Proves that stabilizing switched linear systems with full-history controllers implies existence of memoryless homogeneous degree one controllers depending only on current state (and mode if applicable).
Alves Lima, M
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abstract
In this paper, we study stabilizability of discrete-time switched linear systems where the switching signal is considered as an arbitrary external input (and not a control variable). We characterize feedback stabilization via a hierarchy of necessary and sufficient linear matrix inequalities (LMIs) conditions based on novel graph structures. We analyze both the cases in which the controller has (or has not) access to the current switching mode, the so-called mode-dependent and mode-independent settings, providing specular results. Moreover, our approach provides explicit piecewise-linear and memory-dependent linear controllers, highlighting the connections with existing stabilization approaches. The effectiveness of the proposed technique is finally illustrated with the help of some numerical examples.
fields
math.OC 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Fixed-time stabilizability of discrete-time switched linear systems is equivalent to arbitrarily fast exponential stabilizability via a geometric structural decomposition and constructive state-feedback design.
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Feedback Stabilization of Switched Systems: Memory is not needed
Proves that stabilizing switched linear systems with full-history controllers implies existence of memoryless homogeneous degree one controllers depending only on current state (and mode if applicable).
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Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems
Fixed-time stabilizability of discrete-time switched linear systems is equivalent to arbitrarily fast exponential stabilizability via a geometric structural decomposition and constructive state-feedback design.