Robust analysis and control of parameter-dependent uncertain descriptor systems

In this paper, we address the robust admissibility analysis and control of descriptor systems with parameter-dependent, possibly time-varying, uncertainties. First, we propose a new necessary and sufficient condition for the admissibility of linear time-invariant (LTI) descriptor systems. This condition uses a strict linear matrix inequality (LMI) formulation and involves two additional matrix variables usually called slack variables. Then, we present an extension of this condition to robust admissibility of time-varying parameter-dependent descriptor systems. Using parameter-dependent Lyapunov functions and employing two slack variables, this extension states robust admissibility LMI conditions that are less restrictive, as supported by our numerical examples, than the existing ones. Our robust admissibility analysis result, which can be directly used for state estimation, cannot be so for state-feedback control design. This is due to the absence of duality between state estimation and state-feedback control in the case of parameter-dependent systems with uncertain parameters as recently reported in the literature. In order to overcome this problem, we also present in this paper a new robust admissibility analysis result, involving only one slack variable, which we apply to state-feedback control design.