Finite-time Issue of Discrete-time Linear Switched Systems With Partial Finite-time Unstable Modes Based on an Inverse Weighted Switching Scheme

The work proposes a multiple convex Lyapunov function and an inverse weighted switching scheme to investigate the finite-time stability and finite-time boundedness for a class of discrete-time switched linear systems with partial finite-time unstable modes. A multiple convex Lyapunov function is put forth by constructing a convex combination of positive definite matrices, which can relax the restricted conditions of the Lyapunov function and make it carry more decision variables than traditional Lyapunov function methods. Besides, the inverse weighted switching scheme is devised by summing the reciprocal of each dwell time with weighting coefficients, by which tighter dwell time bounds are ensured. On the basis of the new Lyapunov function and switching scheme, the finite-time control for a class of switched linear systems with partial finite-time unstable modes is addressed. Different from other researches that require all subsystems to be controllable, we only require the existence of one controllable subsystem. In the end, two numerical examples and a tunnel diode circuit example are provided to verify the effectiveness of the developed results.