# American Institute of Mathematical Sciences

June  2015, 4(2): 159-175. doi: 10.3934/eect.2015.4.159

## Constrained controllability for lumped linear systems

 1 Mohammed V University, Ecole Normale Supérieure de Rabat, BP 5118, Rabat, Morocco

Received  May 2014 Revised  September 2014 Published  May 2015

We consider linear lumped control systems of the form $y'(t)=Ay(t)+Bu(t)$ where $A \in \mathbb{R}^{m\times m}$, $B \in \mathbb{R}^{m\times p}$. Taking into account eventual control constraint (such as saturation), we study the problem of controllability by using a general variational approach. The results are applied to the following saturation constraints on the control $u(t)=(u_{1}(t), ..., u_{p}(t))$: (i) the quadratic one specified by $\underset{j=1}{\overset{p}\sum}\left|u_{j}(t)\right|^{2} \leq 1$ for all $0\leq t\leq T$ and (ii) the polyhedral one characterized by $\underset{1 \leq j \leq p}{\max}\left|u_{j}(t)\right| \leq 1$ for all $0\leq t\leq T$.
Citation: Larbi Berrahmoune. Constrained controllability for lumped linear systems. Evolution Equations & Control Theory, 2015, 4 (2) : 159-175. doi: 10.3934/eect.2015.4.159
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