Linear Systems, Static Output Feedback, Discrete-Time, Dissipativity Theory
Abstract
This paper presents a new set of necessary and sufficient conditions for linear static output feedback (SOF) asymptotic stabilization of linear time-invariant (LTI) systems in discrete-time. These conditions are derived by applying the notion of strict QSR-dissipativity of a system, i.e., strict dissipativity with quadratic supply rates, which in the case of LTI models can be verified using linear matrix inequalities (LMIs). Closed-loop stabilization, though, requires the feasibility not only of a dissipation inequality, but it also demands certifying an additional nonlinear constraint. In order to solve this challenging control problem, we apply in this work a set of recurrent dissipativity-based inequalities (DBIs), whose continuous-time counterpart are known in literature and are adapted in this work to the discrete-time scenario. We propose a simple iterative procedure to determine a stabilizing gain, which, as opposed to most strategies in the field, does not demand any kind of initializations of decision variables. Numerical examples are provided in order to verify the applicability of our strategy.
