Generating chaos for a class of linear switching control systems: A hybrid approach

This paper investigates a class of linear continuous-time “periodic” switching systems and proposes a new approach to generate chaos by designing a hybrid switching rule. First, Lyapunov exponents of the system are derived by extending the Floquet theorem to a class of linear continuous-time switching systems. Then, a novel switching rule is proposed to gain global boundedness property as well as the required placement of Lyapunov exponents for chaos. A numerical example is given to illustrate the chaotic dynamic behavior of the generated system. Furthermore, the corresponding bifurcation diagrams are sketched, which, together with other phase portraits, clearly verify the validity of the main result.