# Asymptotic Properties of Nonlinear Feedback Control Systems

@inproceedings{Liberzon1998AsymptoticPO, title={Asymptotic Properties of Nonlinear Feedback Control Systems}, author={Daniel Liberzon}, year={1998} }

This page is a substitute for the real page 2, the signature page. I am inserting it so that subsequent page numbers will appear on the correct side in the top margin. iii ACKNOWLEDGEMENTS First of all, I would like to express my deep gratitude to my advisor, Professor Roger W. Brockett of Harvard University. His boundless knowledge has made it possible for me to write this thesis, and his unfailing enthusiasm has made it impossible not to write it. I consider myself extremely lucky to have had…

No Paper Link Available

## 10 Citations

### Quantized Sampled-Data Feedback Stabilization for Linearand Nonlinear Control

- Mathematics, Computer Science
- 1999

A new control strategy which uses quantized sampled data of the states with quan-tizer sensitivities that vary as the system evolves is proposed, which globally exponentially stabilizes the systems.

### Quantized sampled-data feedback stabilization for linear and nonlinear control systems

- Mathematics, Computer ScienceProceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)
- 1999

A new control strategy which uses quantized sampled data of the states with quantizer sensitivities that vary as the system evolves is proposed, which globally and exponentially stabilizes the systems.

### " Switching Systems and Control " by Daniel Liberzon

- Computer Science

This book will especially appeal to control theorists who want to explore the discrete nature of some variables to simplify the analysis and design of nonlinear systems.

### Quantized feedback stabilization of linear systems

- Mathematics, Computer ScienceIEEE Trans. Autom. Control.
- 2000

A new control design methodology is proposed, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves, which yields global asymptotic stability.

### Spectral Analysis of Fokker--Planck and Related Operators Arising From Linear Stochastic Differential Equations

- MathematicsSIAM J. Control. Optim.
- 2000

The spectrum of the Fokker--Planck operator is completely described on an appropriate invariant subspace of rapidly decaying functions to provide information about the speed of convergence of the corresponding probability distribution to steady state, important for stochastic estimation and control applications.

### Nonlinear feedback systems perturbed by noise: steady-state probability distributions and optimal control

- MathematicsIEEE Trans. Autom. Control.
- 2000

A class of nonlinear feedback systems perturbed by white noise is described for which explicit formulas for steady-state probability densities can be found and relationships with Lyapunov functions for the corresponding deterministic systems are established.

### On explicit steady-state solutions of Fokker-Planck equations for a class of nonlinear feedback systems

- MathematicsProceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)
- 1998

We study the question of existence of steady-state probability distributions for systems perturbed by white noise. We describe a class of nonlinear feedback systems for which an explicit formula for…

### Quantized feedback systems perturbed by white noise

- MathematicsProceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)
- 1998

This paper treats a class of nonlinear feedback systems perturbed by white noise, the nonlinearity being given by a piecewise constant function of a certain type. We obtain explicit formulae for…

### Étude du bruit de procédé et de mesure pour des systèmes avec contrôleurs commutants dans un cadre scalaire et stationnaire

- Physics
- 2012

Les procedes chimiques sont constamment soumis a la variabilite des conditions d'operation, par exemple: la concentration des reactifs, l'activite des catalyseurs, etc. Il en resulte que les produits…

### On explicit steady-state solutions for a class of nonlinear

- Mathematics
- 1998

We study the question of existence of steady-state probability distributions for systems perturbed by white noise. We describe a class of nonlinear feedback systems for which an explicit formula for…

## References

SHOWING 1-10 OF 53 REFERENCES

### Multivariable Nyquist criteria, root loci, and pole placement: A geometric viewpoint

- Mathematics
- 1981

Classical control theory is concerned with the topics in our title in the context of single-input/single-output systems. There is now a large and growing literature on the extension of these ideas to…

### Some Extensions of Liapunov's Second Method

- Mathematics
- 1960

>In the study of the stability of a system, it is never completely satisfactory to know only that an equilibrium state is asymptotically stable. As a practical matter, it is necessary to have some…

### Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems

- MathematicsProceedings of the 27th IEEE Conference on Decision and Control
- 1988

The author establishes a number of properties associated with the dynamical system H=(H,(H,N)), where H and N are symmetric n-by-n matrices and (A,B)=AB-BA. The most important of these come from the…

### Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback

- Computer Science, MathematicsIEEE Trans. Autom. Control.
- 1999

A new class of feedback control problems is introduced, which cannot be asymptotically stabilized if the underlying dynamics are unstable, and a weaker stability concept called containability is introduced.

### Control of Continuous Plants by Symbolic Output Feedback

- MathematicsHybrid Systems
- 1994

It is shown that, if certain observability conditions hold, the continuous plant state can be reconstructed from a sequence of measurement events and can be transferred to any desired point in IRn by applying a suitable sequence of control events.

### Stabilizing a linear system with quantized state feedback

- Mathematics
- 1990

The problem of stabilizing an unstable, time-invariant, discrete-time, linear system by means of state feedback when the measurements of the state are quantized is addressed. It is found that there…

### Nonlinear Systems and Nonlinear Estimation Theory

- Economics
- 1981

This research was supported in part by the Army Research Office under Grant DAAG29-76-C-0139, the U.S. Office of Naval Research under the Joint Services Electronics Program Contract N00014–75-C-0648…

### Minimum attention control

- MathematicsProceedings of the 36th IEEE Conference on Decision and Control
- 1997

A measure of complexity is proposed and optimization problems involving both a measure of the desirability of the trajectories and the difficulty of implementing the control law are formulated.

### Stochastic control and the second law of thermodynamics

- Mathematics1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes
- 1978

The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average…