Abstract
This note is concerned with presenting new dissipativity-based conditions for the stabilizability of discrete-time systems with time-varying delays by linear static output feedback (SOF). We demonstrate that the feasibility of nonlinear matrix inequalities for the design of feedback stabilizing gains derived from the literature is equivalent to the feasibility of a linear matrix inequality establishing dissipativity of the system plus one matrix inequality constraint. An iterative strategy allowing the computation of stabilizing SOF gains is then developed based on a new relaxed sufficient condition. Compared with other popular approaches in the literature, such as the celebrated cone complementarity linearization (CCL) method, the strategy avoids providing initial “guesses” for the matrix variables, which is especially complicated when dealing with a large number of matrices. Due to being a particular case of SOF with an identity output matrix, static state feedback (SSF) gains can also trivially be computed by exploiting the developed conditions.
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