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On design of dynamic output feedback controller for GCS of large-scale systems with delays in interconnections: LMI optimization approach. (English) Zbl 1066.93003

The author considers the large scale system \[ \dot{x}_i(t) = A_ix_i(t) + \sum_{j\neq i}^nA_{ij}x(t-h_{ij}) + B_iu_i(t) \]
\[ y_i=C_ix_i\;\;,\;i=1,\dots,n \] where for each subsystem a local dynamic feedback controller is considered: \[ \dot{\xi}_i = A_{ci}\xi_i + B_{ci}u_i \]
\[ y_i = C_{ci}\xi_i \] To each subsystem the following quadratic cost is associated: \[ J_i = \int_0^\infty(x_i^T(t)Q_ix_i(t) + u_i^T(t)R_iu_i(t))dt \] The paper aims to give a synthesis procedure for the controllers in order to make the resulting closed loop exponentially stable and \(J_i\leq J_i^*\) where \(J_i^*\) are specified constants. Two criteria for the existence of these guaranteed cost stabilization controllers are obtained using the Lyapunov theory and expressed through Linear Matrix Inequalities.

MSC:

93A15 Large-scale systems
93D15 Stabilization of systems by feedback
93C05 Linear systems in control theory
93C23 Control/observation systems governed by functional-differential equations
15A39 Linear inequalities of matrices

Software:

LMI toolbox
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References:

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