On switched linear copositive Lyapunov function method

摘要

The paper proposes a series of developments to the switched linear copositive Lyapunov function (SLCLF) method, applied for the stability analysis of arbitrary switching discrete-time linear systems. The new results refer to the integration of quantitative information on the SLCLF decreasing rate with the existing SLCLF framework that mainly operates in qualitative terms. This integration first yields an algebraic characterization of SLCLFs based on the solvability of a set of weak quasi-linear inequalities, defined by nonnegative square matrices. Next, for these matrices the theory of column representatives is applied in order to test the existence and construct SLCLFs; the construction of SLCLFs with the fastest decreasing rate relies on the Perron-Frobenius eigenstructure of the representatives exhibiting the greatest eigenvalue. To illustrate the applicability of our developments, two numerical examples are considered, derived from a case study already discussed in literature.