Nested saturation with guaranteed real poles

Abstract

The global stabilization of asymptotically nullcontrollable linear systems with bounded controls has been studied extensively. An early contribution was by Teel [6] who proposed a set of nested saturators to globally asymptotically stabilize the special case of nintegrators with one input. Using this law however, the closed loop system pole locations depend on the choice of coordinate transformation used to arrive at the control law. In this paper we suggest an approach that allows the designer to pick transformations that facilitate the placement of the closed loop poles on the negative real axis.

Stabilization of Lebesgue sampled systems with bounded controls: the chain of integrators case

“…A discussion on how tuning these parameters can be found in [Johnson and Kannan, 2003] for a very similar control law. For (2), variable saturation levels proposed in [Marchand and Hably, 2005] could be adapted to improve the convergence of the system.…”

Bounded control of an underactuated biomimetic aerial vehicle—Validation with robustness tests

“…It can be stabilized using the control developed in [30] combining the amelioration proposed by [18,31] in order to define variable bounds of the control laws and to accelerate their convergence by means of a pole placement at {−b 1 , −b 2 , −b 3 }. Define the matrix Π:…”

“…. , p 9 ) is then ensured using [18,31,33]. Finally, the desired roll angle η 1 d defines a desired orientation of the body (the desired pitch and yaw angles are 0):…”

Attitude and Position Control of a Flapping Micro Aerial Vehicle

“…Where C( j,i)is a function representing the sum of product combination of the system's poles (Johnson and Kannan, 2003).…”