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

@article{Zhang2000RobustnessOD, title={Robustness of discrete periodically time-varying control under LTI unstructured perturbations}, author={Jingxin Zhang and Cisheng Zhang}, journal={IEEE Trans. Autom. Control.}, year={2000}, volume={45}, pages={1370-1374} }

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…

## Figures and Topics from this paper

## 7 Citations

THE PERFORMANCE OF DISCRETE LINEAR TIME VARYING CONTROL OF LINEAR PERIODIC PLANTS

- Mathematics
- 2008

This paper analyzes the performance of discrete linear time varying (LTV) control of discrete linear periodically time varying (LPTV) plants for l2 disturbance rejection. It extends the results of…

Limitations of nonlinear discrete periodic control for disturbance attenuation and robust stabilization

- Mathematics, Computer ScienceAutom.
- 2006

This paper presents a performance analysis of nonlinear periodically time-varying discrete controllers acting upon a linear time-invariant discrete plant. Time-invariant controllers are distinguished…

Limitations of nonlinear discrete periodic control for robust stabilization

- Mathematics2004 5th Asian Control Conference (IEEE Cat. No.04EX904)
- 2004

This paper presents a performance analysis of nonlinear periodically time varying discrete controllers for the robust stabilization of a linear time invariant discrete plant subject to l/sub p/…

Discrete-Time Noncausal Linear Periodically Time-Varying Scaling for Robustness Analysis and Controller Synthesis

- Mathematics
- 2013

Since modeling of real plants inevitably gives rise to modeling errors regarded as uncertainties, considering robustness for the uncertainties is important in actual control problems. For tackling…

Robust Performance Controller Synthesis Based on Discrete‐Time Noncausal Linear Periodically Time‐Varying Scaling

- Engineering
- 2012

This paper is concerned with the technique called discrete-time noncausal linear periodically time-varying (LPTV) scaling for robust stability analysis and synthesis. It is defined through the…

Robust Observer-Based Output Feedback Control of a Nonlinear Time-Varying System

- Computer Science
- 2016

A class of time-varying systems can be quadratically stabilized with satisfactory performance by a modified time-invariant-based observer by derived from the minimi‐ zation of the cost of error dynamics with modified least-squares algorithms.

Numerical Simulation in Aortic Arch Aneurysm

- Medicine
- 2011

This chapter is to describe the numerical simulation and computer modeling work in aortic arch aneurysm, one of the most complex flow situations found in the cardiovascular system.

## References

SHOWING 1-10 OF 28 REFERENCES

On the robust stability of linear time-invariant plants with unstructured uncertainty

- Mathematics
- 1987

We consider general families of linear time-invariant plants described by a nominal plant model with unstructured uncertainty. We show, under a rather weak assumption, that when a family of systems…

Nonlinear time-varying controllers for robust stabilization

- Mathematics
- 1987

In this paper we consider the problem of robust stabilizallon for a certain class of plants with unstructured, infinite-dimensional uncertainty. We demonstrate that for the problem of robustly…

Analysis of H2 and H∞ performance of discrete periodically time-varying controllers

- Mathematics, Computer ScienceAutom.
- 1997

Analysis of the H 2 and H ∞ performance of discrete linear periodically time-varying controllers for control of linear time-invariant plants shows that the multiple transfer channels of the system time-Varying dynamics amplify the overall system gain.

Robust control of linear time-invariant plants using periodic compensation

- Mathematics
- 1985

This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of…

Robust stabilization of sampled-data systems to structured LTI perturbations

- Computer Science, MathematicsIEEE Trans. Autom. Control.
- 1993

Sampled-data systems with stable, structured, LTI (linear time-invariant) perturbations in the half-plane algebra applied to the continuous-time plant are considered and the small gain theorem can be an extremely conservative robustness test in this sampled-data context.

Analysis of time-varying control strategies for optimal disturbance rejection and robustness

- Mathematics
- 1992

Analysis of linear time-invariant systems that are controlled by time-varying controllers is given. The problems of disturbance rejection and robustness are formulated and analyzed using functional…

Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers

- Mathematics
- 1988

This paper considers the control of a linear time-invariant plant by a digital controller composed of a sampler. a periodic discrete-time component, and a zero-order hold. The stability of such a…

Periodic Control of Linear Time-invariant Systems - A Critical Point of View

- Mathematics
- 1993

Abstract The use of periodic control in various forms has a long history in the control literature. It has been argued that a periodic feedback gain or controller when applied to an LTI system can…

Time-varying versus time-invariant compensation for rejection of persistent bounded disturbances and robust stabilization

- Mathematics
- 1991

It is shown that time-varying compensation does not improve the optimal rejection of persistent bounded disturbances. This result is obtained by exploiting a key observation that any time-varying…

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

- Mathematics
- 1992

A simple method (based on Floquet theory) for obtaining the characteristic equation (and hence stability) of periodic discrete-time systems is presented. Using this method it is shown that 2-periodic…