  This paper addresses the stabilisation of discrete-time switching linear
systems (DTSSs) with control inputs under arbitrary switching, based on the
existence of a common quadratic Lyapunov function (CQLF). The authors have
begun a line of work dealing with control design based on the Lie-algebraic
solvability property. The present paper expands on earlier work by deriving
sufficient conditions under which the closed-loop system can be caused to
satisfy the Lie-algebraic solvability property generically, i.e. for almost
every set of system parameters, furthermore admitting straightforward and
efficient numerical implementation.
