Nonlinear Analysis-Hybrid Systems最新文献

This paper develops new practical stability criteria for impulsive stochastic functional differential systems with distributed-delay dependent impulses by using the Lyapunov–Razumikhin approach and some inequality techniques. In the given systems, the state variables on the impulses are concerned with a history time period, which is very appropriate for modelling some practical problems. Moreover, different from the existing practical stabilization results for the systems with unstable continuous stochastic dynamics and stabilizing impulsive effects, we take the systems with stable continuous stochastic dynamics and destabilizing impulsive effects into account. It shows that under the impulsive perturbations, the practical exponential stability of the stochastic functional differential systems can remain unchanged when the destabilizing distributed-delay dependent impulses satisfy some conditions on the frequency and amplitude of the impulses. In other words, it reveals that how to control the impulsive perturbations such that the corresponding stochastic functional differential systems still maintain practically exponentially stable. Finally, an example with its numerical simulation is offered to demonstrate the efficiency of the theoretical findings.

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is constrained by labeled graphs, namely constrained switching linear systems. In order to do so, we provide chance-constrained bounds on stability guarantees, that can be obtained from a finite number of observations with bounded noise. We first present a method providing stability guarantees from sampled trajectories in the hybrid state space of the system. We then study the harder situation where one only observes the continuous part of the hybrid states. We show that in this case, one may still obtain formal chance-constrained stability guarantees. For this latter result we provide a new upper bound of general interest, also for model-based stability analysis.

In this work, we address the minimum realization problem for controllability of both continuous-time switched linear systems and reversible discrete-time switched linear systems. For both classes of $n$-dimensional switched linear systems, we show that $\frac{n(n+1)}{2}-1$ switches are the tight upper bound for controllability switching realization. The minimum realization problem for observability is also addressed by means of the duality principle.

In this paper, we consider the stability of impulsive logical dynamic systems (ILDNs) from two aspects: impulsive disturbance and impulsive control. The existing results on the stability of ILDNs only consider the stability of ILDNs under a given impulsive instant sequence (IIS), which has some limitations and motivates us to consider the stability of ILDNs under any IIS. By constructing a merged ILDN, under the assumption that the non-impulsive process and impulsive process are all globally stable, a necessary and sufficient condition on the stability of ILDNs under any IIS is proposed at first. Unfortunately, the obtained result is too restrictive, and in practice, it is not common that a stable LDN is still stable under any IIS. The fact is that for any stable LDN, there exist some IISs such that its stability is destroyed, and these IISs are called impulsive disturbances; for any unstable LDN, there exist some IISs such that the stability can be achieved, and these IISs are called impulsive control. To investigate the stability of ILDNs, the concept of average impulsive interval is first introduced to ILDNs, and several sufficient conditions are proposed to ensure the stability of LDNs under the time-triggered IISs with the property of average impulsive interval. Moreover, the obtained results are applied to the set stability of ILDNs.

This paper addresses the global output-feedback stabilization for a class of uncertain nonlinear systems via a switching event-triggered approach. Typically, the system growth rates are allowed to be arbitrary unknown non-polynomial functions of system output. Note that such nonlinearities cannot be handled by generalizing the design rationales employed in polynomial rate cases. For this reason, an event-triggered mechanism together with a logic-based switching mechanism is proposed to determine not only when to sample but also when to switch the control parameter. With the help of the switching control parameter, an observer-based control scheme is developed to achieve global output-feedback stabilization. Particularly, the control parameter can be adaptively adjusted to a sufficiently large value, so the proposed control scheme has a stronger capability to deal with large uncertainties, inherent nonlinearities, and sampling errors of the system. For more efficient resource saving, an extended investigation is presented by constructing a dynamic event-triggered scheme. Finally, two simulation examples are given to illustrate the effectiveness of the switching event-triggered schemes.

The problem of global exponential stability (GES) for nonlinear delay impulsive systems is investigated in this paper. By extending the traditional comparison principle, delay effects on continuous and discrete dynamics of the system are estimated, based on which, the internal relationship between delays, parameters of impulsive control, and continuous dynamics of the system is revealed. Then some sufficient criteria are obtained for GES, which quantitatively shows the beneficial influences of delays in impulses on the system performance. Finally, two numerical examples are given to illustrate the effectiveness of the proposed result.

The adaptive distributed observer for a leader system is a fully distributed dynamic compensator for estimating the state variables and the system matrix of a linear leader system over a communication network. In this paper, we first propose an event-triggered implementation of the output-based adaptive distributed observer for a linear leader system over jointly connected communication networks. Then we show that the proposed triggering mechanism not only retains the exponential convergence property of the analog adaptive distributed observer but also prevents the Zeno phenomenon from happening. Our result includes several existing results as special cases and is applicable when the state of the leader system is unavailable. Finally, we apply the proposed event-triggered output-based adaptive distributed observer to solve the cooperative linear output regulation problem. A numerical example is used to validate our design.

In the recent paper (Fei et al., 2019), the study of delay-dependent stability of hybrid stochastic differential delay equations (SDDEs) was generalized to superlinear ones (namely, do not satisfy the usual linear growth condition). However, the theory developed there could not be applied to hybrid SDDEs with non-differentiable time delays, or whose drift coefficients miss the key decomposition in (Fei et al., 2019) (see Assumption 1 below). This paper therefore is to deal with these two challenging problems so that the delay-dependent stability criteria derived in (Fei et al., 2019) could be improved. The decomposition scheme is modified in order to include more general hybrid SDDEs. The differentiability assumption on time-varying delays is replaced by a relatively weaker one. Also the Lyapunov functional used in this paper is modulated to adapt to these new changes. Finally, two interesting examples, an application to mosquito model, and design of nonlinear delay feedback control, respectively, are given to demonstrate the effectiveness of our new theory.

This paper is focused on analysis of Euler–Maruyama-type approximations for stochastic functional differential equations with impulsive perturbations and Markovian switching. The motivation stems from a wide range of applications. The paper establishes mean square convergence of the approximations under a local Lipschitz condition and a linear growth condition. In addition, this work ascertains the rates of convergence of the numerical solutions under the global Lipschitz condition. Finally, the performance of the algorithm is demonstrated through a numerical example.

The article is focused on the problems of positivity and decentralized $L_1$ control for nonlinear interconnected switched positive systems(NISPSs) under mode-dependent dwell time(MDDT) constraint, which includes mode-dependent constant dwell time(MDCDT), mode-dependent minimum dwell time(MDMDT) and mode-dependent ranged dwell time(MDRDT) constraints. Both nonlinear subsystems and nonlinear interconnections are included in the considered NISPSs. First, a sufficient and necessary condition of positivity is presented for NISPSs. Next, by applying a novel discretized linear copositive Lyapunov function method, a sufficient condition of exponential stability with $L_1$-gain performance is provided for NISPSs under MDCDT, MDMDT and MDRDT constraints, respectively. Further, by applying the matrix decomposition technology to the decentralized controller gain matrix, an effective mode-dependent piece-wise design scheme of decentralized $L_1$ controller in the solvable linear programming(LP) form is proposed for NISPSs under MDCDT, MDMDT and MDRDT constraints, respectively. The proposed decentralized $L_1$ controller design scheme for NISPSs under MDDT constraint can be degenerated into the one in mode-independent constraint case accordingly. At last, four examples with comparisons are given to illustrate the importance and effectiveness of the obtained results.