This paper proposes a novel composite boundary feedback control law that ensures input-to-state stability (ISS) for a coupled ODE-parabolic PDE system with time-varying coefficients in both subsystems. In controller design, we circumvent the need to directly solve coupled time-varying parabolic-hyperbolic kernel equations by employing an analytic pre-defined gain function and a time-varying Volterra kernel function to design the control law explicitly. In stability analysis, to address the simultaneous challenges of Dirichlet boundary disturbances and time-varying coefficients, we employ the square root of a time-varying positive definite matrix and a superlinear function to construct a nonquadratic Lyapunov function for the ODE and a generalized Lyapunov functional for the PDE, respectively, in the target system, thereby establishing the ISS in the $L^2$-norm of the closed-loop system. Numerical simulations are presented to illustrate the effectiveness of the proposed control scheme.
This paper addresses the observer‐based output‐feedback boundary control design for a system of ‐coupled parabolic partial differential equations (PDEs) with spatially varying diffusion coefficients without any ordering conditions. First, a boundary observer is proposed to estimate the system states, with its gain de...
Seyedamin Hatami, Mohammad Keyanpour· Mathematical methods in the...· 0 citations
This paper investigates adaptive observer design for a class of ordinary differential equation–partial differential equation (ODE–PDE) cascaded systems featuring time-delay characteristics, unknown parameters and inherent non-linear terms. The framework consists of a primary ODE subsystem, whose output is observed th...
Xiao-Jing Wang, Jun-Jun Liu, Ren-Ren Zhao· IMA Journal of Mathematical...· 0 citations
The paper considers a system of unidirectional first-order hyperbolic partial differential equations (PDEs) coupled with ordinary differential equations (ODEs), modeling two-phase advective transport processes subject to both boundary and distributed input delays. To address the system defined over two spatial domains,...
Sanguan Zhong, Jie Qi· IEEE Transactions on Automat...· 0 citations
This paper primarily investigates the finite-time stabilization problem for a class of non-strict-feedback stochastic nonlinear systems. In contrast to existing results, this work has two main features: (1) More relaxed assumptions are imposed on the uncertain nonlinearities; (2) unknown parameters appear in both the d...
A hyperbolic function is adopted to convert the unconstrained control command into a bounded signal so that the actuator constraints are strictly respected, and a Lyapunov-based design is carried out to derive the finite-time adaptive control protocol.
This paper addresses the problem of gain-scheduled $H_{\infty } $ dynamic output-feedback control for Markov linear parameter-varying systems. Unlike most existing results that assume bounded parameter variation rates, a switching approach is designed to handle the time derivative of the Lyapunov matrix, allowing arbit...
