Abstract
This paper aims at characterizing the most destabilizing switching law for discrete-time switched systems governed by a set of bounded linear operators. The switched system is embedded in a special class of discrete-time bilinear control systems. This allows us to apply the variational approach to the bilinear control system associated with a Mayer-type optimal control problem, and a second-order necessary optimality condition is derived. Optimal equivalence between the bilinear system and the switched system is analyzed, which shows that any optimal control law can be equivalently expressed as a switching law. This specific switching law is most unstable for the switched system, and thus can be used to determine stability under arbitrary switching. Based on the second-order moment of the state, the proposed approach is applied to analyze uniform mean-square stability of discrete-time switched linear stochastic systems. Numerical simulations are presented to verify the usefulness of the theoretic results.
| Original language | English |
|---|---|
| Pages (from-to) | 165-171 |
| Number of pages | 7 |
| Journal | Systems and Control Letters |
| Volume | 94 |
| DOIs | |
| Publication status | Published - 1 Aug 2016 |
| Externally published | Yes |
Keywords
- Bilinear system
- Discrete-time
- Optimal control
- Stability analysis
- Switched linear stochastic system