Robust control through piecewise Lyapunov functions for discrete time-varying uncertain systems

This paper is concerned with the robust stabilization by state feedback of a linear discrete-time system with time-varying uncertain parameters. An optimization problem involving a set of linear matrix inequalities and scaling parameters provides both the robust feedback gain and the piecewise Lyapunov function used to ensure the closed-loop stability. In the case of linear time-varying systems involving the convex combination of two matrices, only two scaling parameters constrained into the interval [0, 1] are needed, allowing a simple numerical solution as illustrated by means of examples.