Sufficient Conditions For Input-to-state Stability Research Articles

Intermittent event‐triggered control for input‐to‐state stability of stochastic systems

AbstractIn this article, we investigate the input‐to‐state stability (ISS) of stochastic systems via intermittent event‐triggered control. The control update sequence during the control intervals is determined through an event‐triggered mechanism (ETM), where the periodic ETM and continuous ETM are considered separately. For the continuous ETM, a positive minimum inter‐execution time is ensured by adding waiting time, which avoids Zeno behavior. For the periodic ETM, with the help of Halanay‐like inequality, the maximum allowable bound of the sampling period is given. The number of control updates is further reduced by adding a dynamic term. In addition, sufficient conditions for ISS in stochastic systems are proposed by designing an auxiliary timer and applying the Lyapunov method. Finally, two numerical examples are presented to verify the validity of the results.

Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems

This paper investigates the Lyapunov characterizations of input-to-output stability (IOS) and input-to-state stability (ISS) for nonlinear switched systems. The restriction on the negativity of derivatives of Lyapunov functions is relaxed; additionally, subsystems are not restricted to be ISS/IOS throughout the state space. These problems are overcome by a newly proposed method, which extends multiple Lyapunov functions (MLFs) to an indefinite form. Indefinite multiple Lyapunov functions (iMLFs) are proposed on the basis of an inequality to estimate the upper boundary of the system state. Moreover, we apply the iMLFs method to verify the extended notions of IOS in a switched system. More relaxed sufficient conditions for ISS and IOS are proposed, a simulation experiment is carried out on a numerical example of the system, which demonstrates their effectiveness and superiority.

Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well-established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way so that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and time-varying, switched and nonswitched, impulsive and nonimpulsive systems in several directions.

Input-to-State Stability of Time-Delay Systems With Delay-Dependent Impulses

This paper studies input-to-state stability (ISS) of general nonlinear time-delay systems subject to delay-dependent impulse effects. Sufficient conditions for ISS are constructed by using the method of Lyapunov functionals. It is shown that, when the continuous dynamics are ISS but the discrete dynamics governing the delay-dependent impulses are not, the impulsive system as a whole is ISS provided the destabilizing impulses do not occur too frequently. On the contrary, when the discrete dynamics are ISS but the continuous dynamics are not, the delayed impulses must occur frequently enough to overcome the destabilizing effects of the continuous dynamics so that the ISS can be achieved for the impulsive system. Particularly, when the discrete dynamics are ISS and the continuous dynamics are also ISS or just stable for the zero input, the impulsive system is ISS for arbitrary impulse time sequences. Compared with the existing results on impulsive time-delay systems, the obtained ISS criteria are more general in the sense that these results are applicable to systems with delay dependent impulses while the existing ones are not. Moreover, when consider time-delay systems with delay-free impulses, our result for systems with unstable continuous dynamics and stabilizing impulses is less conservative than the existing ones, as a weaker condition on the upper bound of impulsive intervals is obtained. To demonstrate the theoretical results, we provide two examples with numerical simulations, in which distributed delays and discrete delays in the impulses are considered, respectively.

Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative

This paper investigates the input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained, where both types of impulses, stabilizing impulses and destabilizing impulses, are considered. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite, that allows wider applications than existing results in the literature. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.

Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

Analysis of input-to-state stability for discrete time nonlinear systems via dynamic programming

The input-to-state stability (ISS) property for systems with disturbances has received considerable attention over the past decade or so, with many applications and characterizations reported in the literature. The main purpose of this paper is to present analysis results for ISS that utilize dynamic programming techniques to characterize minimal ISS gains and transient bounds. These characterizations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimization problems in nonlinear dissipative systems theory (including L 2 -gain analysis and nonlinear H ∞ theory). As such, the results presented address an obvious gap in the literature.