The Markus–Yamabe conjecture provides a foundational criterion for the global asymptotic stability of equilibrium points in smooth dynamical systems. This paper investigates its validity within the framework of planar continuous piecewise linear systems. We focus on systems whose phase space is partitioned into \({{{{{\varvec{{n}}}}} + 1}}\) zones by \({{{{{\varvec{n}}}}}}\) parallel switching lines, a structure commonly arising in models with multi-stage stiffness. The main result establishes that if every linear subsystem defined within each zone is asymptotically stable, meaning its Jacobian matrix is Hurwitz, and the overall vector field is continuous across all switching lines, then the system possesses a unique, globally asymptotically stable equilibrium point. This finding extends the validity of the Markus–Yamabe conjecture to a broader class of piecewise-linear systems with multiple parallel switching boundaries, thereby complementing existing results for single-switching-line systems and addressing the gap for multi-zone configurations. A physical model of a single-degree-of-freedom oscillator with multi-stage spring stiffness is presented to illustrate the practical applicability of the theoretical framework, accompanied by numerical simulations confirming the global attracting property.
