Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Sensors (Basel). 2021 May 10;21(9):3285. doi: 10.3390/s21093285.


Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller-which was jointly optimized with a linear derivative estimator-with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

Keywords: estimation and filtering; linear control; output feedback control; robust linear matrix inequalities; stochastic optimal control problems; uncertainty descriptions.