${H} _{ {\infty}} $ analysis and switching control for uncertain discrete switched time-delay systems by discrete Wirtinger inequality

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Comparing our results in this paper with some published ones: Some results to guarantee the stabilization and $\pmb{H_{\infty} }$ performance of system ( 11a )-( 11h ) with ( 19 )

Results		Number of LMI variable elements
[16, 18]	τ = 15, fail to guarantee the $H_{\infty} $ performance by switching signal design	–
[19]	τ = 1, $H_{\infty} $ performance γ = 0.3048 (Switching signal design + switching control)	460 (Program running time about 1 minute)
Our result	τ = 15, $H_{\infty} $ performance γ = 0.2951 (Theorem 2) (Switching signal design + switching control)	45 (Program running time about 1 second)

Results		Number of LMI variable elements
[16, 18]	τ = 15, fail to guarantee the \(H_{\infty} \) performance by switching signal design	–
[19]	τ = 1, \(H_{\infty} \) performance γ = 0.3048 (Switching signal design + switching control)	460 (Program running time about 1 minute)
Our result	τ = 15, \(H_{\infty} \) performance γ = 0.2951 (Theorem 2) (Switching signal design + switching control)	45 (Program running time about 1 second)