Abstract
This note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non-invariant set {\cal X} of states. The approach relies on introducing fake dynamics outside {\cal X} and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function via linear programming. The existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in {\cal X}. The procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset {\cal X} of the state space, and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain {\cal X}.
Original language | English |
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Article number | 6475975 |
Pages (from-to) | 2359-2365 |
Number of pages | 7 |
Journal | IEEE Transactions on Automatic Control |
Volume | 58 |
Issue number | 9 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- Model predictive control (MPC)
- piecewise affine (PWA)
- piecewise quadratic (PWQ)
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering