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Lyapunov function construction by linear programming. (English) Zbl 0885.93050

The paper deals with quadratic Liapunov functions of the form

$V\left(x\right)={|Wx|}_{\infty }$

where $W$ is a $m×n$ full rank matrix $\left(m\ge n\right)$ and ${|·|}_{\infty }$ is the infinity norm on ${ℝ}^{m}$. This function is applied to obtain stability of time-varying linear systems. Some examples show that such Liapunov functions, with $W$ suitably chosen, via linear programming methods, may improve known results.

##### MSC:
 93D30 Scalar and vector Lyapunov functions 90C05 Linear programming 93C99 Control systems, guided systems 93B40 Computational methods in systems theory