Finite-Time Control of Linear Systems: A Survey

Temporal and One-Step Stabilizability and Detectability of Time-Varying Discrete-Time Linear Systems

“…, [13], [14] is that ours does not impose any restrictions on the magnitude of the state inside the interval. The advantage of Definition 5 is that it matches LQ control design as opposed to finitetime stability that relates to control system design using matrix inequalities [13] that is generally much more complicated.…”

“…The advantage of Definition 5 is that it matches LQ control design as opposed to finitetime stability that relates to control system design using matrix inequalities [13] that is generally much more complicated.…”

“…This property is derived from a measure of temporal stability also proposed in this note that measures the maximum growth of the state over an arbitrary interval. Our concept of stability over a finite time interval differs from what is called finite-time stability [13], [14]. The reason we make a different choice is that our measures, their computation and the associated control system designs, come down to solving standard LQ problems.…”

“…They are characterized by a control penalty that tends to zero. Computations and control system design associated to finite-time stability concern matrix inequalities [13], [14]. Generally these are much more difficult to solve.…”

Shifting finite time stability and boundedness design for continuous-time LPV systems

“…In fact, when the behavior of the system over a fixed time interval is of interest, a system could be referred to as stable when, given some initial conditions, the state remains within some desired bounds in such time interval, and unstable when it does not [3]. It is worth recalling that the idea of FTS is independent from the classical Lyapunov asymptotic stability, since a system can be finite time stable but not asymptotically stable, and vice versa [4].…”