LP-based mode-dependent piece-wise event-triggered finite-time L1 control for switched positive systems under MDMDT constraint

Abstract

This paper addresses the design of a finite-time (FT) $L_1$ control utilizing an event-triggered (ET) mechanism for a category of switched positive systems (SPSs) while taking into account the constraint of mode-dependent minimum dwell time (MDMDT). First, a novel ET approach utilizing 1-norm criteria is introduced to formulate the FT control design, and a positivity condition is established. Then, a new class of discretized linear copositive Lyapunov function (DLCLF) is created for the MDMDT constraint, and an ET-FT $L_1$ control scheme in a novel mode-dependent piece-wise format is designed for SPSs subject to the MDMDT constraint. It is noteworthy that through the utilization of matrix decomposition technology on the controller gain matrices $F_{i,s}^{+}$ and $F_{i,s}^{-}$, the proposed conditions for the devised ET-FT $L_1$ control scheme are formulated in the linear programming (LP) form, rather than the traditionally employed linear matrix inequality (LMI) form. This approach offers a simpler structure and reduced computational complexity compared to the latter. Furthermore, to facilitate the development of FT $L_1$ control, a time-triggered (TT) mechanism is also specifically integrated, and an LP-based TT-FT $L_1$ control scheme in a mode-dependent piece-wise format is designed for SPSs under the MDMDT constraint. With the LP conditions, three examples are presented to show the efficacy and veracity of the devised ET-FT $L_1$ control. Furthermore, a comparative analysis is conducted between the formulated ET-FT $L_1$ control and the TT-FT $L_1$ control, highlighting the superiority of the former.