Observer‐based controller of uncertain Switching Positive Linear Systems: A unilaterally tracking scheme

Abstract

This paper deals with designing a unilateral tracking controller for the Switching Positive Linear Systems (SPLSs). Positive systems are widespread, and most biological, economic systems, and so on, with nonnegative variables, belong to this class of systems. System states are assumed partially unmeasurable; thus, a reduced‐order positive switching observer is utilized to improve the closed‐loop system response. Also, interval uncertainty is considered to provide a more practical result. In addition, a unilateral tracking controller is developed in this study. The unilateral tracking controller keeps the system and observer states in the same direction as the reference system and system output. Also, the unilateral tracking method avoids overshoot. System stability is presented in synchronous and asynchronous switching conditions. In asynchronous switching mode, controller switches have a time lag behind the system's switching. The switching time lag in asynchronous mode is assumed unknown with a known upper bound for each subsystem. The closed‐loop system's stability is guaranteed by utilizing multiple Lyapunov functions, and the Mode Dependent Average Dwell Time (MDADT) strategy. The designed unilateral tracking controller is developed to track a reference system. Also, sufficient conditions are provided to guarantee the L1‐gain performance of the closed‐loop system. Finally, an illustrative example is provided to demonstrate the proposed scheme's effectiveness compared with the foremost existing solutions.