On Existence of Solution for Impulsive Perturbed Quantum Stochastic Differential Equations and the Associated Kurzweil Equations

Existence of solution of impulsive Lipschitzian quantum stochastic differential equations (QSDEs) associated with the Kurzweil equations are introduced and studied. This is accomplished within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus and the associated Kurzweil equations. Here again, the solutions of a QSDE are functions of bounded variation, that is they have the same properties as the Kurzweil equations associated with QSDEs introduced in [1, 4]. This generalizes similar results for classical initial value problems to the noncommutative quantum setting

Integral Input-to-State Stability of Nonlinear Time-Delay Systems with Delay-Dependent Impulse Effects

This paper studies integral input-to-state stability (iISS) of nonlinear impulsive systems with time-delay in both the continuous dynamics and the impulses. Several iISS results are established by using the method of Lyapunov-Krasovskii functionals. For impulsive systems with iISS continuous dynamics and destabilizing impulses, we derive two iISS criteria that guarantee the uniform iISS of the whole system provided that the time period between two successive impulse moments is appropriately bounded from below. Then we provide an iISS result for systems with unstable continuous dynamics and stabilizing impulses. For this scenario, it is shown that the iISS properties are guaranteed if the impulses occur frequently enough. For impulsive systems with stabilizing impulses and stable continuous dynamics for zero input, we obtain an iISS result which shows that the entire system is uniformly iISS over arbitrary impulse time sequences. As applications, iISS properties of a class of bilinear systems are studied in details with simulations to demonstrate the presented results

Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results

Strong exponential stability of switched impulsive systems with mode-constrained switching

Strong stability, defined by bounds that decay not only over time but also with the number of impulses, has been established as a requirement to ensure robustness properties for impulsive systems with respect to inputs or disturbances. Most existing results, however, only consider weak stability. In this paper, we provide a method for calculating the maximum overshoot and the decay rate for strong (and weak) global uniform exponential stability bounds for non-linear switched impulsive systems. We consider the scenario of mode-constrained switching where not all transitions between subsystems are allowed, and where subsystems may exhibit unstable dynamics in the flow and jump maps. Based on direct and reverse mode-dependent average dwell-time and activation-time constraints, we derive stability bounds that can be improved by considering longer switching sequences for computation. We provide numerical examples that illustrate the weak and strong exponential stability bounds and also how the results can be employed to ensure the stability robustness of nonlinear systems that admit a global state weak linearization.Comment: 23 pages, 4 figure

Robust Tracking Control for Switched Fuzzy Systems with Fast Switching Controller

This paper addresses the problem of designing robust tracking controls for a class of switched fuzzy (SF) systems with time delay. A switched fuzzy system, which differs from existing ones, is firstly employed to describe a nonlinear system. Next, a fast switching controller consisting of a number of simple subcontrollers is proposed. The smooth transition is governed by using the fast switching controller. Tracking hybrid control schemes which are based upon a combination of the H∞ tracking theory, fast switching control algorithm, and switching law design are developed such that the H∞ model referent tracking performance is guaranteed. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are conducted to demonstrate the effectiveness of the proposed control design approach. All results illustrate good control performances as desired

On Stability and Stabilization of Hybrid Systems

The thesis addresses the stability, input-to-state stability (ISS), and stabilization problems for deterministic and stochastic hybrid systems with and without time delay. The stabilization problem is achieved by reliable, state feedback controllers, i.e., controllers experience possible faulty in actuators and/or sensors. The contribution of this thesis is presented in three main parts. Firstly, a class of switched systems with time-varying norm-bounded parametric uncertainties in the system states and an external time-varying, bounded input is addressed. The problems of ISS and stabilization by a robust reliable $H_{\infty}$ control are established by using multiple Lyapunov function technique along with the average dwell-time approach. Then, these results are further extended to include time delay in the system states, and delay systems subject to impulsive effects. In the latter two results, Razumikhin technique in which Lyapunov function, but not functional, is used to investigate the qualitative properties. Secondly, the problem of designing a decentralized, robust reliable control for deterministic impulsive large-scale systems with admissible uncertainties in the system states to guarantee exponential stability is investigated. Then, reliable observers are also considered to estimate the states of the same system. Furthermore, a time-delayed large-scale impulsive system undergoing stochastic noise is addressed and the problems of stability and stabilization are investigated. The stabilization is achieved by two approaches, namely a set of decentralized reliable controllers, and impulses. Thirdly, a class of switched singularly perturbed systems (or systems with different time scales) is also considered. Due to the dominant behaviour of the slow subsystem, the stabilization of the full system is achieved through the slow subsystem. This approach results in reducing some unnecessary sufficient conditions on the fast subsystem. In fact, the singular system is viewed as a large-scale system that is decomposed into isolated, low order subsystems, slow and fast, and the rest is treated as interconnection. Multiple Lyapunov functions and average dwell-time switching signal approach are used to establish the stability and stabilization. Moreover, switched singularly perturbed systems with time-delay in the slow system are considered