On the transient estimate for linear systems with time-varying uncertain parameters

A transient estimate for a discrete-time system, with respect to a certain norm /spl par//spl middot//spl par/, is a pair of positive constants (C, /spl lambda/) having the property that /spl par/x(t)/spl par//spl les/C/spl par/x(0)/spl par//spl lambda/' for all initial conditions x(0). We consider in this paper the problem of determining the "best" transient estimate for a linear system with time-varying unknown parameters in the sense that it involves the smallest /spl lambda/ and the smallest C compatible with such a /spl lambda/. We perform the computation by constructing a proper polyhedral Lyapunov function. We show how the technique ran be used to manage continuous-time systems.