On the stability problem of intertwining continuous-time systems in Hilbert spaces

1996 ◽  
Vol 13 (2) ◽  
pp. 157-171
Author(s):  
J Wu
Keyword(s):  
Hilbert Spaces ◽  
Continuous Time ◽  
Stability Problem ◽  
Continuous Time Systems ◽  
The Stability ◽  
Time Systems

scholarly journals Stability of fractional positive nonlinear systems

2015 ◽  
Vol 25 (4) ◽  
pp. 491-496 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Lyapunov Method ◽  
Linear Part ◽  
Stability Conditions ◽  
Continuous Time Systems ◽  
Nonlinear Vector ◽  
The Stability ◽  
Metzler Matrix ◽  
Time Systems

AbstractThe conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.

scholarly journals Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 202 ◽  
Author(s):  
Angelo Alessandri
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Estimation Error ◽  
State Observers ◽  
Continuous Time Systems ◽  
Estimation Problems ◽  
The Stability ◽  
Time Systems

Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general. In this paper, we present an approach to the construction of Lyapunov funtions to prove stability in estimation problems. To this end, we motivate the adoption of input-to-state stability (ISS) to deal with the estimation error involved by state observers in performing state estimation for nonlinear continuous-time systems. Such stability properties are ensured by means of ISS Lyapunov functions that satisfy Hamilton–Jacobi inequalities. Based on this general framework, we focus on observers for polynomial nonlinear systems and the sum-of-squares paradigm to find such Lyapunov functions.

Sign in / Sign up

Export Citation Format

Share Document