Global stabilization of nonlinear cascade systems
Systems & Control Letters
Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
Planar nonlinear systems: practical stabilization and Hermes controllability condition
Systems & Control Letters
Global stabilizability and observability imply semi-global stabilizability by output feedback
Systems & Control Letters
A Smooth Converse Lyapunov Theorem for Robust Stability
SIAM Journal on Control and Optimization
Cascaded control of feedback interconnected nonlinear systems: application to robots with AC drives
Automatica (Journal of IFAC)
A Unifying Integral ISS Framework for Stability of Nonlinear Cascades
SIAM Journal on Control and Optimization
On non-local stability properties of extremum seeking control
Automatica (Journal of IFAC)
Brief Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems
Automatica (Journal of IFAC)
Practical Stability of Nonlinear Time-Varying Cascade Systems
Journal of Dynamical and Control Systems
Brief paper: Spacecraft relative rotation tracking without angular velocity measurements
Automatica (Journal of IFAC)
Leader-follower formation control of underactuated AUVs with leader position measurement
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Nonsmooth stabilization of a class of nonlinear cascaded systems
Automatica (Journal of IFAC)
Reduction theorems for stability of closed sets with application to backstepping control design
Automatica (Journal of IFAC)
Hi-index | 22.15 |
It is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ''adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when decoupled, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, e.g. in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, etc. After giving a rigorous framework for the analysis of such stability properties, this paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition on its solutions, the cascade of two USPAS systems remains USPAS. An analogous result is derived for uniformly semiglobally asymptotically stable (USAS) systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems affected by unknown non-dissipative forces and considering the dynamics of the DC motors.