- Miroslav Krstic, University of California, San Diego, California, USA
- Hugo Lhachemi, University College Dublin, Ireland
- Andrii Mironchenko, University of Passau, Germany
- Pierdomenico Pepe, University of l’Aquila, Italy
- Christophe Prieur, CNRS, Université Grenoble Alpes, France
- Fabian Wirth, University of Passau, Germany
In this workshop we provide to a broad audience an overview of key concepts, results and applications of the infinite-dimensional input-to-state stability theory. The scope of techniques which we discuss includes Lyapunov functions, semigroup theory, spectral methods, boundary control and nonlinear systems theory. We discuss the applications of these methods to robust stability of boundary control systems, robust control of partial differential equations and to stability of networks with infinite-dimensional components.
All posters related to the workshop subject are welcome and will be presented during the poster session. To ease the organization of the poster session, please send the poster titles to one of the workshop organizers.
Introduction and motivation
Lyapunov characterizations of input-to-state stability, Fabian Wirth
ISS analysis for linear and non-linear PDE systems: Lyapunov methods, Christophe Prieur
In this presentation, an overview of the Lyapunov framework for the stability analysis will be given. A broad scope of infinite-dimensional systems will be considered, like those described by parabolic or hyperbolic partial differential equations. Some recent results dealing with conditions written in terms of matrix inequalities will be also given, as well as those with isolated nonlinearities. Some potential applications will be overviewed at the end of this presentation.
Poster Session and coffee-break
Stability of networks of infinite-dimensional systems, Andrii Mironchenko
Complexity of large-scale nonlinear systems makes a direct stability analysis of such systems ultimately challenging. ISS small-gain theorems help to overcome this obstruction and to study stability of a complex network consisting of input-to-stable systems, provided the interconnection structure characterized by a certain gain operator, satisfies the small-gain condition. Originally developed for the interconnections of 2 ODE systems, they have been recently extended to the finite networks of infinite-dimensional systems as well as to countably infinite networks. In this talk we give an overview of these results as well as their connection of the fundamentals of ISS theory.
Feedback stabilization of diagonal infinite-dimensional systems with delay boundary control, Hugo Lhachemi
Delays are ubiquitous in control applications. Their occurrence in partial differential equations (due to either structural delays or delays introduced by the control strategy itself) raise many control design challenges. In this context, this talk will embrace the subjects of stabilization, input-to-state stabilization, and output regulation control of heat-like equations in the presence of (possibly uncertain) delays, either in the control input or in the state.
Input-to-state stability of time-delay systems: Lyapunov-Krasovskii characterizations and feedback control redesign, Pierdomenico Pepe
The input-to-state stability notion is introduced for nonlinear functional systems, that is for systems described by Retarded Functional Differential Equations, Neutral Functional Differential Equations, Functional Difference Equations. Characterizations in terms of Lyapunov-Krasovskii functionals are presented. The problem of the input-to-state stabilization with respect to actuation disturbances is studied and a solution provided for stabilizable systems. An example of application to chemical reactors is shown.
Poster session and coffee-break
PDE small-gain results in various norms, Miroslav Krstic
In this talk, small-gain results that guarantee global exponential stability for various semilinear PDEs will be given. The results can guarantee stability for various state norms, like the sup norm or the L2 norm. The talk will cover the cases of in-domain and boundary interconnections for (i) first-order transport PDEs, (ii) parabolic PDEs, (iii) a parabolic PDE with ODEs, and (iv) a transport PDE with a parabolic PDE. Small-gain arguments will be employed for the stability analysis of each case and applications will also be given. This is a joint work with Dr. Iasson Karafyllis.
Open discussion: challenges and open problems