Diagonal Stability of Discrete-Time $k$-Positive Linear Systems With Applications to Nonlinear Systems

A linear dynamical system is called $k$ -positive if its dynamics maps the set of vectors with up to notation="LaTeX">$k-1$ sign variations itself. For notation="LaTeX">$k=1$ , this reduces important class positive systems. Since stable time-invariant systems always admit a diagonal quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that holds also for We show that, in general, not case both continuous-time and discrete-time (DT) case. then focus on DT introduce new notion xmlns:xlink="http://www.w3.org/1999/xlink">DT $k$-diagonal stability . It shown necessary condition standard diagonal stability. demonstrate an application analysis nonlinear