Bounded Real Lemma Research Articles

Fault detection in finite frequency domains for multi‐delay uncertain systems with application to ground vehicle

SummaryThis paper is concerned with the actuator fault detection (FD) problem in finite frequency domains for multi‐delay systems subject to time‐varying affine uncertainties. Because of the existence of time‐varying uncertain parameters, the generalized Kalman–Yakubovic–Popov lemma based finite frequency FD filter design approaches cannot be applied. To tackle this difficulty, a new delay‐dependent bounded real lemma (BRL) is established by using Lyapunov theory and Parseval's theorem to characterize the finite frequency disturbance attenuation and fault sensitivity performances. Moreover, via the obtained BRL, convex FD filter design conditions are then derived by constructing a hyperplane tangent. Finally, the effectiveness and advantages of the proposed FD method are illustrated through a simulation example on a ground vehicle. Copyright © 2014 John Wiley & Sons, Ltd.

Event-based [formula omitted] filtering for sampled-data systems

This paper is concerned with event-based H∞ filtering for sampled-data systems. First, an event-based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated. As a result, communication resources can be saved significantly while preserving the desired H∞ performance. Second, the resulting filtering error system is modeled as a system with an interval time-varying delay. By employing the Lyapunov–Krasovskii functional approach, a new bounded real lemma (BRL) is established such that the filtering error system is asymptotically stable with the prescribed H∞ performance. Third, by performing an invertible linear transformation on the filtering error system, a linear matrix inequality (LMI)-based sufficient condition, which is equivalent to the condition in the BRL, is obtained on the feasibility of the event-based H∞ filtering problem. Consequently, suitable H∞ filters and the event parameters in the event condition can be co-designed provided that a set of LMIs are satisfied. Finally, a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method.

Fault detection for singular multiple time-delay systems with application to electrical circuit

In this paper, an H−/H∞ fault detection (FD) filter is designed for linear singular systems with multiple state delays. System faults and unknown disturbances are assumed to reside in finite frequency ranges. By combining the Parseval theorem and the strict S-procedure, both time domain and frequency domain approaches are used to formulate a new delay-dependent finite frequency bounded real lemma (BRL), which includes some existing results as special cases. Based on the obtained BRL, convex FD filter design conditions are derived in terms of solving a set of linear matrix inequalities (LMIs). The effectiveness of the proposed finite frequency FD method is illustrated through a simulation example on the electrical circuit.

H∞ control for discrete-time singular Markovian jump systems based on the novel bounded real lemma

This paper considers the H∞ control problem for the discrete-time singular Markovian jump systems with partially unknown transition probabilities. First, a new formulation of the bounded real lemma (BRL) for discrete-time singular Markovian jump systems is given by referencing slack variables technique, which ensures the considered systems to be regular, causal and stochastically stable with given H∞ performance index γ. Then, based on this new BRL, the desired controller gains are also presented by solving a set of strict linear matrix inequalities. A numerical example is provided to show the effectiveness and less conservativeness of the proposed methods.

연속과 이산시간 폴리토픽 불확실성을 가지는 특이시스템의 산일성 필터링

This paper considers the problem of continuous and discrete time dissipative filter design method for the -singular systems with polytopic uncertainties. Two bounded real lemmas (BRL) for the robust filters of dissipative singular systems along with the polytopic uncertainties are proposed on the basis of Lyapunov criterion. The sufficient conditions for both continuous and discrete time dissipative filter design methods are derived using the obtained BRL by linear matrix inequality (LMI) approach. Finally, the validities of the proposed methods are shown by numerical examples.

DistributedH∞Sampled-Data Filtering over Sensor Networks with Markovian Switching Topologies

This paper considers a distributedH∞sampled-data filtering problem in sensor networks with stochastically switching topologies. It is assumed that the topology switching is triggered by a Markov chain. The output measurement at each sensor is first sampled and then transmitted to the corresponding filters via a communication network. Considering the effect of a transmission delay, a distributed filter structure for each sensor is given based on the sampled data from itself and its neighbor sensor nodes. As a consequence, the distributedH∞sampled-data filtering in sensor networks under Markovian switching topologies is transformed intoH∞mean-square stability problem of a Markovian jump error system with an interval time-varying delay. By using Lyapunov Krasovskii functional and reciprocally convex approach, a new bounded real lemma (BRL) is derived, which guarantees the mean-square stability of the error system with a desiredH∞performance. Based on this BRL, the topology-dependentH∞sampled-data filters are obtained. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Improve results on delay-dependent robust H<SUB align="right">∞ control for uncertain systems with interval time-varying delay

This paper considers the delay-dependent robust H∞ control problem for a class of linear systems with interval time-varying delay and norm-bounded uncertainties. An improved delay-dependent bounded real lemma (BRL) for the systems is established based on a new candidate Lyapunov-Krasovskii (L-K) functional and linear matrix inequality (LMI). Then by applying the BRL, a memoryless state feedback H∞ controller such that the resulting closed-loop system is asymptotically stable and satisfied a prescribed H∞ performance level for all admissible uncertainties is deduced. Finally, numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method.

New delay-dependent bounded real lemmas of polytopic uncertain singular Markov jump systems with time delays

This paper addresses the H∞ performance analysis problem for singular Markov jump delayed systems with polyhedral parameter uncertainties. By introducing two useful inequalities (see Lemma 2), some new bounded real lemmas (BRLs) are obtained based on a novel parameter-dependent Lyapunov functional. The presented BRLs can guarantee that the considered system is stochastically admissible and satisfies a prescribed H∞ performance level. Two numerical examples are provided to demonstrate the improvement of the proposed method over the existing methods.

Exponential $H_{\infty}$ Filtering for Singular Markovian Jump Systems With Mixed Mode-Dependent Time-Varying Delay

This paper is concerned with the exponential H∞ filter design for a class of continuous-time singular Markovian jump systems with mixed mode-dependent time-varying delay. By constructing a new Lyapunov-Krasovskii functional and utilizing some advanced techniques, a less conservative delay-dependent bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs), which guarantees the considered system is exponentially admissible with H∞ performance. Based on the BRL, the H∞ filtering problem is solved and an explicit expression of the desired filter can be given. Two numerical examples are presented to illustrate the effectiveness and the potential of the proposed techniques.

Fault detection, isolation and estimation for Takagi–Sugeno nonlinear systems

This article is dedicated to the problem of fault detection, isolation and estimation for nonlinear systems described by a Takagi–Sugeno (T–S) model. One of the interests of this type of models is the possibility to extend some tools and methods from the linear system case to the nonlinear one. The principle of the proposed strategy is to transform the problem of simultaneously minimizing the perturbation effect and maximizing the fault effect, on the residual vector, in a simple problem of L2-norm minimization. A linear system is used to define the ideal response of the residual signal to the fault. Then the aim is to synthesize a residual generator that both minimizes the difference between real and ideal responses and the influence of the disturbance. The minimization problem is formulated by the bounded real lemma (BRL) and linear matrix inequality (LMI) formalism. After studying the general framework, a special case of systems with actuator and sensor faults is considered where the fault incidence matrix is not full column rank. Simulation examples are given to illustrate the proposed method. Finally, Polya's theorem is used to reduce the conservatism of the proposed result. The obtained relaxation is also illustrated by a numerical example.

H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities

AbstractThis paper focuses on mode‐dependent H∞ state‐feedback control for a class of discrete‐time Markovian jump systems (MJSs) with partial information on transition probabilities (TPs). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma (BRL) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H∞ controllers are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.

H ∞ output tracking control for delta operator systems with insensitivity to controller coefficient variations

The problem of designing insensitive H ∞ output tracking controller for discrete-time systems is studied in a unified framework by using the delta operator approach. A type of coefficient sensitivity performance measure is first developed tomeasure the sensitivity of the transfer function with respect to controller coefficient variations, and the corresponding controller design problem is naturally reformulated as a mixed-objective H ∞ control problem. It is worth mentioning that a novel bounded real lemma (BRL), i.e. Theorem 1 in this article, for delta operator systems is obtained, which is adapted to deal with the multi-objective optimisation problem or polytopic uncertain systems in a potentially less conservative framework. Then, based on the novel lemma, an linear matrix inequality (LMI)-based design method is proposed for achieving the output tracking purpose. Finally, a numerical example based on the linearised model of F-18 aircraft is given to illustrate the effectiveness of the proposed method.

Improved H ∞ analysis of Markovian jumping stochastic systems with time-varying delays

This article investigates the problems of H ∞ analysis for Markovian jump stochastic systems with both nonlinear disturbance and time-varying delays. By virtue of the delay partition approach, the improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump stochastic systems are obtained in terms of linear matrix inequalities (LMIs). The proposed approach involves neither free weighting matrices nor any model transformation, and it is shown that the new criteria have the capability of providing less conservative results than the state-of-the-art. Two numerical simulations are conducted to demonstrate the effectiveness of the proposed method in comparison with existing methods.

Delay-DependentH∞Control for Descriptor Markovian Jump Systems with Time-Varying Delay

This paper is concerned with the delay-dependentH∞control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribedH∞performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.

A Novel Approach toH∞Control Design for Linear Neutral Time-Delay Systems

This paper is concerned with the problem ofH∞control of linear neutral systems with time-varying delay. Firstly, by applying a novel Lyapunov-Krasovskii functional which is constructed with the idea of delay partitioning approach, appropriate free-weighting matrices, an improved delay-dependent bounded real lemma (BRL) for neutral systems is established. By using the obtained BRL, a delay-dependent sufficient condition for the existence of a state-feedback controller, which ensures asymptotic stability and a prescribedH∞performance level of the corresponding closed-loop system, is formulated in terms of linear matrix inequalities. Some numerical examples are given to illustrate the effectiveness of the proposed design method.

Monotonically convergent ILC systems designed using bounded real lemma

This article is devoted to iterative learning control (ILC) systems design for multiple-input multiple-output (MIMO), linear time-invariant (LTI) plants. With the bounded real lemma (BRL) applied, a linear matrix inequality (LMI) design approach is presented to develop sufficient conditions for the monotonic convergence of the ILC process. It is shown that regardless of a system relative degree, the convergence conditions can be expressed in terms of LMIs, and formulas can be derived for the learning gain matrices design. For ILC determined in this way, two illustrative examples are provided to verify its effectiveness and robustness against structured and polytopic-type uncertainties.

A New Approach to $H_{\infty}$ Filter Design for Systems With Time-Varying State Delay

This brief revisits the robust H∞ filter design problem for systems with a time-varying state delay by an indirect approach. By employing a two-term approximation method, the filtering error system with a time-varying delay is reformulated into a feedback interconnection form, which contains a forward system with two constant time delays and a feedback system with uncertainties. Then, based on the scaled small gain theorem, the asymptotic stability of the filtering error system is examined, and a new delay-dependent bounded real lemma (BRL) is obtained. Based on the BRL, both the full- and reduced-order filter design approaches are proposed. Moreover, immediate extensions of the results are made to systems with polytopic uncertainties. Finally, two illustrative examples are presented to demonstrate the validity of the proposed methods.

Formula omitted] filtering of periodic Markovian jump systems: Application to filtering with communication constraints

In this note, a bounded real lemma (BRL) is established for discrete-time periodic Markov jump linear systems (MJLS) with nonhomogeneous finite state Markov chain. The BRL is formulated as a finite linear matrix inequality (LMI) feasibility problem. An application to H∞ filtering for systems subject to limited communication capacity is then presented.

Delay-dependent [formula omitted] control for singular Markovian jump systems with time delay

This paper deals with the problem of delay-dependent H∞ control for singular Markovian jump systems with time delay. Based on the delay subinterval decomposition approach, a new Lyapunov–Krasovskii functional is proposed to develop the new delay-dependent bounded real lemma (BRL), which ensures the considered system to be regular, impulse-free and stochastically stable with given H∞ performance index γ. Based on this new BRL, the explicit expression of the desired controller gains is also presented by solving a set of strict LMIs. Some numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump linear systems with interval time-varying delays. By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method, the free weighting matrix method, the convex combination method and the delay decomposition approach integratedly, some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.