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We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if and only if it is ISS w.r.t. constant inputs.…

Optimization and Control · Mathematics 2017-06-23 Andrii Mironchenko , Iasson Karafyllis , Miroslav Krstic

Due to unbounded input operators in partial differential equations (PDEs) with boundary inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and finite gains cannot be established with respect to…

Optimization and Control · Mathematics 2015-05-26 Iasson Karafyllis , Miroslav Krstic

Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects…

Optimization and Control · Mathematics 2022-03-09 Felix Schwenninger

This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid…

Optimization and Control · Mathematics 2017-11-01 Jun Zheng , Guchuan Zhu

This paper presents a maximum principle-based approach in the establishment of input-to-state stability (ISS) for a class of nonlinear parabolic partial differential equations (PDEs) over higher dimensional domains with variable…

Analysis of PDEs · Mathematics 2020-05-25 Jun Zheng , Guchuan Zhu

This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…

Analysis of PDEs · Mathematics 2018-11-19 Jun Zheng , Hugo Lhachemi , Guchuan Zhu , David Saussi

In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with boundary disturbances. Based on the weak maximum principle, a…

Analysis of PDEs · Mathematics 2020-04-13 Jun Zheng , Guchuan Zhu

This paper addresses the problem of stabilization of $1$-D parabolic equations with destabilizing terms and Dirichlet boundary disturbances. By using the method of backstepping and the technique of splitting, a boundary feedback controller…

Optimization and Control · Mathematics 2024-07-23 Jun Zheng , Guchuan Zhu

We consider the problem of output feedback regulationfor a linear first-order hyperbolic system with collocatedinput and output in presence of a general class of disturbancesand noise. The proposed control law is designed through…

Analysis of PDEs · Mathematics 2017-10-20 Pierre-Olivier Lamare , Jean Auriol , Florent Di Meglio , Ulf Jakob F. Aarsnes

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 of Dirichlet-Robin boundary disturbances, as well as…

Optimization and Control · Mathematics 2026-02-11 Yongchun Bi , Jun Zheng , Guchuan Zhu

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 function in $ L^2- $norm is considered and discretised to…

Optimization and Control · Mathematics 2020-06-05 Gediyon Yemane Weldegiyorgis , Mapundi Kondwani Banda

Input-to-state stability (ISS) allows estimating the impact of inputs and initial conditions on both the intermediate values and the asymptotic bound on the solutions. ISS has unified the input-output and Lyapunov stability theories and is…

Optimization and Control · Mathematics 2023-02-02 Andrii Mironchenko

This paper investigates robust synchronization for multi-agent systems (MASs) governed by parabolic partial differential equations in the presence of both observable and unobservable disturbances. Using only boundary output measurements, a…

Systems and Control · Electrical Eng. & Systems 2026-05-20 Yongchun Bi , Jun Zheng , Guchuan Zhu , Jiye Zhang

The concept of input-to-state stability (ISS) proposed in the late 1980s is one of the central notions in robust nonlinear control. ISS has become indispensable for various branches of nonlinear systems theory, such as robust stabilization…

Optimization and Control · Mathematics 2024-11-14 Rahma Heni

Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an…

Systems and Control · Electrical Eng. & Systems 2023-05-01 Preston Culbertson , Ryan K. Cosner , Maegan Tucker , Aaron D. Ames

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 estimating the impact of inputs and initial conditions on both the…

Optimization and Control · Mathematics 2020-03-09 Andrii Mironchenko , Christophe Prieur

This note establishes the Exponential Input-to-State Stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed…

Optimization and Control · Mathematics 2021-08-18 Hugo Lhachemi , David Saussié , Guchuan Zhu , Robert Shorten

This paper addresses input-to-state stability (ISS) properties with respect to boundary and in-domain disturbances for a class of semi-linear partial differential equations (PDEs) subject to Dirichlet boundary conditions. The developed…

Optimization and Control · Mathematics 2024-10-30 Jun Zheng , Guchuan Zhu

We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…

Systems and Control · Electrical Eng. & Systems 2025-12-01 Michael Tang , Miroslav Krstic , Jorge Poveda

This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equations (PDEs) with different types of boundary disturbances…

Analysis of PDEs · Mathematics 2020-06-24 Jun Zheng , Guchuan Zhu
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