Abstract
The paper proposes an algebraic setting for the concrete construction of linear copositive Lyapunov functions associated with arbitrary switching positive systems; this approach complements a series of already reported results that are limited to the existence problem. Our development encompasses both discrete- and continuous-time dynamics, in a unifying manner, based on sets of quasi-linear inequalities and their solvability. The construction procedure can provide the linear copositive Lyapunov function exhibiting the optimal or e-suboptimal decreasing rate. The procedure exploits the Perron-Frobenius eigenstructure of the representative matrix (built for columns), which possesses the greatest eigenvalue; the role of (ir)reducibility of this matrix is analyzed for some of mostly encountered practical cases. To illustrate the applicability of our developments, a numerical example from literature is considered.
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