The quadratic matrix inequality in singular H∞ control with state feedback
SIAM Journal on Control and Optimization
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Interconnected automata and linear systems: a theoretical framework in discrete-time
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
On the Optimal Control Law for Linear Discrete Time Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Logic-based switching algorithms in control
Logic-based switching algorithms in control
Controllability and reachability criteria for switched linear systems
Automatica (Journal of IFAC)
Control of systems integrating logic, dynamics, and constraints
Automatica (Journal of IFAC)
Solution of the state feedback singular H∞ control problem for linear time-varying systems
Automatica (Journal of IFAC)
Stabilization and optimization of switched linear systems
Automatica (Journal of IFAC)
Analysis and synthesis of switched linear control systems
Automatica (Journal of IFAC)
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This paper addresses the singular state feedback H∞ control for switched linear systems. The singular problem for switched linear systemS means that the gain matrix between the control input and the controlled output for each subsystem is not full column rank (FCR). First, the switched state feedback H∞ control problem is studied in the regular case. Then we show that, in the singular case, the singular H∞ control problem for the original switched linear system is equivalent to another H∞ control problem related to a reduced-order switched linear system. If this problem turns out to be regular, it can be solved. Conversely, we can iterate the reduction procedure. This iterative algorithm terminates when either a trivial problem is encountered or the last reduced-order problem is regular.