L1 finite-time stabilization for positive semi-Markovian switching systems

This paper investigates robust finite-time stabilization scheme for positive semi-Markovian switching systems (S-MSSs). Semi-Markovian process (SMP), external disturbances, and transient performances at a finite-time level may appear in a controlled system. A more general system model for S-MSSs that covers Markovian switching systems (MSSs) as a special case is suitable for describing some complex systems that are subject to random abrupt changes in structure and parameter. The main motivation for this is that finite-time problems can be used to describe the transient performance of practical industrial control processes. First, under the framework of stochastic semi-Markovian Lyapunov functions theory, some sufficient conditions for finite-time boundedness (FTBs) and L-1 FTBs criteria for positive S-MSSs are proposed for all admissible disturbances. Then, a novel L-1 finite time controller design method that employs the gain matrix decomposition method is presented to reduce some conservativeness, thereby guaranteeing that the resulting closed loop system (RLCS) could achieve positivity, FTBs, and attain a prescribed L-1 noise attenuation performance index in standard linear programming (LP). Finally, a practical example is introduced to show the effectiveness of the main theory (C) 2018 Elsevier Inc. All rights reserved.