Generalized Linear Delay Systems Optimization Problems

A delay-dependent robust stabilization controller for uncertain singular linear systems with multiple input delays and a delay-dependent robust dissipativity con-troller for singular linear parameter-varying (LPV) systems with multiple input delays are designed in this thesis. Moreover, a new method of designing observer for singular LPV systems is proposed.Firstly, a delay-dependent robust stabilization controller for uncertain singular linear systems with multiple input delays is designed. A less conservative delay-dependent stabilization criterion is achieved by constructing Lyapunov functional method and using the linear matrix inequality(LNII) technique. From the criterion, the considered robust stabilization control problem via state feedback controller is solved.Secondly, the problem of a delay-dependent robust dissipativity controller for singular linear parameter-varying (LPV) systems with multiple input delays is con-sidered. A mistake in [IMA J. Math. Control Inform..2009.26(1).45-58/is firstly pointed out and corrected. Furthermore, by constrecting parameter-dependent Lya-punov functional, a delay-dependent robust dissipativity criterion for singular LPV systems with multiple state time-delays is given. From the criterion, the considered robust dissipativity control problem via state feedback controller is solved.Thirdly, The design of a generalized observer for continuous-time generalized LPV systems is investigated. This considered observer problem is firstly transformed to observer design for generalized LPV systems by convex combination method, then the generalized observer is scheduled by an multi-section interpolation function, and the gain matrices of the generalized observer are obtained by solving a LAII.The effectiveness of these methods proposed in this thesis are demonstrated by numerical examples and simulation results.