Smooth Control for Continuous-Time Switched System with Multiple Equilibrium State/Input

This paper is devoted to the issue of the smooth controller design of a class of continuous-time switched linear systems with unique equilibrium states and control input, where they are mode-dependent and change at the instant of the mode switching. The cases of equilibrium change are considered in system modeling and control design, and the regional stability concept is given together with an equilibrium state-related multi-Lyapunov approach, which facilitates the further control transition, unlike the conventional switched system with common equilibrium stabilization requirement regardless of the change of trim control inputs. The smoothly switched controller is designed by interpreting gains, equilibrium state, and control input together in the continuous-time domain rather than converting the differential dynamic model into discrete cases and ignoring the possible equilibrium state and control input change. The effectiveness and advantages of the proposed controller are demonstrated through numerical examples and a simulation for the task of airdrop and recovery of a fixed-wing aircraft.