Benefits of redundant channels in observer-based H_∞ control for discrete-time switched linear systems

In this paper, the H_∞control problem is investigated for a class of discrete-time switched linear systems with modal persistent dwell-time (MPDT) switching. The redundant channels are considered to use in the data transmission to benefit the capability of overcoming the fragility of networks commonly configured by a single channel in the communication networks subject to random packet losses. In light of a new class of Lyapunov functions, the desired observer-based quasi-time-dependent controllers, which have less conservatism than the time-independent ones, are designed such that the resulting closed-loop system is exponentially mean-square stable with a guaranteed H_∞ disturbance attenuation performance. The MPDT can be minimized while ensuring the existence of such a class of observer-based controllers for a given period of persistence. An example of DC-DC boost converter is provided to verify the effectiveness of theoretical findings.