Sufficient conditions for the genericity of feedback stabilisability of switching systems via Lie-algebraic solvability
For control theorists, this provides a theoretical foundation for generic stabilisation of switching systems, though it is an incremental extension of prior work.
The paper derives sufficient conditions for generic feedback stabilisability of discrete-time switching linear systems under arbitrary switching, enabling efficient numerical implementation via Lie-algebraic solvability.
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.