H_∞-control of linear state-delay descriptor systems: An LMI approach

For continuous-time, linear descriptor system with state-delay a H_∞-control problem is solved. Sufficient conditions for delay-dependent/delay-independent stability and L₂-gain analysis are obtained in terms of linear matrix inequalities (LMIs). A bounded real lemma and state-feedback solutions are derived for systems which may contain polytopic parameter uncertainties. The filtering problem is also solved and an output-feedback controller is then found by solving two LMIs. The first LMI is associated with a proportional-derivative state-feedback control. The second LMI is derived in two different forms, the first one corresponds to the adjoint of the system that describes the estimation error and the other stems from the original system. These two forms lead to different results. Numerical examples are given which illustrate the effectiveness of the new theory.