L2-gain Performance Research Articles

On finite-time stability and stabilization of positive systems with impulses

This study investigates finite-time stability and stabilization problems for positive systems with impulses. By constructing a time-varying copositive Lyapunov function and utilizing the average impulsive interval approach, the finite-time stability criterion is established for the first time by exposing different impulsive effects. The relationship between the impulses and the length of the finite time interval is revealed via both theoretical analysis and simulations. As an extension, the finite-time L1 gain performance is also addressed. Based on the finite-time stability results, the finite-time controller design problem is studied to guarantee the positivity and finite-time stability of the corresponding closed-loop system. The obtained criteria can be checked by the linear programming method. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Asynchronous Switching Control for Continuous-time Switched Linear Systems with Output-feedback

This paper investigates the asynchronous switching control problem for continuous-time switched linear systems via dynamic output-feedback, where the dynamic output-feedback controller contains an impulsive reset law to reset the controller state. A time-varying multiple Lyapunov-like-function (MLF) approach is employed to analyze the stability and weighted L2-gain of the closed-loop systems. The switching stability criteria for the closed-loop systems are established in terms of linear matrix inequalities (LMIs), which are dependent on the upper and lower bounds of the switching interval and the asynchronous delays. The switching logic is designed to guarantee the closed-loop systems achieving the weighted L2-gain performance. Two numerical examples are provided to show the effectiveness of the proposed method.

L1 filtering for continuous-discrete T-S fuzzy positive Roesser model

This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l1 performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l1-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results.

Stochastic Stability, ℒ1-gain and Control Synthesis for Positive Semi-Markov Jump Systems

This paper treats the problems of stochastic stability, ℒ1-gain and control synthesis for positive semi-Markov jump systems (S-MJSs). The system under consideration involves semi-Markov stochastic process related to Weibull distribution. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing works have some conservation. To deal with these problems, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear co-positive Lyapunov function. Then, some sufficient conditions for ℒ1-gain constraint are also presented, upon which, a state feedback controller is designed by decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable with ℒ1-gain performance in the form of standard linear programming (LP). The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, numerical examples are given to demonstrate the validity of the main results.

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

SummaryThis paper presents a novel design approach for the finite frequency (FF) H∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ℓ2 gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ℓ2 gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.

H∞ output-feedback control for discrete-time switched linear systems via asynchronous switching

In this paper, we consider the H∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l2-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l2-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.

Stability and L1-gain analysis for switched positive T–S fuzzy systems under asynchronous switching

This paper is concerned with the exponential stability and L1-gain analysis problem for switched positive T–S fuzzy systems under both time-varying delays and asynchronous switching. By permitting the increase of the designed multiple Lyapunov functionals during the running time of the activated subsystem, solvable conditions for the stability and L1-gain are developed by adopting the mode-dependent average dwell time (MDADT) technique. The desired controllers guaranteeing the stability and the L1-gain performance are designed based on the obtained solvable conditions. An example is given to demonstrate the effectiveness of the proposed methods.

Stochastic stability and [formula omitted]-gain analysis for positive nonlinear semi-Markov jump systems with time-varying delay via T-S fuzzy model approach

This paper treats the issues of stochastic stability and L1-gain analysis for continuous-time positive fuzzy semi-Markov jump systems (PFSMJSs) with time-varying delay. The system under consideration involves semi-Markov stochastic process related to Weibull distribution. The practical systems such as Lotka–Volterra population model described by PFSMJSs always need to consider the sudden change in the operating process. To deal with these problems, a sufficient condition for stochastic stability of PFSMJSs is established, which is dependent of the bound of time-varying delay. Then, based on the obtained results, L1-gain performance is analyzed in standard linear programming (LP). Finally, Lotka–Volterra population model shows the validity of the conclusions.

Dwell-time-dependent asynchronous H∞ filtering for discrete-time switched systems with missing measurements

Abstract This paper investigates the asynchronous H∞ filtering problem for discrete-time switched systems under dwell time constraint and missing measurements. Based on the proposed dwell-time-dependent Lyapunov function (DTDLF) technique, a novel switching strategy consisting of a time-dependent mechanism and a state-dependent switching mechanism is constructed, such that the resultant filtering error systems are exponentially mean square stable with a weighted l2-gain performance. In addition, the value of the DTDLF is allowed to increase at both the unmatched interval and switching instants. The desired dwell-time-dependent asynchronous H∞ filter is designed in forms of linear matrix inequalities. More incisively, the proposed method is also applicable to switched systems with unstable subsystems. Finally, three simulation examples are provided to illustrate the effectiveness and potential of the developed results.

Linear-parameter-varying-based adaptive sliding mode control with bounded L2 gain performance for a morphing aircraft

Large-scale morphing aircraft can adaptively alter configuration according to the different flight conditions or a variety of missions to ensure the optimal aerodynamic performance. However, this will certainly put forward a higher request to modeling method and controller performance. In this paper, we propose an adaptive sliding mode control strategy with bounded L2 gain performance based on linear-parameter-varying methodology for the robust control of a morphing aircraft with variable span and variable sweep angle. Using the Kane method, the longitudinal dynamic model of the morphing aircraft is derived. Moreover, the linearized linear-parameter-varying model of the aircraft in the wing varying process is formulated for controller synthesis. The adaptive sliding mode control synthesis for this uncertain linear-parameter-varying system consists of two steps. Firstly, based on the full block S-procedure, the sufficient condition in form of linear matrix inequality constrains is derived for the existence of a reduced-order sliding mode dynamics. Then, the synthesized adaptive sliding mode control is proved to drive the linear-parameter-varying system trajectories onto the predefined switching surface without the information of upper bound of external disturbances. The performance and robustness of the proposed controller are verified by the numerical results.

Asynchronous L1-gain control of uncertain switched positive linear systems with dwell time

In this paper, dwell time (DT) stability, L1-gain performance analysis and asynchronous L1-gain controller design problems of uncertain switched positive linear systems (SPLSs) are investigated. Via a time-scheduled multiple linear co-positive Lyapunov function (TSMLCLF) approach, convex sufficient conditions of DT stability and L1-gain performance of SPLSs with interval and polytopic uncertainties are presented. Furthermore, by utilizing the feature that the TSMLCLF keeps decreasing even if the controller is running asynchronously with the system, the asynchronous L1-gain controller design problem of SPLSs with interval and polytopic uncertainties is investigated. Convex sufficient conditions of the existence of time-varying asynchronous state-feedback controller which can ensure the closed-loop system's positivity, stability and L1-gain performance are established, and the controller gain matrices can be calculated instantaneously online. The obtained L1-gain in the paper is standard. All the results are presented in terms of linear programming. A practical example is provided to show the effectiveness of the results.

Distributed optimal control and [formula omitted] gain performance for the multi-agent system with impulsive effects

In this paper, we investigate the distributed optimal control and L2 gain performance for the multi-agent system with impulsive effects. First, we obtain sufficient conditions to ensure that the distributed protocols can minimize the desired performance index with state-control cross weighting terms. Second, we propose and solve the bounded L2 gain synchronization problem for the impulsive system with hybrid disturbance inputs. Finally, an example is presented to illustrate the efficiency of the obtained results.

Linear Parameter-varying Approach for Modeling and Control of Rapid Thermal Processes

In the present paper, a new approach is presented to model and control single wafer rapid thermal processing (RTP) systems. In the past decade, RTP has achieved acceptance as the mainstream technology for semiconductor manufacturing. Thermal processing is one of the most efficient ways to control the phase-structure properties. Moreover, the time duration of RTP systems reduces the so-called thermal budget significantly compared to the traditional methods. RTP implementation is based on the use of light from heating lamps to provide a heat flux. This process is highly nonlinear due to the radiative heat transfer and material properties. By invoking the first principles-based models, we develop in this paper a linear parameter-varying (LPV) model to directly account for the nonlinearities within the system. The model is then discretized into a high-order LPV model; thereafter, principal component analysis (PCA) method is utilized to reduce the number of LPV model’s scheduling variables, followed by the use of proper orthogonal decomposition (POD) for model order reduction. Using the reduced order model, we then design a gain-scheduled controller to satisfy an induced L2 gain performance for tracking of a temperature profile and show improvement over other controller design methods suggested in the literature.

Networked active vibration control of structural systems: A nonsmall input delay approach

This paper investigates the networked active vibration control for a multi-degree-of-freedom structural system subject to modeling uncertainties, stochastic sensor faults, and earthquake excitations. By adopting a positive velocity feedback controller and introducing a communication network that produces proper network-induced delays and packet dropouts in the feedback control loop, the closed-loop system is first modeled by an uncertain stochastic system with a nonsmall interval time-varying input delay. Then a delay-dependent criterion is derived by employing a complete Lyapunov–Krasovskii functional such that the stochastic system with the proper nonzero input delay is stochastically stable with L2-gain performance, but unstable without delay. An iterative algorithm is presented to design the networked controller. A three-storey shear-beam building model subject to the El Centro 1940 earthquake is given to validate the proposed approach.

L2-gain filter design for continuous-time LPV systems in finite frequency domain

Abstract This paper provides an approach for synthesizing gain-scheduled and robust filters for linear parameter-varying continuous-time systems in finite frequency ranges with guaranteed L2-gain performance. The technique is based on the well-known generalized KYP lemma, which relates frequency-domain inequalities to semi-definite constraints. The time-varying parameters are assumed to be measurable online and, furthermore, to have known bounds of variation. Filtering design conditions with guaranteed L2-gain performance are proposed in the form of parameter-dependent linear matrix inequalities (LMIs), which can be solved in terms of LMI relaxations. Numerical examples borrowed from the literature illustrate the advantages (improved performance) of the proposed approach when compared to other available methods.

Stability analysis and L1-gain controller synthesis of switched positive T–S fuzzy systems with time-varying delays

Abstract This paper is concerned with the stability analysis and L1-gain controller synthesis problem of continuous-time switched positive T–S fuzzy systems with time-varying delays. Some sufficient conditions guaranteeing the stability and a desired L1-gain performance of an autonomous switched positive T–S fuzzy system are first presented. The sufficient conditions are developed by adopting the mode-dependent average dwell time (MDADT) technique. Then, fuzzy controllers of two classes of switched positive T–S fuzzy systems are designed without using iterative algorithm. A simulation example is presented to show the effectiveness of the obtained theoretical results.

Stability and L 1-Gain Analysis for Switched Positive T–S Fuzzy Systems with Time-Varying Delay

This paper deals with the problems of stability and L 1-gain analysis for a class of continuous-time switched positive T–S fuzzy systems with time-varying delay by implying average dwell time switching signals. Firstly, by implying the multiple linear co-positive Lyapunov–Krasovskii functional and average dwell time methods, some sufficient conditions are derived to guarantee the exponential stability of switched positive T–S fuzzy systems with time-varying delay. Then, the weighted L 1-gain performance is investigated for the system considered. Finally, a real-world example about the Lotka–Volterra population model is given to demonstrate the validity of the main results.

Finite frequency filter design for nonlinear 2-D continuous systems in T–S form

This paper considers the problem of filter design for two-dimensional (2-D) continuous nonlinear systems in Takagi–Sugeno (T–S) form. Disdomain. The so-called FF L2 gain is defined for 2-D continuous systems which extends the standard L2 gain. Our attention is focused on designing filters that guarantee the bounded-input-bounded-output (BIBO) stability and the FF L2 gain performance of the filtering error system. The existence conditions of fuzzy filters are obtained in terms of solving linear matrix inequalities (LMIs). An example is given to validate the proposed methods.

Exponential stability and [formula omitted]-gain analysis for positive time-delay Markovian jump systems with switching transition rates subject to average dwell time

The paper deals with the problems of exponential stability and L1-gain analysis for positive time-delay Markovian jump systems (MJSs) with switching transition rates. Another set of useful regime-switching model is given, which extends fixed transition rates to time-varying transition rates. By resorting to the linear co-positive Lyapunov function and average dwell time, sufficient conditions for exponential stability are proposed in terms of standard linear programming. Based on the obtained results, L1-gain performance is analyzed. Finally, an example is proposed to illustrate the validity of the main results.

ℓ2 gain analysis and state feedback stabilization of switched systems with multiple additive time-varying delays

This paper focuses on the problem of ℓ2 gain analysis and state feedback stabilization for a class of switched systems with multiple additive time-varying delays. First, a new model about switched systems with multiple additive time-varying delays is given. Then, based on the extended dynamic delay interval (EDDI) method, we construct a new multiple Lyapunov function. Combing average dwell-time method, reciprocally convex combination technique and Wirtinger interval inequality to estimate the bounding of the integral term, the stability criteria and ℓ2 gain performance of switched systems are given. At last, based on the stability results, the state feedback stabilization problem of the switched systems is studied. The results of sufficient conditions are shown in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the effectiveness of the proposed methods.