Reduced-order full information estimation observer-based dissipative control for nonlinear discrete-time switched singular systems with unknown inputs

The dissipative control problem for nonlinear discrete-time switched singular systems (NDSSSs) is investigated via a novel reduced-order observer in this paper. Firstly, based on the generalized Sylvester equations and the introduced nonlinear injection term, a novel reduced-order observer is designed for each subsystem. The designed reduced-order observer can still produce accurate full-information estimation even though the dynamics and the output of the systems both contain unknown inputs. Then, by using average dwell-time scheme and multi-Lyapunov functions, some new sufficient conditions are proposed such that the resulted closed-loop NDSSSs are regular and causal, have a unique solution, and are globally uniformly asymptotically stable with a strict $(Q,S,V)$-γ-dissipative. A novel relaxation technique is proposed for decoupling nonlinear inequalities involving products of multiple nonsquare unknown variables. The design procedures of reduced-order observer and controller are presented by a specific algorithm. Finally, two numerical examples and an electronic circuit example are provided to illustrate the effectiveness of the theoretical results.