This paper introduces a new framework for controller synthesis in switched dynamical systems using seminorm-based contraction analysis. It overcomes limitations of traditional contraction theory by leveraging seminorms to ensure contraction even when individual modes are non-contracting. The methodology includes a mode-dependent feedback control structure, LMI-based synthesis conditions, and a convex optimization formulation for controller design.
Key findings
A mode-dependent feedback control structure enables semi-contraction within specific subspaces.
Sufficient conditions for controller synthesis are derived in the form of Linear Matrix Inequalities (LMIs).
A separating family framework combines subspace controllers to ensure global contraction.
Mode-dependent average dwell time (MDADT) constraints are established for switching signals.
The controller synthesis problem is formulated as a convex optimization problem for efficient numerical solution.
Limitations & open questions
The paper does not discuss the computational complexity of the proposed method.
The effectiveness of the approach is demonstrated only through numerical validation on benchmark problems.