KYP lemma based stability and control law design for differential linear repetitive processes with applications

Paszke, Wojciech; Rogers, Eric; Gałkowski, Krzysztof

doi:10.1016/j.sysconle.2013.03.010

Cited by 24 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More importantly, one can observe that this paper method converges the error faster than the method in [22]. Moreover, when using the LMI test provided in [16] or [21] (after obvious transformation from repetitive process results into ILC design procedures), infeasibility occurs even when the LMI computations are performed for middle frequency range only (the frequency range [1,10] or [20,40]). It means that the many approaches for computing the control law matrices of (5) fail while the presented approach succeeds.…”

Section: Examplementioning

confidence: 88%

“…As discussed earlier, the representation (6) can facilitate stability analysis and control synthesis. Specifically, based on the results provided in [7], [16], [17], the process (6) is said to be stable along the trial if det(sI − A)det(zI − D 0 ) = 0, and…”

Section: A Stability Analysismentioning

confidence: 99%

“…which is equivalent to the condition (16). Additionally, it is worthwhile noting that the choice of Π as diag{ε −1 1 , ε 1 } makes possible to rewrite the inequality (13) as…”

Section: A Stability Analysismentioning

confidence: 99%

See 2 more Smart Citations

Iterative Learning Control for Linear Differential Systems With Additional Performance Requirements

et al. 2020

Self Cite

View full text Add to dashboard Cite

This paper develops the systematic procedure for designing of iterative learning control (ILC) algorithms through the differential repetitive process setting. This means that the proposed approach can be directly applied to plants with differential dynamics and allows to satisfy the additional requirements on the resulting dynamics. In particular, the proposed design procedure enforces a required frequency attenuation over a finite frequency range and includes regional pole constraints. Additionally, an important result extension to the plants with relative degree greater than unity is presented. The sufficient conditions for the existence of the controllers are derived in terms of linear matrix inequalities, which are immediately extended to deal with time varying uncertainties. Finally, the simulations for a typical actuator of tracking servo system prove that the design is effective and brings some advantages when compared to the existing alternatives. INDEX TERMS Convergence analysis, iterative learning control, linear differential repetitive processes, regional pole constraints.

show abstract

Section: Examplementioning

confidence: 88%

Section: A Stability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Iterative Learning Control for Linear Differential Systems With Additional Performance Requirements

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, using the results we obtained in this paper one can obtain the theorems for the stability along the pass of the differential repetitive processes as in Paszke et al (2013). In the following, an example will be used to illustrate the effectiveness of the results in this section.…”

Section: Theorem 2 For a Given Positive Integer N Suppose The Frequmentioning

confidence: 89%

“…Following the similar line of Paszke et al (2013), the existence of a positive definite Hermitian matrix P 2 ( jω) such that…”

Section: Lemmamentioning

confidence: 99%

Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma

Wang

Gao

et al. 2015

Multidim Syst Sign Process

View full text Add to dashboard Cite

This paper investigates the problem of stability and robust stabilization of two-dimensional (2-D) continuous-discrete systems in Roesser model. Based on KalmanYakubovich-Popov (KYP) lemma, sufficient conditions of stability of the systems are proposed in terms of linear matrix inequalities (LMIs). Moreover, combining generalized KYP lemma with frequency-partitioning idea, the conservativeness of the stability conditions may be further reduced. Robust stabilization using state feedback is studied as well and stabilizing feedback gain matrices are constructed based on the solutions of certain LMIs. In addition, the stability analysis of a class of differential repetitive processes, a special case of 2-D continuous-discrete systems in Roesser model, can adopt the results in this manuscript. Numerical examples are presented to verify the effectiveness of the method.

show abstract

Kalman–Yakubovich–Popov Lemma

Brogliato¹,

Lozano²,

Maschke³

et al. 2019

Dissipative Systems Analysis and Control

View full text Add to dashboard Cite

KYP lemma based stability and control law design for differential linear repetitive processes with applications

Cited by 24 publications

References 14 publications

Iterative Learning Control for Linear Differential Systems With Additional Performance Requirements

Iterative Learning Control for Linear Differential Systems With Additional Performance Requirements

Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma

Kalman–Yakubovich–Popov Lemma

Contact Info

Product

Resources

About