Scalable decay factor and ISS gain for disturbed linear polytopic discrete-time systems

In this paper, Input-to-State Stability conditions are proposed for disturbed linear polytopic discrete-time systems. The conditions allow to optimize, independently in a certain extent, both the bounds on the decay rate and on the ISS gain, two central quantites. Indeed, the decay factor characterizes the transient behaviour of the state while the ISS gain characterizes the sensitivity with respect to the disturbances. The conditions are expressed in terms of tractable Matrix Inequalities. It is shown that the conditions are more general than existing ones proposed so far in the literature and thus less conservative. The conditions hold both for analysis or synthesis purposes. Two illustrative examples addressing the problem of polytopic observer design are given.