State estimators for discrete-time descriptor linear systems with mixed uncertainties and state constraints

This article presents two novel mixed-uncertainty state estimators for discrete-time descriptor linear systems, namely linear time-varying mixed-uncertainty filter (LTVMF) and linear time-invariant mixed-uncertainty filter (LTIMF). The former is based on the minimum-variance approach, from which quadratic and explicit (special case of quadratic) formulations are derived and addressed to LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The LTIMF algorithm is based on the mixed H2/H infinity$$ {H}_2/{H}_{\infty } $$ criterion and addressed to LTI systems, with the low-cost computation being its motivation. Both LTVMF and LTIMF algorithms solve state-estimation problems in which the uncertainties are combined to yield the so-called mixed-uncertainty vector, which is composed by set-bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed-uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto-optimal front. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples.