8 papers · 1 filter
Unified Lyapunov Method for ISS of PDEs: A Tutorial on Constructing Generalized Lyapunov Functionals for Parabolic and Hyperbolic Equations
Jun Zheng, Guchuan Zhu
This tutorial provides an overview of the generalized Lyapunov method (GLM) for analyzing input-to-state stability (ISS) of partial differential equations (PDEs). We begin by revis…
A Spectral-based ISS small-gain theorem for boundary control systems with infinite couplings
Yassine El Gantouh, Jun Zheng, Guchuan Zhu +1
We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of posit…
Well-posedness of boundary control systems and application to ISS for coupled heat equations with boundary disturbances and delays
Yassine El Gantouh, Jun Zheng, Guchuan Zhu
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable condit…
Input-to-state stabilization of an ODE cascaded with a parabolic equation involving Dirichlet-Robin boundary disturbances
Yongchun Bi, Jun Zheng, Guchuan Zhu
This paper focuses on the input-to-state stabilization problem for an ordinary differential equation (ODE) cascaded by parabolic partial differential equation (PDE) in the presence…
Local integral input-to-state stability for non-autonomous infinite-dimensional systems
Yongchun Bi, Panyu Deng, Jun Zheng +1
In this paper, we prove comparison principles for nonlinear differential equations with time-varying coefficients and develop Lyapunov analytical tools for the integral input-to-st…
Finite-time input-to-state stability for infinite-dimensional systems
Xiaorong Sun, Jun Zheng, Guchuan Zhu
In this paper, we extend the notion of finite-time input-to-state stability (FTISS) for finite-dimensional systems to infinite-dimensional systems. More specifically, we first prov…