Sampled-data stabilization of Markovian jumping conic-type nonlinear systems via an augmented looped functional

Abstract

This paper addresses the growing concern of stability analysis and controller design in Markovian jumping conic-type nonlinear systems, particularly in light of their increasing applications in various fields such as the optimization and motor device control systems, making the understanding of time-varying delays crucial. Utilizing variable-period mode-dependent sampled-data control, an augmented looped Lyapunov–Krasovskii (L–K) functional is constructed to accurately capture the impacts of sampling intervals and time-varying delays on system stability. The introduction of an augmented term leads to a non-convex cross-quadratic term in the derivative of the looped functional. To manage this complexity, a novel matrix inequality is proposed to effectively bound this non-convex term. By employing the free-weighting matrices method alongside the second-order canonical Bessel–Legendre inequality, sufficient conditions for system stabilization are derived, accommodating a broader range of time-varying delays and sampling intervals in the form of linear matrix inequalities (LMIs), which facilitate the determination of controller gains. Finally, a simulation of a time-delayed Chua’s circuit is presented to validate the effectiveness of these findings.