Reference:
S. Lin and
B. De Schutter,
"Controller design for stabilizing bilinear systems with state-based
switching," Nonlinear Analysis: Hybrid Systems, vol. 41, p.
101009, Aug. 2021.
Abstract:
Some nonlinear systems can be approximated by switching bilinear
systems. In this paper, we proposed a method to design state-based
stabilizing controller for switching bilinear systems. Based on the
similarity between switching bilinear systems and switching linear
systems, corresponding switching linear systems are obtained for
switching bilinear systems by applying state-based feedback control
laws. Instead, we consider asymptotically stabilizing the
corresponding switching linear system through solving a number of
relaxed LMI conditions. Stabilizing controllers for switching bilinear
systems can be derived based on the results of the corresponding
switching linear systems. The stability of the controller is proved
step by step through the decreasing of the multiple Lyapunov functions
along the state trajectory. The effectiveness of the method is
demonstrated by both a theoretical example and an example of urban
traffic network with traffic signals.