Robust stability, H₂ and H∞ guaranteed costs for discrete time-varying uncertain linear systems with constrained parameter variations

This paper is concerned with the problems of robust stability analysis and computation of H2 or H∞ (>ℓ2-gain) guaranteed costs for discrete-time linear systems with time-varying parameters. Two cases are investigated: i) the time-varying parameters are assumed to belong to a known interval and to have bounded rates of variation; ii) the time-varying parameters follow a known dynamics that can be represented through a discrete-time state space equation. A Lyapunov function that depends on the uncertain matrix of the system up to a certain degree κ-1 provides certificates for robust stability and guaranteed costs that can be cast as linear matrix inequality optimization problems, with sharper results as κ increases. Numerical examples illustrate that the proposed conditions can be more accurate than other techniques from the literature with lower complexity.