Periodic discrete-time systems: stability analysis and robust control using zero placement

Das, Sarit K.; Rajagopalan, P. K.

doi:10.1109/9.119641

Cited by 26 publications

(6 citation statements)

References 10 publications

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“…The results of [19] have been extended to investigate the robustness of LPTV control system under LTI unstructured perturbations. A necessary and sufficient condition (7) for robust stability of an LPTV control system subject to LTI perturbations has been derived. This condition is less conservative than small gain condition and allows unstable LTI perturbations.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Consider the LTI plant P (z) = k(1 0 2z 01 )=(1 0 3z 01 ). This is an example studied by many authors, e.g., [12], [7], [8]. It is shown in [12] that with LTI controller the gain margin := k max =k min = 2:25 for k > 0.…”

Section: Examplementioning

confidence: 97%

“…It is shown in [12] that with LTI controller the gain margin := k max =k min = 2:25 for k > 0. Whereas in [7] it is shown that with the LPTV controller (in time delay operator form) K(q 01 ) = 1 + (01) t + [6 + 6(01) t ]q 01 , the gain margin is infinite for k < 05 and k > 4. Using bilinear transform and the well-known procedure given in [5], it can readily be shown that the optimal H1 controller for the plant is K 3 LTI = 2:5=1:5k 0 and the resulting all-pass and k 0 independent LTI closed loop system is S 3 LTI Indeed, the LPTV control K provides a very large gain margin, but the resultant [Ŝ] is very large as well.…”

Section: Examplementioning

confidence: 99%

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Robustness of discrete periodically time-varying control under LTI unstructured perturbations

Zhang

2000

IEEE Trans. Automat. Contr.

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This note investigates robustness of linear periodically time varying (LPTV) control of discrete linear time invariant (LTI) plants subject to LTI unstructured perturbations. The note first derives a necessary and sufficient condition for robust stability of an LPTV system subject to LTI perturbations, which is less conservative than the well known small gain condition. It then presents a quantitative analysis on the robustness of LPTV control under LTI unstructured perturbations in comparison with that of LTI control. It is shown that under the normal value of the controller period suggested in the previous literature, the stability margin is deteriorated by LPTV control if LTI unstructured perturbations are considered. Hence LTI control is superior to LPTV control in this respect.Abstract-This paper presents a new and simple solution to the optimal unbiased reduced-order (or functional) filtering problem for linear timevarying systems. Necessary and sufficient conditions for the existence of the obtained filter are given. Stability and convergence conditions are developed for the time-invariant systems. Both continuous-and discrete-time cases are considered.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Examplementioning

confidence: 97%

Section: Examplementioning

confidence: 99%

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Robustness of discrete periodically time-varying control under LTI unstructured perturbations

Zhang

2000

IEEE Trans. Automat. Contr.

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“…2 ) Some attempts have been made in literature to provide improved robust compensation to such plants using linear but periodically-time-varying (PTV) controllers. [3][4][5][6][7] The improvement arises from the fact that the ensuing systems can now be seen to have become multi-input-multi-output (MIMO), LTI ones whose loop zeros are arbitrarily assignable. 3,4,[6][7][8][9] (LTI controllers, it may be noted, do not have such zero-placement capability.)…”

Section: Introductionmentioning

confidence: 99%

LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

Bhattacharya

Garg

Das

2022

Intl J Robust & Nonlinear

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Use of 2‐rate controllers for robust control via zero‐placement is a topic of interest in current literature. This paper proposes a 2‐degree‐of‐freedom, 2‐rate, dynamic, output feedback controller to compensate single‐input single‐output (SISO), unstable, non‐minimum phase (NMP), discrete, linear time‐invariant (LTI) plants of relative degree unity; and achieves exactly the same loop and input‐output properties as can be achieved by a linear quadratic regulator (LQR) for the equivalent lifted LTI plant using state feedback. Such LQR‐like loop and input‐output properties, it may be noted, cannot be attained by LTI or even the existing 2‐rate output feedback controllers for plants with NMP zeros. Examples presented illustrate the efficacy of the proposed controller with respect to the existing ones.

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“…Periodic controllers, owing to their zero‐placement capabilities, have been used in literature to obtain improved gain, phase margin compensations, 1‐15 infinite sector absolute stability, 16 and to remove decentralized fixed modes 1,17,18 for non‐minimum phase (NMP), linear time‐invariant (LTI) plants. The additional parameters of periodic controllers also help achieve simultaneous stabilization; see Reference 18 and references therein.…”

Section: Introductionmentioning

confidence: 99%

Periodic compensation of continuous‐time linear systems with norm‐bounded parametric uncertainties

Deshmukh

Garg

2021

Intl J Robust & Nonlinear

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This article employs a recently proposed high frequency, continuous‐time periodic controller to compensate single‐input‐single‐output linear plants with norm‐bounded time‐varying uncertainties. To this end, the design of periodic controller is converted into designing a linear time‐invariant (LTI) controller for a single‐input‐two‐output equivalent uncertain system, following averaging technique. To represent this equivalent uncertain system into a standard form of linear uncertain systems, where uncertainties appear in system matrix A and input matrix B, the observer canonical form description of the original uncertain plant is exploited. Using the relationship between quadratic stability and ℋ∞‐norm minimization result available in literature, it is proved that the presence of virtual output with the periodic feedback introduces a feedforward action on the disturbance input of the generalized plant, unlike an LTI one. By virtue of this, the proposed periodic controller can tolerate more uncertainty bound in the input matrix B than its LTI counterpart, while keeping the bound on system matrix A the same. Finally, a linear matrix inequality‐based method is used to design the periodic controller to achieve quadratic stability along with robust linear quadratic performance. Suitable examples are considered to show the superiority of the periodic control as compared to LTI ones.

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Periodic discrete-time systems: stability analysis and robust control using zero placement

Cited by 26 publications

References 10 publications

Robustness of discrete periodically time-varying control under LTI unstructured perturbations

Robustness of discrete periodically time-varying control under LTI unstructured perturbations

LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

Periodic compensation of continuous‐time linear systems with norm‐bounded parametric uncertainties

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