Finite-region dissipative control for 2-D switched systems via mode-dependent average dwell time

Dissipativity is a significant concern for 2-D switched systems, but existing research often overlooks the transient dynamics occurring within a finite region. This paper aims to address finite-region dissipativity and dissipative control for a class of Fornasini-Marchesini local state-space (FMLSS) type 2-D switched systems. The analysis employs the mode-dependent average dwell time approach. Firstly, the concept of dissipativity on finite-region for 2-D switched systems is introduced. Then, a sufficient condition under which the considered systems can demonstrate the finite-region boundedness with the external disturbances is established by the special recursive formulas. Additionally, a sufficient condition for finite-region dissipativity of the considered systems is provided. Furthermore, the dissipative state feedback controller is derived to ensure the finite-region dissipativity of the closed-loop systems. To illustrate the effectiveness of the proposed controller design approach, an example is presented.