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Lyapunov function construction by linear programming. (English) Zbl 0885.93050
The paper deals with quadratic Liapunov functions of the form \[ V(x)= |Wx |_\infty \] where \(W\) is a \(m\times n\) full rank matrix \((m\geq n)\) and \(|\cdot |_\infty\) is the infinity norm on \(\mathbb{R}^m\). 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 Lyapunov and storage functions
90C05 Linear programming
93C99 Model systems in control theory
93B40 Computational methods in systems theory (MSC2010)
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