Efficient criteria for the stabilization of planar linear systems by hybrid feedback controls (Q1773531)

In the paper, the following linear control \(2\times 2\) system is considered: \[ \dot x=Ax+Bu,\quad y=Cx, \tag{1} \] where \(t\in [0,\infty)\), \(x\in\mathbb R^2\) is a state variable, \(y\in\mathbb R^m\) is an output variable, \(u\in\mathbb R^l\) is a control, \(A\), \(B\), and \(C\) are real matrices. The authors suggest some criteria for the stabilization of the zero solution of the system (1) via linear hybrid feedback controls. The obtained results are formulated in terms of the input matrices \(A\), \(B\), and \(C\) and are realized as an algorithm which is directly suitable for a computer implementation. This algorithm allows one to check easily whether the system (1) can be stabilized (a) by a linear ordinary feedback control or (b) by a linear hybrid feedback control.