Theory and Modern Applications
From: Global dynamics of a state-dependent feedback control system
Cases | \(\boldsymbol {A_{h}}\) and \(\boldsymbol {A_{h_{1}}}\) | Ï„ | \(\boldsymbol {y^{*}}\) | Interval of \(\boldsymbol {y^{*}}\) |
---|---|---|---|---|
(SC123) | \(A_{h}\leq0\), × | τ>0 | EG | \(Y_{D}^{1}= [\tau, Y_{is}^{h}+\tau ]\) |
\(A_{h}<0\), × | τ = 0 | EG | \(y^{*}=0\) | |
\(A_{h}=0\), × | ENS | \(\forall y^{*}\in [0, Y_{is}^{h} ]\) | ||
(SC11) | \(A_{h}> 0\), \(A_{h_{1}}\geq0\) | \(\frac{A_{h}}{p}<\tau\leq\tau_{2}^{h_{1}}\) | NE | Â |
\(\tau_{2}^{h_{1}}<\tau\) | ES | \((Y_{\max}^{h_{1}}, Y_{is}^{h_{1}}+\tau ]\) | ||
τ = 0 | EU | \(y^{*}=0\) | ||
(SC12) | \(A_{h}\leq0\), \(A_{h_{1}}\geq0\) | \(\tau_{3}^{h_{1}}\leq\tau\leq\tau_{2}^{h_{1}}\) | NE | Â |
\(0<\tau<\tau_{3}^{h_{1}}\) | ES | \((0, Y_{\min}^{h_{1}} )\) | ||
\(\tau>\tau_{2}^{h_{1}}\) | ES | \((Y_{\max}^{h_{1}}, Y_{is}^{h_{1}}+\tau ]\) | ||
\(A_{h}<0\), × | τ = 0 | ES | \(y^{*}=0\) | |
\(A_{h}=0\), × | ENS | \(\forall y^{*}\in [0, Y_{\min }^{h_{1}} )\) | ||
(SC2) | \(A_{h}>0\), × | \(\frac{A_{h}}{p}<\tau<\tau_{M}\) | NE |  |
\(\tau_{M}\leq \tau\leq\tau_{2}\) | EU | \([Y_{\max}^{h}, \frac{b}{p}+\tau ]\) | ||
\(\tau_{2}<\tau\) | ES | \([Y_{\max}^{h}, \frac{b}{p}+\tau ]\) | ||
τ = 0 | EU | \(y^{*}=0\) |