Full order dynamic output feedback ℋ∞ control design for discrete-time switched linear systems

The main purpose of this paper is to design, in a discrete-time framework, a switching function together with a dynamic output feedback switched controller that render the associated closed-loop switched linear system globally asymptotically stable and impose a pre-specified upper bound to the ℒ2 gain from the exogenous input to the controlled output. Sufficient conditions for the existence of a solution are expressed in terms of Riccati-Metzler inequalities being numerically handled by means of any LMI solver coupled to a line search. Compared to the results available in the literature to date, the ones presented here lead, in general, to less conservative conditions. The paper ends with an example of practical importance consisting the control of a mass-spring system with two conflicting criteria, representing a simplified model of flexible structures.