Feedback stabilisation of switched systems via iterative approximate eigenvector assignment
For control engineers working on switched systems, this provides a structured design method that reveals closed-loop system properties, though it is limited to single-input systems and is incremental over existing LMI approaches.
The paper presents an iterative algorithm for designing state feedback gains that stabilize discrete-time switched systems under arbitrary switching by assigning a common quadratic Lyapunov function, offering an alternative to LMI-based methods that provides insight into closed-loop structure. Numerical examples demonstrate the algorithm's effectiveness for single-input systems.
This paper presents and implements an iterative feedback design algorithm for stabilisation of discrete-time switched systems under arbitrary switching regimes. The algorithm seeks state feedback gains so that the closed-loop switching system admits a common quadratic Lyapunov function (CQLF) and hence is uniformly globally exponentially stable. Although the feedback design problem considered can be solved directly via linear matrix inequalities (LMIs), direct application of LMIs for feedback design does not provide information on closed-loop system structure. In contrast, the feedback matrices computed by the proposed algorithm assign closed-loop structure approximating that required to satisfy Lie-algebraic conditions that guarantee existence of a CQLF. The main contribution of the paper is to provide, for single-input systems, a numerical implementation of the algorithm based on iterative approximate common eigenvector assignment, and to establish cases where such algorithm is guaranteed to succeed. We include pseudocode and a few numerical examples to illustrate advantages and limitations of the proposed technique.