New Results on Stability Analysis and Estimator Design for Switched Positive Linear Systems: A Reverse-Timer-Dependent Linear Co-Positive Lyapunov Function Approach

In this brief, the stability and estimator design issues are addressed for switched positive linear systems (SPLSs) with average dwell time (ADT). Based on a reverse timer which starts timing at the end of the activated time of a subsystem, a reverse-timer-dependent linear co-positive Lyapunov function (RLCLF) is constructed. With the help of the RLCLF approach, a new stability criteria is derived. Then, based on the stability criteria, a sufficient condition checking the existence of state estimator is derived for SPLSs with ADT. All the results can be relaxed into sum of square (SOS) program by using a SOS approximation approach. It's shown that the results obtained by RLCLF approach are less conservative compared with those of the literature. Finally, the advantages of the results are illustrated within two examples.