Matrix analysis
Partial Stability and Control
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
A Control Lyapunov Approach to Predictive Control of Hybrid Systems
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Brief Analysis of discrete-time piecewise affine and hybrid systems
Automatica (Journal of IFAC)
Survey Constructive nonlinear control: a historical perspective
Automatica (Journal of IFAC)
Input-to-state stability for discrete-time nonlinear systems
Automatica (Journal of IFAC)
Stabilizing low complexity feedback control of constrained piecewise affine systems
Automatica (Journal of IFAC)
Applications of hybrid reachability analysis to robotic aerial vehicles
International Journal of Robotics Research
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Although control Lyapunov functions (CLFs) provide a mature framework for the synthesis of stabilizing controllers, their application in the field of hybrid systems remains scarce. One of the reasons for this is conservativeness of Lyapunov conditions. This article proposes a methodology that reduces conservatism of CLF design and is applicable to a wide class of discrete-time nonlinear hybrid systems. Rather than searching for global CLFs off-line, we focus on synthesizing CLFs by solving on-line an optimization problem. This approach makes it possible to derive a trajectory-dependent CLF , which is allowed to be locally non-monotone. Besides the theoretical appeal of the proposed idea, we indicate that for systems affine in control and CLFs based on infinity norms, the corresponding on-line optimization problem can be formulated as a single linear program.