**Reference:**

I. Necoara,
B. De Schutter,
W.P.M.H. Heemels,
S. Weiland,
M. Lazar, and
T.J.J. van den Boom,
"Control of PWA systems using a stable receding horizon method:
Extended report," Tech. rep. 04-019a, Delft Center for Systems and
Control, Delft University of Technology, Delft, The Netherlands, 26
pp., Oct. 2004. A short version of this report has been published in
the *Proceedings of the 16th IFAC World Congress*, Prague,
Czech Republic, July 2005. Paper 2794/Tu-E21-TO/2.

**Abstract:**

In this paper we derive stabilization conditions for the class of PWA
systems using the linear matrix inequality (LMI) framework. We
consider the class of piecewise affine feedback controllers and the
class of piecewise quadratic Lyapunov functions that guarantee
stability of the closed-loop system. We take into account the
piecewise structure of the system and therefore the matrix
inequalities that we solve are less conservative. We prove that the
infinite-horizon quadratic cost is bounded if certain LMIs are
satisfied. Using the upper bound of the infinite-horizon quadratic
cost as a terminal cost and constructing also a convex terminal set we
show that the receding horizon control stabilizes the PWA system. We
derive also an algorithm for enlarging the terminal set based on a
backward procedure; therefore, the prediction horizon can be chosen
shorter, removing some computations off-line.

Technical report: pdf file (254 KB)

@techreport{NecDeS:04-019a,

author={I. Necoara and B. {D}e Schutter and W.P.M.H. Heemels and S. Weiland and M. Lazar and T.J.J. van den Boom},

title={Control of {PWA} systems using a stable receding horizon method: Extended report},

number={04-019a},

institution={Delft Center for Systems and Control, Delft University of Technology},

address={Delft, The Netherlands},

month=oct,

year={2004},

note={A short version of this report has been published in the \emph{Proceedings of the 16th IFAC World Congress}, Prague, Czech Republic, July 2005. Paper 2794\,/\,Tu-E21-TO/2}

}

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