Mixed L 1/H-infinity control for uncertain linear singular systems

Abstract

The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and * -norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.

The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

“…In other words, the mixed  ∞ ∕ 1 approach separately optimizes over two different classes of input signals, while the approach considered in our paper performs a double optimization (peak and energy) over the same class of inputs. Moreover, in [21,29] the authors consider an infinite time-horizon control problem, which constraints the proposed approach to deal with time-invariant and asymptotically stable systems, while the  ∞ /FTS methodology works over finite-time intervals, allows treatment of linear time-varying systems and, in principle, does not require asymptotic stability of the system under consideration.…”

“…To fix ideas and make a comparison between the two methodologies, let us assume that R = Γ in the approach dealt with in this paper; then, roughly speaking, given a signal in , the /FTS approach tries to minimize both the energy and the peak of the corresponding output; conversely the technique (see , and, more recently, ) for a given input in ( ), tries to minimize the peak (energy) of the corresponding output. In other words, the mixed approach separately optimizes over two different classes of input signals, while the approach considered in our paper performs a double optimization (peak and energy) over the same class of inputs.…”

“…Moreover, in the authors consider an infinite time‐horizon control problem, which constraints the proposed approach to deal with time‐invariant and asymptotically stable systems, while the /FTS methodology works over finite‐time intervals, allows treatment of linear time‐varying systems and, in principle, does not require asymptotic stability of the system under consideration.…”