Observer-Based Control for Switched Systems With Limited Statistical Information

This article is concerned with stability analysis and observer-based control synthesis for a class of discrete-time switched linear systems with limited statistical information. Instead of commonly studied switching signals such as dwell-time (DT) or Markov chain, a more general class of switching signals, random mode-dependent persistent sojourn-time (RMPST) switching, is investigated. It is composed of fixed parts with no mode switching, random parts without distribution restrictions, and intervals where arbitrary switching is allowed. To tackle the challenges posed by inaccessible modes, unknown transition probabilities, and partially unknown sojourn-time distribution, stability analysis is performed via constructing a Lyapunov function tailored to accommodate the characteristics of RMPST switching. The proposed Lyapunov function is not only mode-dependent but also elapsed-time and quasi-time dependent during fixed-random parts and arbitrary switching intervals, respectively. By means of the new Lyapunov function, an observer-based control approach is introduced for underlying switched systems, and criteria for the existence of observers and controllers are established with the set of admissible switching signals. A novel algorithm is also developed to solve the existence condition by extending the traditional cone complementary linearization (CCL) technique. The effectiveness and applicability of the theoretical results are revealed by a practical space robot manipulator system.