Exponential stabilization of distributed parameter switched systems under dwell time constraints

The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.

Control of switched systems with actuator saturation

This paper is concerned with controller synthesis for linear switched systems with actuator saturation. Based on common Lyapunov function technique and multiple-Lyapunov function technique, two methods for designing state feedback controller are proposed respectively in terms of linear matrix inequalities for the switched systems with saturation. An approach on enlarging the attractive domain is then investigated, The application of the presented approach is illustrated finally by a numerical example.

Delay-dependent robust H∞ control for a class of uncertain switched systems with time delay

For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H∞ feedback controller was formulated in nonlinear matrix inequalities solvable by an LMI-based iterative algorithm. Compared with the conventional state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.

Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems

A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality （LMI） approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

Distributed H2/H∞ Filter Design for Discrete-Time Switched Systems

This paper addresses an infinite horizon distributed H2/H∞ filtering for discrete-time systems under conditions of bounded power and white stochastic signals. The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling. Herein, we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed H2 and H∞ schemes over a finite horizon. A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances. It is shown that the stability of the overall filtering-error system with H2/H∞ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed. A simulation example is given to show the effectiveness of the proposed approach.

H_∞ Control Based on LMIs for a Class of Time-delay Switched Systems

The problem of H∞ stability analysis and control synthesis of switched systems with delayed states under arb/trary switchirg laws is considered. By means of Lyapunov function and linear matrix inequality tools, sufficient ctmdition of H∞ stability is presented in terms of linear matrix inequalities. Furthermore, the robust H∞ control synthesis via state feedback and output feedack is studied. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Optimization problems for switched systems with impulsive control

By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybridcontrols, which includes continuous control and impulsive control. The linear quadratic optimizationproblems without constraints such as optimal hybrid control, optimal stability and optimalswitching instants are addressed in detail. These results are applicable to optimal control problemsin economics,mechanics, and management.

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function （SLF） method with Finsler＇s Lemma. Based on linear matrix inequality （LMI） a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.

A notion of passivity for switched systems with state-dependent switching

A passivity concept for switched systems with state-dependent switching is presented. Each subsystem has a storage function to describe the ＂energy＂ stored in the subsystem. The passivity property of a switched system is given in terms of multiple storage functions. Each storage function is allowed to grow on the ＂switched on＂ time sequence but the total growth is bounded by a certain function. Stability is inferred from passivity and asymptotic stability is achieved under further assumptions of a detectivity property of a local form and boundedness of the total change of some storage function on its inactive intervals. A state-dependent switching law that renders the system passive is also designed.

Control synthesis of linear distributed parameter switched systems

The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.

An LMI-based variable structure control for a classof uncertain singular Markov switched systems

An H-infinifty variable structure control is presented for singular Markov switched systems with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances. It is shown that the sliding mode dynamics on the given switching surface is regular, impulse-free, and stochastically stable and satisfies H-infinity performance. A variable structure controller is designed to guarantee that the system trajectory converges to the linear switching surface in some finite time. Finally, a numerical example is solved to show the effectiveness and validness of the theoretical results.

Observer-based adaptive control of uncertain time-delay switched systems with stuck actuator faults

This paper concerns the observer-based adaptive control problem of uncertain time-delay switched systems with stuck actuator faults. Under the case where the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and a suitable switching logic is incorporated to ensure the closed-loop system stability and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained in terms of linear matrix inequalities based on piecewise Lyapunov stability theory. On the other hand, adaptive laws for on-line updating of some of the controller parameters are also designed to compensate the effect of stuck failures. Finally, simulation results for reference [1] model show that the design is feasible and efficient.

Robust H_∞ output feedback controller design for linear uncertain discrete-time switched systems via state reset

This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller under arbitrary switching signals,in which an H∞ performance is required. The condition is shown in the form of linear matrix inequalities (LMI). Finally,a numerical example shows the feasibility of the designed controller and illustrates that the new sufficient condition has lower conservation and more optimized H∞ tfperformance.

Output Feedback Robust H_(∞) Control for Discrete 2D Switched Systems

The two-dimensional(2-D)system has a wide range of applications in different fields,including satellite meteorological maps,process control,and digital filtering.Therefore,the research on the stability of 2-D systems is of great significance.Considering that multiple systems exist in switching and alternating work in the actual production process,but the system itself often has external perturbation and interference.To solve the above problems,this paper investigates the output feedback robust H_(∞)stabilization for a class of discrete-time 2-D switched systems,which the Roesser model with uncertainties represents.First,sufficient conditions for exponential stability are derived via the average dwell time method,when the system’s interference and external input are zero.Furthermore,in the case of introducing the external interference,the weighted robust H_(∞)disturbance attenuation performance of the underlying system is further analyzed.An output feedback controller is then proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed disturbance attenuation levelγ.All theorems mentioned in the article will also be given in the form of linear matrix inequalities(LMI).Finally,a numerical example is given,which takes two uncertain values respectively and solves the output feedback controller’s parameters by the theorem proposed in the paper.According to the required controller parameter values,the validity of the theorem proposed in the article is compared and verified by simulation.

Event-triggered finite-time guaranteed cost control of asynchronous switched systems under the round-robin protocol via an AED-ADT method

This paper focuses on addressing the problems of finite-time boundedness and guaranteed cost control in switched systems under asynchronous switching.To reduce redundant information transmission and alleviate data congestion of sensor nodes,two schemes are proposed:the event-triggered scheme(ETS)and the round-robin protocol(RRP).These schemes are designed to ensure that the system exhibits good dynamic characteristics while reducing communication resources.In the field of finite-time control,a switching signal is designed using the admissible edge-dependent average dwell time(AED-ADT)method.This method involves a slow AED-ADT switching and a fast AED-ADT switching,which are respectively suitable for finite-time stable and finite-time unstable situations of the controlled system within the asynchronous switching interval.By constructing a double-mode dependent Lyapunov function,the finite-time bounded criterion and the controller gain of the switched systems are obtained.Finally,the validity of the proposed results is showcased by implementing a buck-boost voltage circuit model.

Interpolated Bumpless Transfer Control for Asynchronously Switched Linear Systems

This paper revisits the problem of bumpless transfer control(BTC) for discrete-time nondeterministic switched linear systems. The general case of asynchronous switching is considered for the first time in the field of BTC for switched systems. A new approach called interpolated bumpless transfer control(IBTC) is proposed, where the bumpless transfer controllers are formulated with the combination of the two adjacent modedependent controller gains, and are interpolated for finite steps once the switching is detected. In contrast with the existing approaches, IBTC does not necessarily run through the full interval of subsystems, as well as possesses the time-varying controller gains(with more flexibility and less conservatism) achieved from a control synthesis allowing for the stability and other performance of the whole switched system. Sufficient conditions ensuring stability and H_(∞) performance of the underlying system by IBTC are developed, and numerical examples verify the theoretical findings.

EXPONENTIAL STABILITY OF LINEAR DISTRIBUTED PARAMETER SWITCHED SYSTEMS WITH TIME-DELAY

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems(DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS' exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities(LOIs)where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities(LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

Fault Detection for Uncertain Delta Operator Systems with Two-Channel Packet Dropouts via a Switched Systems Approach

This paper utilizes a switched systems approach to deal with the problem of fault detectio for uncertain delta operator networked control system with packet dropouts and timevarying delays.Uncertainties exist in the matrices of the systems and are norm-bounded time-varying.Two parts of packet dropouts are considered in this paper:From sensors to controllers,and from controllers to actuators.Two independent Bernoulli distributed white sequences are introduced to account for packet dropouts.Then an FD filter is designed under an arbitrary switching law.Furthermore,the sufficient conditions for the NCSs under consideration that are exponentially stable in the mean-square sense and satisfy H∞performance are obtained in terms of linear matrix inequalitie,multiple Lyapunov function and average dwell-tim approach.The explicit expression of the desired filter parameters is given.Finally,a numerical example verifies the effectiveness of the proposed method.

L_2-gain Analysis and Anti-windup Design of Discretetime Switched Systems with Actuator Saturation

This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach.For a given set of anti-windup compensation gains,we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances.Then,the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances.Furthermore,the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality(LMI) constraints.A numerical example is given to illustrate the effectiveness of the proposed design method.

A switched system approach to stabilization of networked control systems

A switched system approach is proposed to model networked control systems （NCSs） with communication constraints. This enables us to apply the rich theory of switched systems to analyzing such NCSs. Sufficient conditions are presented on the stabilization of NCSs. Stabilizing state/output feedback controllers can be constructed by using the feasible solutions of some linear matrix inequalities （LMIs）. The merit of our proposed approach is that the behavior of the NCSs can be studied by considering switched system without augmenting the system. A simulation example is worked out to illustrate the effectiveness of the proposed approach.