Theory and Modern Applications
Results | Number of LMI variable elements | |
---|---|---|
[4] | Fail to justisfy the stability (when zero state feedback and perturbations) | – |
[16] | Fail to justisfy the stability (when zero state feedback and \(\Xi_{i} = 0\), \(\Xi_{zi} = 0\), i = 1,2) | – |
[21] | Fail to justisfy the stability (when zero state feedback and \(\Xi_{i} = 0\), \(\Xi_{zi} = 0\), i = 1,2) | – |
[18] | τ = 12, \(H_{\infty} \) performance γ = 0.2546, \(\bar{\Omega}_{1} = \{ [ x_{1} \ x_{2} ]^{T} \in R^{2}:0.244x_{1}^{2} - 0.0038x_{1}x_{2} - 0.4426x_{2}^{2} \le 0 \}\) | 339 (Program running time about 1 minute) |
Our results (Theorem 1) | τ = 12, \(H_{\infty} \) performance γ = 0.2512, \(\bar{\Omega}_{1} = \{ [ x_{1} \ x_{2} ]^{T} \in \Re^{2}: - 0.0327x_{1}^{2} + 0.000594x_{1}x_{2} + 0.07687x_{2}^{2} \ge 0 \}\) | 31 (Program running time about 1 second) |
τ = 316, \(H_{\infty} \) performance γ = 0.254, \(\bar{\Omega}_{1} = \{ [ x_{1} \ x_{2} ]^{T} \in \Re^{2}: - 0.0487x_{1}^{2} - 0.00194x_{1}x_{2} + 0.0865x_{2}^{2} \ge 0 \}\) |