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In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) 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 subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov–Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

A small-gain approach is presented for analyzing exponential stability of a class of (dynamical) hybrid systems. The systems considered in the paper are composed of finite-dimensional dynamics, represented by a linear ordinary differential equation (ODE), and infinite-dimensional dynamics described by a parabolic partial differential equation (PDE). Exponential stability is established under conditions involving the maximum allowable sampling period (MASP). This new stability result is shown to be useful in the design of sampled-output exponentially convergent observers for linear systems that are described by an ODE–PDE cascade. The new stability result also proves to be useful in designing practical approximate observers involving no PDEs. [ABSTRACT FROM AUTHOR]

The problem of observer design is addressed for output-injection nonlinear systems. A major difficulty with this class of systems is that the state equation involves an output-dependent term that is explicitly dependent on unknown parameters. As the output is only accessible to measurement at sampling times, the output-dependent term turns out to be (almost all time) subject to a double uncertainty, making previous adaptive observers inappropriate. Presently, a new hybrid adaptive observer is designed and shown to be exponentially convergent under ad-hoc conditions. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of Wiener system identification. The underlying linear subsystem is stable but not necessarily parametric. The nonlinear element in turn is allowed to be nonparametric, noninvertible, and nonsmooth. As Wiener models are uniquely defined up to an uncertain multiplicative factor, it makes sense to start the frequency identification process estimating the system phase (which is common to all models). To this end, a consistent estimator is designed using analytic geometry tools. Accordingly, the system frequency behavior is characterized by a family of Lissajous curves. Interestingly, all these curves are candidates to modelling the system nonlinearity, but the most convenient one is the less spread of them. Finally, the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates. [ABSTRACT FROM AUTHOR]