Title :
Further Results on “Infinity Norms as Lyapunov Functions for Linear Systems”
Author :
Christophersen, Frank J. ; Morari, Manfred
Author_Institution :
Autom. Control Lab., Eidgenossische Tech. Hochschule, Zurich
fDate :
3/1/2007 12:00:00 AM
Abstract :
This note continues on the results proposed in two previous papers for computing vector 1- or infin-norm based Lyapunov functions for linear discrete-time systems by presenting a finitely terminating algorithm for the construction of Lyapunov functions of that class. The algorithm utilizes the solution of a finite sequence of feasibility linear programs (LPs) with very few constraints or, equivalently, very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved
Keywords :
Lyapunov methods; discrete time systems; linear programming; linear systems; matrix algebra; Lyapunov function; bilinear matrix equation; infinity norms; linear discrete time system; linear programs; Cost function; Equations; Linear systems; Lyapunov method; Optimal control; Predictive control; Predictive models; Stability; Testing; Vectors; 1-norm; $infty$-norm; Lyapunov function; Lyapunov stability; discrete-time system; linear system; model predictive control (MPC) stability; vector norm;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2007.892378