2019/01/24 by Gyunghoon Park, Chanhwa Lee, Park, Gyunghoon +5
Engineering · #Stability and Control of Uncertain Systems #Fault Detection and Control Systems #Adaptive Control of Nonlinear Systems
paper · pdf · doi:10.48550/arxiv.1901.08722
In this paper, we address the problem of robust stability for uncertain\nsampled-data systems controlled by a discrete-time disturbance observer\n(DT-DOB). Unlike most of previous works that rely on the small-gain theorem,\nour approach is to investigate the location of the roots of the characteristic\npolynomial when the sampling is performed sufficiently fast. This approach\nprovides a generalized framework for the stability analysis in the sense that\n(i) many popular discretization methods are taken into account; (ii) under fast\nsampling, the obtained robust stability condition is necessary and sufficient\nexcept in a degenerative case; and (iii) systems of arbitrary order and of\nlarge uncertainty can be dealt with. The relation between sampling\nzeros---discrete-time zeros that newly appear due to the sampling---and robust\nstability is highlighted, and it is explicitly revealed that the sampling zeros\ncan hamper stability of the overall system when the Q-filter and/or the nominal\nmodel are carelessly selected in discrete time. Finally, a design guideline for\nthe Q-filter and the nominal model in the discrete-time domain is proposed for\nrobust stabilization under the sampling against the arbitrarily large (but\nbounded) parametric uncertainty of the plant.\n