### The controllability function method and the feedback synthesis problem for a robust linear system

- Series
- CDSNS Colloquium
- Time
- Friday, February 10, 2023 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Online
- Speaker
- Tetiana Revina – V. N. KARAZIN KHARKIV NATIONAL UNIVERSITY – t.revina@karazin.ua

https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

The talk is about controllability for uncertain linear systems. Our approach is

based on the Controllability Function (CF) method proposed by V.I. Korobov in

1979. The CF method is a development of the Lyapunov function method and the

dynamic programming method. The CF includes both approaches at a certain values

of parameters. The main advance of the CF method is finiteness of the time of motion

(settling-time function).

In the talk the feedback synthesis problem for a chain of integrators system

with continuous bounded unknown perturbations is considered. This problem consist

in constructing a control in explicit form which depends on phase coordinates and

steers an arbitrary initial point from a neighborhood of the origin to the origin in a

finite time (settling-time function). Besides the control is satisfies some preassigned

constrains. The range of the unknown perturbations such that the control solving the

synthesis problem for the system without the perturbations also solves the synthesis

problem for the perturbed system are found. This study shows the relations between

the range of perturbations and the bounds of the settling-time function.

In particular the feedback synthesis problem for the motion of a material

point with allowance for friction is solved.

Keywords: chain of integrators, finite-time stability, robust control, settling

time estimation, uncertain systems, unknown bounded perturbation