Finite-Time Incremental Passivity and Output Tracking Control for Switched Nonlinear Systems

Abstract

This paper studies the finite-time incremental passivity of switched nonlinear systems. Then, the established theory is applied to solve the finite-time output tracking control problem of switched nonlinear systems. First, finite-time incremental passivity is firstly defined for switched nonlinear systems. Each subsystem is finite-time incrementally passive during its active time interval. Unlike incremental passivity, the state trajectories of finite-time incrementally passive system with no external supplied energy can converge to each other in finite time. Second, the criterion of finite-time incremental passivity is established. Third, finite-time incremental passivity is shown to be preserved under the feedback interconnection. A composite switching law design method is provided. Under this switching law, the interconnected switched systems can switch asynchronously. Finally, the finite-time output tracking control problem was solved by the established finite-time incremental passivity theory of the switched nonlinear systems, even if the finite-time output tracking control of individual subsytem is not solvable. The effectiveness of the proposed method is verified by an example. INDEX TERMS Switched nonlinear systems, Finite-time output tracking control, Finite-time incremental passivity.

Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators

“…The fixed point in (10) can be numerically solved by using numerical methods, and its stability can be determined by the following characteristic equation…”

“…[7][8][9]. Since the existence of switches is widespread, and many interesting dynamical phenomena are found in switching systems, several scholars have focused on the switched system, reporting many results in recent years [10][11][12][13].…”

Robust Finite Time Passivity and Stabilization of Uncertain Switched Nonlinear System

“…All results mentioned above studied passivity over infinite-time interval. Subsequently, [25,26] studied finite time passivity of switched nonlinear systems. Moreover, the established finite time passivity theory was applied to solve finite time stabilization and finite time output tracking problems.…”

“…Moreover, the established finite time passivity theory was applied to solve finite time stabilization and finite time output tracking problems. However, the structural uncertainties has not been considered in [25,26]. And finite time passification has not been addressed.…”

“…In contrast to the min-switching law in [25], the designed switching law is dependent on the selection of the smallest continuous function instead of the selection of the smallest Lyapunov function, which provide us more freedom. Second, robust finite time feedback passification is achieved by the design of robust controllers and a state dependent switching law, which has not been investigate in [25,26]. Third, robust finite-time passivity property is shown to be invariable under the feedback interconnection by the design of a composite state-dependent switching law, which allows the interconnected switched system switch asynchronously.…”