Delay-dependent Stabilization Conditions of Controlled Positive Continuous-time Systems

Abstract

The stabilization problem for a class of linear continuous-time systems with time-varying non differentiable delay is solved while imposing positivity in closed-loop. In particular, the synthesis of state-feedback controllers is studied by giving sufficient conditions in terms of linear matrix inequalities (LMIs). The obtained results are then extended to systems with non positive delay matrix by applying a memory controller. The effectiveness of the proposed method is shown by using numerical examples.

Control Design for One Class of Uncertain Metzler-Takagi-Sugeno Time-Delay Systems

“…and force the strictly Metzler and Hurwitz matrices (39) and Metzler matrices A ci , A cs . Hereafter, * denotes the symmetric item in a symmetric matrix.…”

“…Note, the potentially comparable method for stabilization of time-delay positive continuous-time systems presented in [39] produces in general the non-negative gains and the nonnegative closed-loop system matrices although the description of the system is based on the strictly Metzler matrix structures. As a result, there is no comparison base of the design methods for the results presented in this paper for uncertain Mezler-Takagi-Sugeno time-delay systems.…”