In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem, stabilizing controllers and a class of switching signals are designed. The main results are proven by using the multiple Lyapunov-like functions method, the single Lyapunov-like function method and the common Lyapunov-like function method, respectively. Finally, three examples are employed to verify the efficiency of the proposed methods.
In this paper, we develop computational procedures to approximate the spectral abscissa of the switched linear system via square coordinate transformations. First, we design iterative algorithms to obtain a sequence of the least μ1 measure. Second, it is shown that this sequence is convergent and its limit can be used to estimate the spectral abscissa. Moreover, the stopping condition of Algorithm 1 is also presented. Finally, an example is carried out to illustrate the effectiveness of the proposed method.