Energy-based stabilization of forced Hamiltonian systems and its application to power systems (Q2725128)

The authors show that the model of the forced Hamiltonian systems with dissipation: NEWLINE\[NEWLINE\left\{\begin{aligned} \dot x&=(J(x)-R(x))\frac{\partial H}{\partial x}+gu,\quad x\in\mathbb R^n,\\ y&=g^T\frac{\partial H}{\partial x}, \end{aligned}\right.NEWLINE\]NEWLINE where \(J(x)\) is skew-symmetric and \(R(x)\leqslant 0\) is symmetric, is a suitable tool for excitation control by finding the energy-based Lyapunov function and providing the condition for the equilibrium point to be stable. NEWLINENEWLINENEWLINEBased on excitation control and a circuit model, a symplectic manifold with second order tensor field as state space is proposed for the generalized Hamiltonian systems: NEWLINE\[NEWLINE\left\{\begin{aligned} \dot x&=T(x)\frac{\partial H}{\partial x}+\sum_{i=1}^mg_iu_i, \quad x\in\mathbb R^n,\\ y_i&=g_i^T\frac{\partial H}{\partial x},\quad i=1,\dots, m, \end{aligned}\right.NEWLINE\]NEWLINE where \(T(x)\) is an \(n\times n\) matrix with \(C^\infty(\mathbb R^n)\) entries, \(g^i\) are \(C^\infty\) vector fields. A global coordinate free model for such systems is obtained.