Limit Cycles of Controlled Switched Systems: Existence, Stability, Sensitivity
نویسندگان
چکیده
We present a control method which makes the trajectories of a switched system converge to a stable limit cycle lying in a desired region of equilibrium. The method is illustrated on the boost DC-DC converter example. We also point out in this example the sensitivity of limit cycles to parameter variations by showing how the limit cycle evolves in presence of small perturbations of some system parameters. This suggests that limit cycles are good candidates for reliable estimations of the physical parameters of switched systems using an appropriate inverse approach.
منابع مشابه
A new approach based on state conversion to stability analysis and control design of switched nonlinear cascade systems
In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF ...
متن کاملModelling human balance using switched systems with linear feedback control.
We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using linear feedback control. Using these assumptions, we derive a switched model which we then investigate. Stable periodic motions (limit cycle...
متن کاملComputation of Limit Cycles in a Class of Hybrid Dynamical Systems with Certain Symmetric Properties
This paper discusses the existence of limit cycles in a class of hybrid dynamical systems (HDSs), and derives a condition on system parameters for easily checking local stability. In this paper, we focus on piecewise affine (PWA) systems as a special class of HDSs. Assuming some symmetry on PWA systems, we obtain a simplified existence condition and a stability condition of limit cycles.
متن کاملStability of Limit Cycles in Hybrid Systems
Limit cycles are common in hybrid systems. However the nonsmooth dynamics of such systems makes stability analysis difficult. This paper uses recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of nonsmooth limit cycles. The stability of a limit cycle is determined by its characteristic multipliers. The concepts are illustrated using a coupled tank syst...
متن کاملStability of Hybrid System Limit Cycles: Application to the Compass Gait Biped Robot
Limit cycles are common in hybrid systems. However the non-smooth dynamics of such systems makes stability analysis difficult. This paper uses recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of non-smooth limit cycles. The stability of a limit cycle is determined by its characteristic multipliers. The concepts are illustrated using a compass gait bi...
متن کامل