and conversely, that the set of all such transfer operators is dense in a crossed product. It is also shown that crossed product algebras admit causal additive decompositions, and allow a generalized frequency-domain representation.

show abstract

“…We therefore have the result that time-varying discrete-time systems of period 2 can be described by means of the 2 × 2 matrix-value Z-transform given above [14,15,16].…”

Section: O:f ~ (~M Ejm#f2m(1)' Eejm°f 2m+l ( -1) ) Mmentioning

confidence: 99%

“…The first of these is an example which has been discovered independently in one form or another by many researchers. [14,15,16] Example 1. Periodically varying discrete-time systems with integral period.…”

Section: Examplesmentioning

confidence: 99%

Time-varying systems and crossed products

Murray

1984

Math. Systems Theory

View full text Add to dashboard Cite

show abstract

“…It is a fact that every discrete-time periodic system can be expressed as a time-invariant system of higher dimension (see [7]). In our case, this yields a system of order (2N 2 − N )n which we call the "extensive form" of the original system in Problem 1:…”

Section: Combining Communication Constraintsmentioning

confidence: 99%

Stabilization of LTI systems with communication constraints

Hristu

2000

Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)

View full text Add to dashboard Cite

This work is directed towards exploring interactions of communication and control in systems with communication constraints. Examples of such systems include groups of autonomous vehicles, MEMS arrays and systems whose sensors and actuators are distributed across a network. We extend some recent results involving stabilization of LTI systems under limited communication and address a class of feed-forward control problems for the systems of interest.

show abstract

“…with z-transform Then, by Lemma 1, the output asymptotically approaches (ejwh)'G(eJwh)v. While this is never in "steady state" in the strict sense unless X = 1, its modulus I(G(eJwh)u)(0)l remains the same. In other words, the essential part of the asymptotic response is (G(eJwh)w) (8), and each particular response (ejUh)'G(eJwh)u at the kth step is obtained by the phase shift with successive multiplication by eJwh.…”

Section: Let G ( Z ) =mentioning

confidence: 99%

Frequency response of sampled-data systems

Yamämoto

Khargonekar

Proceedings of 32nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

This paper introduces the concept of frequency response for sampled-data systems and explores some basic properties as well as its computational procedures. It is shown that 1) by making use of the lifting technique, the notion of frequency response can be naturally introduced to sampled-data systems in spite of their the-varying characteristics, 2) it represents a frequency domain steady-state behavior, and 3) it is also closely related to the original transfer function representation via an integral formula. It is shown that the computation of the frequency response can be reduced to a finite-dimensional eigenvalue problem, and some examples are presented to illustrate the results. I. JNTRODUCTIONHE importance of the notion of frequency response for T continuous-time, time-invariant systems needs no justification. It is used in various aspects of system performance evaluation and still is at the center of many design methods.This fact is only reinforced by the now-s&ndard H" control theory, and attempts have been made to generalize this design methodology to various new directions. In the setting of sampled-data systems, there are now quite a few investigations along this line-for example, [lo], 171, [171, [181, [31, f271, [26], and [29], to name just a few. The difference here from the classical theory lies in the emphasis upon the importance of built-in intersample behavior in the model, so that it is part of the design specifications. As a result, in this approach the sampled-data systems are viewed as hybrid systems, and their performance is evaluated in the continuous time.An important problem in this context of sampled-data systems is that of frequency domain analysis. In classical treatments (see, e.g., [25]) the frequency domain analysis of sampled-data systems has been carried out. The classical approach is via inffinite sum formulas for sampled signals and their transforms. The mixture of continuous-and discretetime systems introduces a time-varying periodic characteristic in sampled-data systems, and this has made the classical frequency domain treatment of sampled-data systems rather awkward. It should be noted that in the classical treatment the signals are always a.ccompanied with (either real or fictitious) samplers, while in the modern point of view the actual continuous-time response is analyzed. Frequency domain anal-.Publisher Item Identifier S 0018-9286 (96)00974-9. ysis in the setting of sampled-data systems has been revisited in recent years from the modern operator theoretic standpoint in [20] and [ 111, and robust stability condition in the frequency domain has been analyzed in [9]. The works of [32], [l], and [2] pursue the justification of the notion of frequency response as a steady-state response; the former uses so-called lifting, and the latter impulse modulation. Since the advent of the lifting technique [3], [4], [19], [29], [30], it has become possible to view sampled-data systems as time-invariant discrete-time systems with built-in intersample behavior. This time-invariance g...

show abstract

Stability Conditions Derived from Spectral Theory: Discrete Systems with Periodic Feedback

Cited by 61 publications

References 8 publications

Time-varying systems and crossed products

Time-varying systems and crossed products

Stabilization of LTI systems with communication constraints

Frequency response of sampled-data systems

Contact Info

Product

Resources

About