## 3 Citations

Stability analysis of reaction–diffusion PDEs coupled at the boundaries with an ODE

- MathematicsAutomatica
- 2022

Time-Varying Internal Models and Regulation of Unknown Harmonic Signals for Regular Linear Systems

- Mathematics
- 2020

. We introduce general results on well-posedness and output regulation of regular linear systems with nonautonomous controllers. We present a generalization of the internal model principle for…

Output regulation for a first-order hyperbolic PIDE with state and sensor delays

- MathematicsEur. J. Control
- 2022

## References

SHOWING 1-10 OF 35 REFERENCES

Stabilization of PDE-ODE cascade systems using Sylvester equations

- Mathematics, Computer Science2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This work considers the stabilization problem for PDEODE cascade interconnections in which the input is applied to the PDE system, whose output drives the ODE system; and solves the problem using a state transformation obtained by solving a Sylvester equation with unbounded operators.

State and output feedback boundary control for a coupled PDE-ODE system

- MathematicsSyst. Control. Lett.
- 2011

Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

- MathematicsInt. J. Control
- 2019

A two-step backstepping approach is developed, which yields the conventional kernel equations and additional decoupling equations of simple form for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially varying coefficients.

Compensation of Wave Actuator Dynamics for Nonlinear Systems

- MathematicsIEEE Transactions on Automatic Control
- 2014

This is the first global stabilization result for wave equations that incorporate non-collocated destabilizing nonlinearities of superlinear growth in wave PDEs, and presents two numerical examples.

Compensation of Infinite-Dimensional Actuator and Sensor Dynamics

- MathematicsIEEE Control Systems
- 2010

The PDE backstepping approach is a potentially powerful tool for advancing design techniques for systems with input and output delays. Three key ideas are presented in this article. The first idea is…

Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays

- Mathematics2007 46th IEEE Conference on Decision and Control
- 2007

Compensating actuator and sensor dynamics governed by diffusion PDEs

- MathematicsSyst. Control. Lett.
- 2009

The State Feedback Regulator Problem for Regular Linear Systems

- MathematicsIEEE Transactions on Automatic Control
- 2014

Under suitable assumptions, the state feedback regulator problem for infinite-dimensional linear systems is shown to be solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable.