The problems of robust stabilization and robust H∞ control by means of state feedback for uncertain linear systems in polytopic domains are investigated in this paper. New synthesis conditions based on LMI relaxations and search of scalar variables are proposed for both continuous and discretetime systems. The main novelty comes from the fact that the closed-loop stability is certified by means of polynomially parameter-dependent Lyapunov matrices. It is also shown that the proposed conditions contain as particular cases the less conservative conditions available in the literature for this class of systems. Numerical experiments illustrate the efficiency of the proposed relaxations.
This paper presents a new kind of vectorial backstepping sliding mode control (BSMC) for the positioning and trajectory tracking of an autonomous robotic airship. Also, a unified framework basis for the design/analysis of vectorial BSMC, as well as sliding mode control (SMC) and backstepping control (BS) for a system in lower triangular block form is derived. The design framework makes it easier the theoreticalbased comparative analysis of performances/robustness between the three nonlinear control approaches. Simulation results for the positioning and tracking of the autonomous airship illustrate the proposal.
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