Exponential quasi‐(Q,S,R)‐dissipativity and practical stability for switched nonlinear systems

Abstract

In this paper, the problems of exponential quasi‐(Q,S,R)‐dissipativity and practical stability analysis for a switched nonlinear system are addressed. First, the concept of exponential quasi‐(Q,S,R)‐dissipativity for switched nonlinear systems without requiring the exponential quasi‐(Q,S,R)‐dissipativity property of each subsystem is proposed. Then, we show that an exponentially quasi‐(Q,S,R)‐dissipative switched nonlinear system is practically stable. Second, this exponential quasi‐(Q,S,R)‐ dissipativity property for a switched nonlinear system is obtained by the design of a state‐dependent switching law. Third, a composite state‐dependent switching law is designed to render the feedback interconnection of switched nonlinear systems exponentially quasi‐(Q,S,R)‐dissipative. This switching law allows interconnected switched nonlinear systems to switch asynchronously. Finally, the effectiveness of the results is verified by a numerical example.

Exponential Quasi-Incremental-(Q, S, R)- Dissipativity and Practically Incremental Stability for Switched Nonlinear Systems

“…Remark 2. For system with an equilibrium   0 , 0 , Definition 2 is reduced to the quasi-dissipativity definition in [46]…”

“…The conditions ( 8), ( 20), ( 24) are commonly adopted for switched nonlinear systems [39][40][41][42][43][44][45][46][47]. However, checking these conditions may be difficult in practice, so that some literatures proposed an associated sufficient condition corresponding to a feasibility problem over Linear Matrix Inequalities.…”

“…Nevertherless, it is hard to achieve incremental dissipativity due to large uncertainties or switching. As the quasi-dissipativity for switched systems investigated in [45,46], this paper will study quasi-incremental dissipativity. Unlike incremental dissipative systems which do not produce energy by itself, quasi-incrementally dissipative system often contains energy source.…”

Interval estimator design for switched systems with its application

“…Switched systems, occupying a vital position in hybrid systems, are widely recognized in practice due to their flexibilities in describing practical processes, such as switched circuit systems [15] and networked systems [16]. A switched system is usually comprised of a certain constant function often labelled as the switching rule and a series of dynamic equations labelled as the subsystems [17,18]. Plentiful attention has been paid to the study of switched systems with lots of interesting works attained, see [19][20][21] for example.…”

Geometrical Quasi-Passivity and Practical Stability Property for Switched Discrete-Time Nonlinear Systems

“…So it is natural to adopt multiple storage functions to describe the passivity property for a switched system [42]- [44]. Nevertherless, quasi-passivity for switched nonlinear systems has been rarely explored [45]- [48]. For discrete-time switched system, general passivity was defined using a common storage function in [49].…”