Sufficient conditions for the genericity of feedback stabilisability of switching systems via Lie-algebraic solvability

HERNAN HAIMOVICH; JULIO H. BRASLAVSKY

Conferencia; XIV Reunión de trabajo en procesamiento de la información y control; 2011

We address 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 ef- ficient numerical implementation.