Induced \(\mathbf {L}_ 2\)-norm control for LPV systems with bounded parameter variation rates.

*(English)*Zbl 0863.93074The aim of the paper is to develop a useful, somehow ad hoc, but computationally intensive approach to system control and gain-scheduling design for linear, parameter-varying systems. The system parameters are known in real time, they belong to a compact set, and their rates of variation are bounded and known in real time too. The goal of the control is to stabilize the parameter-dependent closed-loop system, and to provide disturbance/error attenuation as measured in induced \(L_2\) norm. The considered method uses a bounding technique based on a parameter-dependent Lyapunov function, and solves the control synthesis problem by reformulating the existence conditions into a semi-finite dimensional convex optimization. The paper proposes also finite dimensional approximations to get sufficient conditions for successful controller design.

Reviewer: S.Curteanu (Iaşi)

##### MSC:

93D21 | Adaptive or robust stabilization |

93C99 | Model systems in control theory |

15A39 | Linear inequalities of matrices |