Bilateral backstepping control of coupled linear parabolic PDEs with spatially varying coefficients

Infinite dimensional backstepping for nonlinear parabolic PDEs

Backstepping observers for a class of parabolic PDEs

In this paper we design exponentially convergent observers for a class of parabolic partial integro-differential equations (P(I)DEs) with only boundary sensing available. The problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system. Observer gain (output injection function) is shown to satisfy a we...

A Convex Approach for Stability Analysis of Coupled PDEs with Spatially Dependent Coefficients

In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This class includes PDEs of the parabolic, elliptic and hyperbolic type as well as coupled systems without boundary feedback. Our approach uses positive matrices to ...

Elliptic and Parabolic Second-order Pdes with Growing Coefficients

We consider a second-order parabolic equation in R with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally Hölder continuous in the space variables. We show that global Schauder estimates hold even in this case. The proof introduces a new localization procedure. Our results show that the constant appearing in the clas...

Boundary Control of a Class of Unstable Parabolic Pdes via Backstepping

In this paper a family of stabilizing boundary feedback control laws for a class of linear parabolic PDEs motivated by engineering applications is presented. The design procedure presented here can handle systems with an arbitrary finite number of open-loop unstable eigenvalues and is not restricted to a particular type of boundary actuation. The stabilization is achieved through the design of ...