Quantity of items: 1135
ALEXIS J. VALLARELLA; HERNÁN HAIMOVICH. Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the cur-rent state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time modelwhose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible toobtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and abound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: i)ensure the stability of the (approximate) discrete-time model, ii) ensure that the stability of the approximate model carries over tothe exact model, iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-timemodel as per task i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varyingsampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these draw-backs by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptoticstability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input maysuccessfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform. Other production. 2018
ALEXIS J. VALLARELLA; HERNÁN HAIMOVICH. Digital controller design for nonlinear systems may be complicated by the fact that an exact discrete-time plant model is not known.One existing approach employs approximate discrete-time models forstability analysis and control design, and ensures different types of closed-loop stability properties based on the approximate model and on specific bounds on the mismatch between the exact and approximate models.Although existing conditions for practical stability exist, some of whichconsider the presence of process disturbances, input-to-state stability withrespect to state-measurement errors and based on approximate discretetimemodels has not been addressed. In this paper, we thus extend existingresults in two main directions: (a) we provide input-to-state stability(ISS)-related results where the input is the state measurement error and(b) our results allow for some specific varying-sampling-rate scenarios.We provide conditions to ensure semiglobal practical ISS, even undersome specific forms of varying sampling rate. These conditions employLyapunov-like functions. We illustrate the application of our results onnumerical examples, where we show that a bounded state-measurementerror can cause a semiglobal practically stable system to diverge. Other production. 2018