473 research outputs found
Input-to-State Stability with Respect to Boundary Disturbances for a Class of Semi-linear Parabolic Equations
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 the appearance of time derivatives of the disturbances in ISS
estimates, some technical inequalities are first developed, which allow
directly dealing with the boundary conditions and establishing the ISS based on
the method of Lyapunov functionals. The well-posedness analysis of the
considered problem is carried out and the conditions for ISS are derived. Two
examples are used to illustrate the application of the developed result.Comment: Manuscript submitted to Automatic
ISS Estimates in the Spatial Sup-Norm for Nonlinear 1-D Parabolic PDEs
This paper provides novel Input-to-State Stability (ISS)-style maximum
principle estimates for classical solutions of highly nonlinear 1-D parabolic
Partial Differential Equations (PDEs). The derivation of the ISS-style maximum
principle estimates is performed by using an ISS Lyapunov Functional for the
sup norm. The estimates provide fading memory ISS estimates in the sup norm of
the state with respect to distributed and boundary inputs. The obtained results
can handle parabolic PDEs with nonlinear and non-local in-domain terms/boundary
conditions. Three illustrative examples show the efficiency of the proposed
methodology for the derivation of ISS estimates in the sup norm of the state.Comment: 20 pages, submitted to ESAIM COCV for possible publicatio
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