Dissipative Control of 2-D Switched Discrete System Via Dwell-Time-Dependent Approach

Dissipative control of 2‐D discrete‐time switched systems via a point‐dependent convex storage function

“…By solving the stability conditions ( 11)-( 13), we can obtain the minimum dwell time 𝜏 * 1 = 𝜏 * 2 = 2. Meanwhile, compared with the minimum dwell time 𝜏 * = 3 obtained by Theorem 1 in the work of Hua et al, 33 the proposed method not only obtains a smaller dwell time, but also provides greater flexibility in not requiring the same dwell time for each subsystem. Figure 1 depicts the corresponding switching signals, where the first and second subsystems are indicated by 1 and 2, respectively.…”

“…Lemma 1 (33). 2-D FMLSS system ( 1) is asymptotically stable with v(i, j) = 0 under the switching signal 𝜎(i, j), if its unidirectional increments…”

“…Compare the performance indicators obtained by the dwell‐time‐dependent Lyapunov function (DTDLF) in the work of Hua et al 33 and PDCSF methods with a dwell time of $$$ \tau =2 $$$, as presented in Table 1. Notably, when compared with the DTDLF method, the PDCSF method can achieve an increased dissipativity of $$$ {\eta}^{\ast }=1.05 $$$, along with a significantly reduced $$$ {L}_2 $$$‐gain index $$$ {\gamma}^{\ast }=0.632 $$$ under the same dwell time.…”