Stability Of Hybrid Systems Research Articles

Stability of short memory fractional-order hybrid systems

The stability theory of short memory fractional-order hybrid systems is studied in this article. Sufficient conditions of asymptotic stability and ultimately bounded stability for the nonlinear short memory fractional-order hybrid systems are proposed respectively. For the convenience of application, a convenient criterion of stability for the nonlinear short memory fractional-order hybrid systems is derived in the study. Demonstrative examples are given to verify the correctness of the proposed theorems in the part of simulation.

Fixed-Time Stability of Time-Varying Hybrid Systems with Time-Delay

Fixed-Time Stability of Time-Varying Hybrid Systems with Time-Delay

Predictor‐based continuous‐discrete nonlinear observer design subject to aperiodic sampled and delayed measurement

AbstractIn this paper, a predictor‐based continuous‐discrete nonlinear observer is proposed for a class of nonaffine Lipschitz nonlinear systems with aperiodic sampled delayed output measurements and external disturbance. Firstly, this study introduces a class of delayed sampling hybrid nonlinear systems. By employing Lyapunov techniques and trajectory‐based stability theory, sufficient conditions are established for ensuring input‐to‐state stability of the delayed sampling hybrid nonlinear system with respect to external disturbances. Then the predictor‐based continuous‐discrete nonlinear observer is designed which consists of a continuous‐time observer, a compensating injector and a predictor. The continuous‐time observer is utilized to obtain continuous and delay‐free state estimation. The compensating injector is designed to compensate for output errors that occur between sampling instants. Furthermore, the predictor is employed to obtain delay‐free output error information, which is then utilized by the continuous‐time observer for feedback correction. The proposed observer's exponential input‐to‐state property against the disturbance is proved via the proposed hybrid system stability theory. The effectiveness of the proposed observers has been demonstrated through numerical simulations and performance comparisons with the zero‐order holder‐based observer and the output predictor‐based observer designs in order to highlight the effectiveness and advantages of the proposed observer.

Conical Transition Graphs for Analysis of Asymptotic Stability in Hybrid Dynamical Systems

A method is proposed for analyzing asymptotic stability in the conical approximation of a hybrid system. Specifically, this paper introduces the conical transition graph (CTG) to simplify the analysis of asymptotic stability in conical approximations by converting solutions to a hybrid system into walks through a discrete graph. By exploiting the fact that pre-asymptotic stability in a conical approximation implies pre-asymptotic stability in the original system, a CTG-based approach can establish asymptotic stability in hybrid systems that have nonlinear flow maps and jump maps without needing to construct a Lyapunov function.

Analysis and verification of uniform moment exponential stability for stochastic hybrid systems with Poisson jump

Analysis and verification of uniform moment exponential stability for stochastic hybrid systems with Poisson jump

A Bidirectional Virtual Inertia Control Strategy for the Interconnected Converter of Standalone AC/DC Hybrid Microgrids

The interconnected converter (IC) links the ac and dc microgrids (MGs) and exchanges powers to maintain the hybrid system stability. However, inertia stored in the ac or dc side cannot be transferred through IC to support each other flexibly according to demand. This paper proposes a novel bidirectional virtual inertia (BVI) control strategy for the IC with an inertia transferring mechanism. IC actively transfers the inertial power to balance the transient performance of both sides of the interconnected MGs. The adaptive strategy is proposed for coefficients of the BVI control to change the inertial power flexibly according to the inertia gap caused by disturbances. Experimental results demonstrate that the proposed strategy of transferring inertia strikes a transient balance between the dc voltage and ac frequency and hence, enhance the transient stability of the hybrid system.

Hybrid System Stability Analysis of Multilane Mixed-Autonomy Traffic

Hybrid System Stability Analysis of Multilane Mixed-Autonomy Traffic

Weak convergence and stability of stochastic hybrid systems with random delay driven by a singularly perturbed Markov chain

This paper focuses on stability of stochastic hybrid systems with random delay driven by a singularly perturbed Markov chain. By weak convergence and the martingale method, the limit system is obtained. Using the limit system as a bridge, this paper establishes the moment exponential stability of the original system by Razumikhin-type techniques. Finally, an example is given to illustrate this result.

Stability of hybrid system with the interaction of continuous and discrete states

Stability of hybrid system with the interaction of continuous and discrete states

Finite-time stability of hybrid systems with continuous and Boolean dynamics

The hybrid systems with continuous and discrete variables can be used to describe many real-world phenomena. In this paper, by generalizing the mathematical form of gene regulatory networks, a novel class of hybrid systems consisting of continuous and Boolean dynamics is investigated. Firstly, the new hybrid system is introduced in detail, and a concept of finite-time stability (FTS) for it is proposed. Next, the existence and uniqueness of solutions are proved by fixed point theory. Furthermore, based on Lyapunov functions and the semi-tensor product (STP), i.e., Cheng product, some sufficient conditions of FTS for the hybrid systems are presented. The main results are illustrated by two numerical examples.

Ergodicity and stability of hybrid systems with piecewise constant type state-dependent switching

To deal with stochastic hybrid systems with general state-dependent switching, we propose an approximation method by a sequence of stochastic hybrid systems with piecewise constant type switching. The convergence rate in the Wasserstein distance is estimated in terms of the difference between transition rate matrices. Our method is based on an elaborate construction of coupling processes in terms of Skorokhod’s representation theorem for jumping processes. Moreover, we establish explicit criteria on the ergodicity and stability for stochastic hybrid systems with piecewise constant type switching. Some examples are given to illustrate the sharpness of these criteria.

Exponential Stability of Fractional-Order Switched Systems With Mode-Dependent Impulses and Its Application.

Most exiting results for impulsive switched systems (ISSs) are mainly built on the synchronous switching and impulses case; however, the impulses can not only occur in switched interval including switched instants but also the switched signals may exist between two impulsive points in practical instants. Under asynchronous impulses and switching signals, the main objective of this article is to study the exponential stability of fractional-order hybrid systems. In order to better characterize stability, some novel criteria are presented by adopting the mode-dependent average impulsive interval and induction method. The obtained impulsive switched criteria lead to a tradeoff between fractional-order α and impulsive strength. Especially, the impulsive effects (positive or negative) with the order α are also discussed in detail, which extends the previous integer order results. Moreover, numerical examples are given to interpret and verify the effectiveness of the obtained criteria.

General stabilization of non-autonomous hybrid systems with delays and random noises via delayed feedback control

The feedback control, derived from delayed state observations, was triumphantly imported to H∞ and exponentially stabilize an unstable nonlinear hybrid system with time-invariant delay and random noise, which is adapt to autonomous systems. Spontaneously, given an unstable non-autonomous hybrid system with time-dependent delay and random noise, can one import a feedback control, derived from delayed state and mode observations, to stabilize it? Fortunately, this will be well done by the approach of multiple Lyapunov functionals. Surprisingly, it is revealed that the stabilization can be achieved not only in the forms of H∞ stability and exponential speed but also of polynomial speed and general speed. Furthermore, the interesting result with respect to polynomial growth at most is as well yielded here.

Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion

G-Brownian motion has potential applications in uncertainty problems and risk measures, which has attracted the attention of many scholars. This study investigates the almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion. Due to the non-linearity of G-expectation and distribution uncertainty of G-Brownian motion, it is difficult to study this issue. Firstly, the existence of the global unique solution is derived under the linear growth condition and local Lipschitz condition. Secondly, the almost sure exponential stability of the system is analyzed by applying the G-Lyapunov function and G-Itô formula. Finally, an example is introduced to illustrate the stability. The conclusions of this paper can be applied to the stability and risk management of uncertain financial markets.

Real time power management strategy for fuel cell hybrid electric bus based on Lyapunov stability theorem

The fuel cell/battery durability and hybrid system stability are major considerations for the power management of fuel cell hybrid electric bus (FCHEB) operating on complicated driving conditions. In this paper, a real time nonlinear adaptive control (NAC) with stability analyze is formulated for power management of FCHEB. Firstly, the mathematical model of hybrid power system is analyzed, which is established for control-oriented design. Furthermore, the NAC-based strategy with quadratic Lyapunov function is set up to guarantee the stability of closed-loop power system, and the power split between fuel cell and battery is controlled with the durability consideration. Finally, two real-time power management strategies, state machine control (SMC) and fuzzy logic control (FLC), are implemented to evaluate the performance of NAC-based strategy, and the simulation results suggest that the guaranteed stability of NAC-based strategy can efficiently prolong fuel cell/battery lifespan and provide better fuel consumption economy for FCHEB.

Globally stable proportional‐integral‐derivative control for spacecraft pose tracking via dual quaternions

Due to the high reliability and simple adjustment, proportional-integral-derivative (PID) control is widely used in practical systems. However, intrinsic non-linearity of the pose dynamics hinders the design of a PID pose controller. Besides, topological constraints on the rigid body configuration space SE(3) prevent a continuous or a memoryless discontinuous state feedback control from achieving robust global stability. For these two issues, this paper develops a dual quaternion-based hybrid PID pose tracking control strategy, where the newly introduced integral term can compensate for constant disturbances, and the hysteretic switching-based hybrid feedback can avoid both unwinding phenomenon and noise sensitivity caused by the topological constraints. In addition, by adjusting the hysteresis width, the proposed hybrid PID controller can also become a continuous or a discontinuous PID controller. The global asymptotic stability in the presence of constant disturbance forces and torques, and robustness to measurement noises are proven by the hybrid system stability theory. Numerical simulations for an earth-orbiting spacecraft pose tracking mission are conducted to illustrate and compare the performances of the proposed hybrid, continuous and discontinuous PID pose tracking control laws.

Exponential stability and hybrid [formula omitted]-gain analysis of hybrid systems via max functions

This paper investigates exponential stability and hybrid L2h-gain performance for a class of hybrid systems. A novel Lyapunov function composed of two max functions, one describing the flow-storage function and the other describing the jump-storage function, is presented to analyze these problems. Due to the effect of flow set, jump set and a timer, the novel Lyapunov function is allowed to increase along flows with a bounded increasing rate and is required to decrease to compensate the possible increasing energy, which relax the constraint on non-increasing requirement of existing common quadratic functions in literature. Then, a stability criterion of hybrid systems is obtained, which can also be used to judge the stability of hybrid systems with unstable flow behaviors. Furthermore, this paper studies the effect of two external disturbances in flows and jumps of hybrid systems, while most literature only study external disturbances existing in flows. The concept of hybrid L2h-gain is first presented to hybrid systems. By analyzing hybrid L2h-gain performance of hybrid systems, one can obtain that L2-gain performance for flows or l2-gain performance for jumps can be improved by degrading the other one. Finally, two numerical examples are provided to illustrate the effectiveness and reliability of the results.

Effect of CTAB surfactant on the stability and thermal conductivity of mono and hybrid systems of graphene and FMWCNT nanolubricant

This experimental investigation focuses on the effect of Cetrimonium bromide (CTAB) surfactant on different categories of nanolubricant in terms of stability and thermal conductivity. There are six categories, four as mono nanolubricant listed as Graphene (GR), GR with CTAB, Functionalised Multi-wall carbon nanotube (FMWCNT), FMWCNT with CTAB, and another two categories as hybrid nanolubricant listed as a hybrid, and hybrid with CTAB nanolubricants. High-grade polyester SL68 Oil is used as a lubricant in this experimental study. Zeta potential measurement, Ultraviolet-visible (UV–vis) spectroscopy, and visual observation by backlighted light-emitting diode (LED) stage are used to evaluate and obtain the nanolubricant stability changes. KD2 Pro Thermal Properties Analyzer is used in thermal conductivity analysis. The study revealed hugely different ratios for the optimum CTAB amount of the studied categories. The best ratio for GR is 1:1, whereas the best ratio for FMWCNT is 1:8. In addition, improvement between 2% and 7% in thermal conductivity is revealed compared to pure oil.

Decomposable dissipativity and stability analysis of hybrid systems

This paper proposes definitions of decomposable dissipativity and decomposable passivity for a class of hybrid systems to investigate stability properties and dissipativity-based control of this kind of hybrid system. Decomposable dissipativity is established via employing multiple flow-storage functions, jump-storage functions, flow-supply rates and jump-supply rates, which allows each subsystem to have its own storage function and supply rate. The decomposable dissipativity reveals the energy changes of activated and inactivated subsystems. Based on the proposed definitions, sufficient conditions of guaranteeing the stability of hybrid systems are derived, which relax the constraint on non-positive supply rates. Then, dissipativity- and passivity-based controllers are designed. In order to demonstrate the usefulness and effectiveness of the obtained results, two examples are provided.

On Stability for State Constrained Hybrid Systems via Barrier Lyapunov Functions

In this paper, the stability of familiar state constrained hybrid systems is considered. In the first, we prove the invariant set stability for the state constrained impulsive hybrid systems. Specifically, a robust control feedback method is applied for state constrained uncertain impulsive hybrid systems. With the auxiliary matrix assistance, some convergence criteria are derived to guarantee robust stability for state constrained uncertain hybrid systems with output disturbance by constructing the symmetric and asymmetric barrier Lyapunov functions (BLF), respectively. Finally, two comparative examples with simulations show that the proposed results are effective and superior.