In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-
state stability (ISS) for infinite-dimensional systems. This property allows for the estimation of …

We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this
class the significance of noncoercive Lyapunov functions is analyzed. It is shown that the …

Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary
observed hyperbolic infinite-dimensional systems, which may be viewed as networks of …

In this article, we develop new methods to construct a Lyapunov function for 1-D linear
hyperbolic equations with variable coefficients. The main focus is on the nonstrictly …

We investigate the relationship between input-to-state stability (ISS) of linear infinite-
dimensional systems and existence of coercive ISS Lyapunov functions. We show that input …

We prove a small-gain theorem for interconnections of n nonlinear heterogeneous input-to-
state stable control systems of a general nature, covering partial, delay, and ordinary …

We study exponential stability of equilibrium in the L p-norm (1< p≤∞, p≠ 2) of nonlinear
1D systems of hyperbolic equations. A method of construction of Lyapunov functions based …

In this paper, we extend the ISS Lyapunov methodology to make it suitable for the analysis
of ISS wrt inputs from L p-spaces. We show that the existence of a so-called L p-ISS …

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one
dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov …

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one
dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov …