Theory and Modern Applications
Table 1 Exact domains of the impulsive set and phase set of model ( 2.2 )
From: Global dynamics of a state-dependent feedback control system
Cases | \(\boldsymbol {(1-\theta)V_{L}}\) | Impulsive set | Phase set |
|---|---|---|---|
(C1) | \((1-\theta)V_{L}< x_{3}^{*}\), \((1-\theta)V_{L}>x_{1}^{*}\) | \({\mathcal{M}}_{1}\) | \({\mathcal{N}}_{1}\) |
\(x_{3}^{*}\leq(1-\theta)V_{L}\leq x_{1}^{*}\) | \({\mathcal{M}}_{2}\) | \({\mathcal{N}}_{2}^{h_{1}}\) | |
(C2) | \((1-\theta)V_{L}\leq x_{4}^{*}\) | \({\mathcal{M}}_{1}\) | \({\mathcal{N}}_{1}\) |
\((1-\theta)V_{L}> x_{4}^{*}\) | \({\mathcal{M}}\) | \({\mathcal{N}}_{2}^{h}\) | |
(C3) | \((1-\theta)V_{L}< x_{2}^{*}\) | \({\mathcal{M}}_{1}\) | \({\mathcal{N}}_{1}\) |