SIAM Journal on Control and Optimization, Vol.46, No.1, 35-60, 2007
Morse decompositions for general dynamical systems and differential inclusions with applications to control systems
The Morse decomposition theory for single-valued dynamical systems is extended to general dynamical systems and differential inclusions. Relations between chain recurrent sets, chain recurrent components (chain control sets), and Morse decompositions for open-loop systems are discussed. The robustness of feedback laws of closed-loop systems with respect to small time delays and sample-hold controls is also addressed.