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Robust simultaneous stabilization of uncertain discrete-time systems

Pakshin P., Soloviev S.

Systems Science

2008

Vol. 34, no 1

39-48

The paper considers a set of linear discrete-time systems with uncertain parameters. A method of synthesis of robust control which simultaneously stabilizes all the systems from this set is proposed. This method consists of two steps. First, a set of stochastic comparison systems with multiplicative noises is constructed such that if the stochastic system from this set is mean square stable then the corresponding system with uncertain parameters from the original set is robustly stable. Second, the simultaneous stabilization problem for the comparison system is solved. To find a gain matrix of the simultaneously stabilizing controller in the case of state feedback an LMI based algorithm is given and in the case of static output feedback a new method and convergent iteration algorithm are obtained.

Parametrization of stabilizing and robust stabilizing output feedback controllers for jump linear discrete-time systems

Pakshin P., Pachaev V.

Systems Science

2005

Vol. 31, no 2

5-14

The paper considers a class of jump discrete-time control systems, described by a set of systems with the transition between them determined by a homogeneous Markov chain taking values in a finite set of modes. When the mode is fixed, the plant state evolves according to the individual linear dynamic corrupted by state and control dependent noises. A parametrization of all linear output feedback controllers which stabilize the system in the mean square sense is presented. Necessary and sufficient conditions for static output feedback controller with only mode dependent gain matrix to be robust stabilizing one against the mode change uncertainty are obtained. A heuristic LMI based algorithm for computation of the gain matrix of this controller is also given.