Admissibility of unbounded control operators
SIAM Journal on Control and Optimization
Analysis designs, and behavior of dissipative joints for coupled beams
SIAM Journal on Applied Mathematics
Exponential Stability of Coupled Beams with Dissipative Joints: A Frequency Domain Approach
SIAM Journal on Control and Optimization
Low-Gain Control of Uncertain Regular Linear Systems
SIAM Journal on Control and Optimization
Coprime Factorizations and Well-Posed Linear Systems
SIAM Journal on Control and Optimization
Integral Control of Infinite-Dimensional Linear Systems Subject to Input Saturation
SIAM Journal on Control and Optimization
Mathematical control theory of couple PDEs
Mathematical control theory of couple PDEs
Optimizability and Estimatability for Infinite-Dimensional Linear Systems
SIAM Journal on Control and Optimization
Survey paper: Transfer functions of distributed parameter systems: A tutorial
Automatica (Journal of IFAC)
Output tracking control for continuous-time networked control systems with communication constraints
ACC'09 Proceedings of the 2009 conference on American Control Conference
The PI-controller for infinite dimensional linear systems in Banach state spaces
ACC'09 Proceedings of the 2009 conference on American Control Conference
Output tracking control for discrete-time networked control systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
Internal Model Theory for Distributed Parameter Systems
SIAM Journal on Control and Optimization
Automatica (Journal of IFAC)
Robust Regulation of Distributed Parameter Systems with Infinite-Dimensional Exosystems
SIAM Journal on Control and Optimization
Hi-index | 22.15 |
In this paper we solve the tracking and disturbance rejection problem for infinite-dimensional linear systems, with reference and disturbance signals that are finite superpositions of sinusoids. We explore two approaches, both based on the internal model principle. In the first approach, we use a low gain controller, and here our results are a partial extension of results by Hamalainen and Pohjolainen. In their papers, the plant is required to have an exponentially stable transfer function in the Callier-Desoer algebra, while in this paper we only require the plant to be well-posed and exponentially stable. These conditions are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable. Our second approach concerns the case when the second component of the plant transfer function (from control input to tracking error) is positive. In this case, we identify a very simple stabilizing controller which is again an internal model, but which does not require low gain. We apply our results to two problems involving systems modeled by partial differential equations: the problem of rejecting external noise in a model for structure/acoustics interactions, and a similar problem for two coupled beams.