This paper provides a solution based on linear programming to the problem of designing observers that ensures guaranteed bounds on the estimated states. Firstly, considering linear systems without uncertainties, we provide a complete solution for the existence of interval observers having minimal l₁-norm of the interval error. Secondly, new type of observers involving dilatation functions, are introduced in order to deal with the robust estimation of systems that are possibly nonlinear and subject to uncertainties. A new methodology is provided for the design and characterization of tight robust interval observers. All the proposed conditions are expressed in term of linear programming.

A recursive algorithm for the automatic tuning of PID regulators is described. The tuning strategy is based on the minimisation of a performance index which considers the quadratic deviations of the predicted output, over the set point, as well as the control efforts, over a time horizon. The adaptive version of this algorithm follows an explicit scheme so that the applications are not limited to self-tuning in the commissioning phase. It can also be applied to parameter adaptive control. The method has been successfully tested and some results are presented.