H∞ control for a class of cascade switched nonlinear systems

In this paper, we investigate the H_∞ control problem for a class of cascade switched nonlinear systems consisting of two nonlinear parts which are also switched systems using the multiple Lyapunov function method. Firstly, we design the state feedback controller and the switching law, which guarantees that the corresponding closed‐loop system is globally asymptotically stable and has a prescribed H_∞ performance level. This method is suitable for a case where none of the switched subsystems is asymptotically stable. Then, as an application, we study the hybrid H_∞ control problem for a class of nonlinear cascade systems. Finally, an example is given to illustrate the feasibility of our results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Singular H∞ control for nonlinear systems

This paper presents a solution to the singular H_∞ control problem via state feedback for a class of nonlinear systems. It is shown that the problem of almost disturbance decoupling with stability plays a fundamental role in the solution of the considered problem. We also point out when the singular problem can be reduced to a regular one or solved via standard H_∞ technique. We must stress that the solution of the singular problem is obtained without making any approximation of it by means of regular problems. © 1997 John Wiley & Sons, Ltd.     

Exponential H∞ filtering for switched linear systems with interval time‐varying delay

This paper deals with the problem of exponential H_∞ filtering for a class of continuous‐time switched linear system with interval time‐varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay‐derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H_∞ noise attenuation level. Based on the free‐weighting matrix approach and the average dwell technology, delay‐dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results. Copyright © 2008 John Wiley & Sons, Ltd.     

Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach

In this paper, the problem of exponential H_∞ filter problem for a class of discrete‐time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete‐time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ‐dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode‐dependent full‐order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H_∞ performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Discrete‐time robust H∞control of a class of nonlinear uncertain systems

This paper presents an approach to discrete‐time robust H^∞ control for a class of nonlinear uncertain systems on the basis of the use of Sum Quadratic Constraints. The approach involves controllers, which include copies of the system nonlinearities in the controller. The nonlinearities being considered are those that satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using linear robust H^∞ control theory, and this leads to a nonlinear controller, which gives an upper bound on the attainable disturbance attenuation level. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ estimation for uncertain systems

This paper deals with the problem of H_∞ estimation for linear systems with a certain type of time-varying norm-bounded parameter uncertainty in both the state and output matrices. We address the problem of designing an asymptotically stable estimator that guarantees a prescribed level of H_∞ noise attenuation for all admissible parameter uncertainties. Both an interpolation theory approach and a Riccati equation approach are proposed to solve the estimation problem, with each method having its own advantages. The first approach seems more numerically attractive whilst the second one provides a simple structure for the estimator with its solution given in terms of two algebraic Riccati equations and a parameterization of a class of suitable H_∞ estimators. The Riccati equation approach also pinpoints the ‘worst-case’ uncertainty.     

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

The current article discusses the H_∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H_∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.     

Robust H∞ nonlinear control via measurement feedback

This paper deals with the problem of finite-time-horizon robust H_∞ control via measurement feedback, for affine nonlinear systems with nonlinear time-varying parameter uncertainty. The problem addressed is the design of a control law, which processes the measured output and guarantees a prescribed level of closed-loop disturbance attenuation. Conditions for the existence of such a controller are obtained by solving an auxiliary control problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. This approach allows us to apply the recently developed H_∞ nonlinear control techniques to solve the robust control problem. The problem is investigated in both the continuous- and discrete-time cases. The results are demonstrated by a simple example. © 1997 by John Wiley & Sons, Ltd.     

Network‐based H∞ control for stochastic systems

This paper investigates the problem of network‐based control for stochastic plants. A new model of stochastic time‐delay systems is presented where both network‐induced delays and packet dropouts are taken into consideration for a sampled‐data network‐based control system. This model consists of two successive delay components in the state, and we solve the network‐based H_∞ control problem based on this model by a new stochastic delay system approach. The controller design for the sampled‐data systems is carried out in terms of linear matrix inequalities. Finally, we illustrate the methodology by applying these results to an air vehicle control problem. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust filtering for a class of discrete-time uncertain nonlinear systems: An H∞ approach

This paper deals with the H_∞ filtering problem for a class of discrete-time nonlinear systems with or without real time-varying parameter uncertainty and unknown initial state. For the case when there is no parametric uncertainty in the system, we are concerned with designing a nonlinear H_∞ filter such that the induced l₂ norm of the mapping from the noise signal to the estimation error is within a specified bound. It is shown that this problem can be solved via one Riccati equation. We also consider the design of nonlinear filters which guarantee a prescribed H_∞ performance in the presence of parametric uncertainties. In this situation, a solution is obtained in terms of two Riccati equations.     

On H∞-control of discrete-time nonlinear systems

Following recent works on continuous-time nonlinear H_∞-control, where connections with game theory and passivity conditions have been set, the present paper studies the corresponding problem for discrete-time systems. The paper describes sufficient conditions for the existence and the construction of a feedback law which imposes a prescribed level of disturbance attenuation with internal stability. Both cases of state feedback and measurement feedback are considered.     

Robust H∞ control for uncertain discrete‐time systems with probabilistic state delays

In this paper, we propose a novel design problem of robust H_∞ control for discrete‐time systems with probabilistic time delay, where both the variation range of the delay and the probability distribution of the delay taking values in an interval are available. Based on the information on the probability distribution of the delay taking values in an interval, a new modeling method is put forward, with which the probabilistic effects of the delay are reflected into a parameter matrix of certain transformed system. Based on such a new model, criteria for the H_∞ control design are derived by using a combination of the convexity of the matrix equations, the Lyapunov functional method and the linear matrix inequality technique. It is shown via numerical examples that our developed method in the paper can lead to less conservative results than those obtained by existing methods and, furthermore, if the probability distribution of the delay occurrence is available, the allowable upper bound of the delay may be larger than those derived for the case when only the variation range of the delay can be known. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new approach to network‐based H∞ control for stochastic systems

This paper deals with the problem of network‐based H_∞ control for a class of uncertain stochastic systems with both network‐induced delays and packet dropouts. The networked control system under consideration is represented by a stochastic model, which consists of two successive delay components in the state. The uncertainties are assumed to be time varying and norm bounded. Sufficient conditions for the existence of H_∞ controller are proposed to ensure exponentially stable in mean square of the closed‐loop system that also satisfies a prescribed performance. The conditions are expressed in the frame of linear matrix inequalities (LMIs), which can be verified easily by means of standard software. Two practical examples are provided to show the effectiveness of the proposed techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

H∞ balancing for nonlinear systems

In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H_∞ control problem for nonlinear systems we define H_∞ balancing. Furthermore, we investigate the monotonicity of the Hamilton-Jacobi-Bellman equations that appear in this balancing method. The method is used as a tool for model reduction.     

Robust H∞ control of uncertain linear impulsive stochastic systems

This paper develops robust stability theorems and robust H_∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H_∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐dependent exponential H ∞ filtering for discrete‐time switched delay systems

In this paper, the problem of delay‐dependent exponential H _∞ filtering for discrete‐time switched delay systems is investigated under average dwell time switching signals. Time delay under consideration is interval time‐varying in the states. By introducing a proper factor to construct a novel Lyapunov‐Krasovskii function and using average dwell time approach, sufficient conditions for the solvability of this problem, dependent on the upper and lower bounds of time‐varying delay, are obtained in terms of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

In this paper, the problem of finite‐time H _∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H _∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H _∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H _∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H _∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal‐switched extended H∞ filter for nonlinear systems with stochastic uncertainties

The extended H_∞ filter (EH_∞F) is a conservative solution with infinite‐horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH_∞F design, we developed an optimal‐switched (OS) filtering mechanism based on the standard EH_∞F to obtain an optimal‐switched extended H_∞ filter (OS‐EH_∞F). The OS mechanism has an error‐tolerant switched (ETS) structure, which switches the filtering mode between optimal and H_∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS‐EH_∞F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS‐EH_∞F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.