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The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time–space propagation of such diseases using a diffusion–reaction epidemiological model of the susceptible–exposed–infected–recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results. • A non-linear observer is proposed for the SEIR model of COVID-19 spread. • Global measurements are considered on the whole the spatial domain. • Lure description of the estimation error system. • The observer design is based on a Lyapunov functional and linear matrix inequalities. • A case study illustrates the good performance. [ABSTRACT FROM AUTHOR]

In this paper, a gain-scheduled Smith Predictor PID controller is proposed for the control of an open-flow canal system that allows for dealing with large variation in operating conditions. A linear parameter varying (LPV) control-oriented model for open-flow canal systems based on a second-order delay Hayami model is proposed. Exploiting the second-order structure of this model, an LPV PID controller is designed using H\infty and linear matrix inequalities pole placement. The controller structure includes a Smith Predictor, real time estimated parameters from measurements (including the known part of the delay) that schedule the controller and predictor and unstructured dynamic uncertainty, which covers the unknown portion of the delay. Finally, the proposed controller is validated in a case study based on a single real reach canal: the Lunax Gallery at Gascogne (France). [ABSTRACT FROM AUTHOR]