Observer Design For a Class of Parabolic Systems With Large Delays and Sampled Measurements

Abstract

In this paper, we design a novel observer for a class of semilinear heat 1D equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of sub-observers. Each sub-observer handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of sub-observers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of LMIs.

Improved observer design for heat equation with constant measurement delay via Legendre polynomials

“…Moreover, the Clearly, an improvement over 20% is achieved by using our new BL inequalities. This implies that our result allows to reduce the order of chain of sub-observers considered in [5] by more than 20%.…”

“…Finally, a numerical example illustrates that our LMIs lead to an improvement over 20%. This implies that our results allow to reduce the order of chain of sub-observers considered in [5] by more than 20%.…”

“…To enlarge the delay size, the concept of chain of subobservers was recently extended to heat equation in [5]. However, construction of these observers involves serious computational complexity when solving chain of subobservers in the form of PDEs.…”

Delayed stabilization of parabolic PDEs via augmented Lyapunov functionals and Legendre polynomials

“…The objective of the present work is the derivation of less conservative L-MI conditions for the stability analysis of heat and KdVB equations with time-delay. In application to chain of subobservers as used in [1], such conditions will allow to reduce the order of the chain.…”

“…For the stability analysis of the closed-loop system, we suggest an augmented Lyapunov functional depending on the state derivative and that is based on Legendre polynomials. Such functionals extend the Lyapunov constructions of [1,8]. Sufficient stability conditions are derived in terms of LMIs that are parameterized by the degree N of the polynomials.…”