Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

Input-to-state stability and gain computation for networked control systems

This paper studies the stability problem for networked control systems.A general result,called network gain theorem,is introduced to determine the input-to-state stability(ISS)for interconnected nonlinear systems.We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS.For the case of linear networked systems,a complete characterisation of the stability condition is provided,together with two distributed algorithms for computing the network gain:the classical Jacobi iterations and a message-passing algorithm.For the case of nonlinear networked systems,characterisation of the ISS condition can be done using M-functions,and Jacobi iterations can be used to compute the network gain.

Estimation of LISS(local input-to-state stability) properties for nonlinear systems

Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.

A Notion of Stochastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems

In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.

Adaptive Fuzzy Torque Control of Passive Torque Servo Systems Based on Small Gain Theorem and Input-to-state Stability

Passive torque servo system （PTSS） simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturbance is called extra torque. The most important issue for PTSS controller design is how to eliminate the influence of extra torque. Using backstepping technique, adaptive fuzzy torque control （AFTC） algorithm is proposed for PTSS in this paper, which reflects the essential characteristics of PTSS and guarantees transient tracking performance as well as final tracking accuracy. Takagi-Sugeno （T-S） fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied using small gain theorem and the control system is proved to be semiglobally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an electric load simulator （ELS）, and the comparative experimental results indicate that AFTC controller is effective for PTSS.

Input-to-state stability of switched nonlinear systems

The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.

Adaptive input-to-state stable synchronization for uncertain time-delay Lur’e systems

This paper is dedicated to the study of adaptive input-to-state stable synchronization of uncertain time-delay Lur’e systems with exterior interference. With the help of the Lyapunov function approach, a sufficient condition for the input-to-state stability of the synchronization-error system is derived, which is theoretically less conservative than a previously reported criterion in the absence of parameter uncertainties. On the basis of the present condition, a co-design of the feedback gain and estimates of the uncertain parameters is given to determine the desired adaptive synchronization controller. Finally, an example with simulations is provided to demonstrate the applicability and superiority of the analysis and design strategies.

Input-to-state stability theorem and strict Lyapunov functional constructions for time-delay systems on time scales

In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one always prefers to construct the strict Lyapunov functionals to analyse stability of time-delay systems.However,it may be not an easy task to do this for some timedelay systems.This paper proposes an input-to-state stability theorem based on a time-scale uniformly asymptotically stable function.The advantage of this theorem is that it is dependent on the non-strict Lyapunov functional,whose time-scale derivative can be non-negative on some time intervals.Then,some approaches are established to construct the strict Lyapunov functionals based on the non-strict ones.It is shown that input-to-state stability theorems can be also formulated in terms of these strict Lyapunov functionals.Finally,to illustrate the effectiveness of the main results,an example is given.

Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

A Nonlinear Observer Approach of SOC Estimation Based on Hysteresis Model for Lithium-ion Battery

In this paper, a state of charge(SOC) estimation approach for lithium-ion battery based on equivalent circuit model and the input-to-state stability(ISS) theory has been proposed. According to the electrochemical performance of lithiumion battery, the equivalent circuit model with two RC networks is established, which includes hysteresis characteristic in inner electrochemical response process. The nonlinear relation between open circuit voltage(OCV) and SOC is obtained from a rapid test. Exponential fitting method is used to identify the parameters of the model. A novel state observer based on ISS theory is designed for lithium-ion battery SOC estimation. The designed observer is tested on AMESim and Simulink co-simulation. The simulation results show that the proposed method has a high SOC estimation accuracy with an error of about 2 percent.

Adaptive stabilization for cascade nonlinear systems

An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.

Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach

A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel distributed compensation （PDC） and linear matrix inequality （LMI） approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling.Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability.Finally,the error caused by fuzzy modeling is considered and the input-to-state stable （ISS） method is used to design the adaptive compensation term to reduce the effect of the modeling error.By the small-gain theorem,the resulting closed-loop system is proved to be input-to-state stable.Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded.The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.

Generic Modeling and Control Framework for Power Systems Dominated by Power Converters Connected Through a Passive Transmission and Distribution Grid

In this paper,a compact mathematical model having an elegant structure,together with a generic control framework,are proposed for generic power systems dominated by power converters that are interconnected through a passive transmission and distribution(T&D)grid,by adopting the port-Hamiltonian(pH)systems theory and the fundamental circuit theory.The models of generic T&D lines are developed and then the model of a generic T&D grid is established.With the proposed control framework,the controlled converters are proven to be passive and Input-to-State Stable(ISS).The compact mathematical model is scalable and can be applied to power systems with multiple power electronic converters with generic passive controllers,passive local loads,and different types of passive T&D lines connected in a meshed configuration without self-loops,so it is very generic.Moreover,the resulting power system is proven to be ISS as well.The analysis is carried out without assumptions on constant frequency/voltage,constant loads,and/or lossless networks,except the need of passivity for all parts involved,and without using the Clarke/Park transformations or the graph theory.To simplify the presentation,three-phase balanced systems are adopted but the results can be easily adapted for single-phase or unbalanced three-phase systems.

Globally Asymptotic Stabilization for Nonlinear Time-delay Systems with ISS Inverse Dynamics

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.

Partial stability analysis of nonlinear time-varying impulsive systems

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect.The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite.With the help of the notion of stable functions,asymptotic partial stability,exponential partial stability,input-to-state partial stability(ISPS)and integral input-to-state partial stability(iISPS)are considered.Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Measurement feedback control of nonlinear systems:a small-gain approach

This paper presents a new tool for feedback control design of nonlinear systems in the presence of non-smooth measurement errors.We introduce a small-gain design approach to robust control of nonlinear uncertain systems with disturbed measurement.As a design ingredient,a modified gain assignment technique for measurement feedback control of nonlinear uncertain systems is proposed.Through a recursive control design approach,the closed-loop system is transformed into a network of input-to-state stable(ISS)systems and the influences of the measurement errors are represented by ISS gains.The feedback control objective is achieved by applying the cyclic-small-gain theorem to the closed-loop system.Moreover,event-triggered control of nonlinear systems is studied in a unified framework of measurement feedback control.

Modular design of adaptive robust controller for strict-feedback stochastic nonlinear systems

A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters.By using Itô’s differentiation rule,nonlinear damping and adaptive Backstepping procedure,the input-to-state stable controller of global stabilization in probability is developed,which guarantees that system states are bounded and the system has a robust stabilization.According to Swapping technique,we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed.Transient performance of the system is estimated by the norm of error.Results of simulation show the effectiveness of the control algorithms.The modular design,which has a concise hierarchy,is more flexible and versatile than a Lyapunov-based algorithm.

Robust Event-Triggered Control of Nonlinear Systems Under a Global Sector-Bound Condition

This paper studies an event-tniggered control problem for nonlinear systems subject to both external disturbancoes and dy namic uncertainties.It is assumed that the system satisfies a global sector bound condition.To avold infnitely fast samplng,a novel eventriggred sampling mechanism is propoeed,which use8 not only the measuned system state but also an estimation of the inluence of the disturbances.With the propoeed design,the intersampling intervals an be lower bounded by a poeitive constant,and it is independent of botb external disturbances and dynamie umcertainties.Moreover,the doeedl loop event-tniggered system i proved to be input-torstate stable with repect to the extemal disturbances.Advanced smalgain techmigues are;used for the stability analysis of the dloeeil-bop system.