Robust $H_{\infty }$ Control of Discrete-Time Nonhomogenous Markovian Jump Systems via Multistep Lyapunov Function Approach

This paper investigates the problems of robust H
_∞
control for a class of discrete-time nonhomogenous Markovian jump linear systems (NMJLSs) by a multistep Lyapunov function (LF) approach. The proposed multistep LF is allowed to increase during the period of several sampling time step ahead of the current time within the Jump mode. First, a less conservative stability criterion is derived based on this multistep LF approach. Second, an H
_∞
performance is analyzed under the multistep case by properly dealing with the knowledge of future states and exogenous noises. These two results are then employed to facilitate a robust H
_∞
control design for NMJLSs, which yields a better disturbance attenuation performance as compared with the existing results. Numerical examples are included to elucidate the effectiveness of the developed results.