State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems

Abstract

In this article, without the help of predesigned dwell time constraints, a new state-dependent switching law with guaranteed dwell time for switched nonlinear systems is studied. Some sufficient conditions for asymptotic stability of switched nonlinear systems are derived. Also, all the abovementioned conditions can be transformed to a set of sum of squares (SOS) constraints, which can be checked by using the bilinear SOS methodology. Meanwhile, an improved path following method is provided to solve a bilinear SOS problem. Finally, three simulation examples are given to demonstrate the effectiveness of the obtained results. K E Y W O R D S computation of Lyapunov functions, dwell time, state-dependent switching law, sum of squares (SOS), switched nonlinear systems 1 3314

Higher‐order derivatives of generalized Lyapunov‐like functions for switched nonlinear systems

“…Proof The proof procedure consists of three major steps: The first step is to present that there exists a positive dwell time constraint between any two consecutive switching instants under the switching law (14). The second step is to prove the stability of the switched system (1). The last step is to show that the switched system (1) is of asymptotic stability. In the first step, owing to conditions (11c) and (11d) in Assumption 1, following the same proof procedure of theorem 1 in Reference 30, we can present that between and , there exists a positive dwell time constraint which is defined in (8d). In the second step, we will prove that the switched system (1) is of the stability by making use of Lemma 1.…”

Stability of nonlinear distributed delay system with parameter uncertainties: Integral‐based event‐triggered impulsive control strategy

“…Assume that matrices U ∈ S + (N+3)n , Q, and S ∈ S + n , T ∈ R n×n , Ω > 0 ∈ R n×n and a positive diagonal matrix Ξ ∈ R n×n , s.t. the LMI (19) and the following LMI (39) and (40) hold.…”

“…Generally speaking, these factors often affect the performance of nonlinear delay system and even cause the instability of the system 12‐15 . Over the past decades, many results regarding nonlinear uncertain system with delays have been investigated 16‐19 …”

“…[12][13][14][15] Over the past decades, many results regarding nonlinear uncertain system with delays have been investigated. [16][17][18][19] Impulsive control, as a low-cost and high-efficient device, allows fewer take-ups of the communication channels, and thus it is often considered as an important controller. [20][21][22][23][24] In the past decades, impulsive control has been widely used in many application models, such as infectious disease model, population migration model, speed bump model, and neural network model.…”

State‐dependent switching stabilization of third‐order switched linear systems consisting of two subsystems with fully positive real part characteristic roots

“…However, when the eigenvalues of each subsystem are fully positive real parts, namely, there is no stabilizing factor for each subsystem, the above switching strategy is no longer feasible. Under such circumstances, one should resort to state-dependent switching mechanism, which is event-driven and depends on state information to determine when and how to switch [29,30]. In essence, state-dependent switching is a closed-loop switching mechanism with strong robustness and weak conservativeness.…”