Composite disturbance‐observer‐based control and H∞ control for complex continuous models

A novel type of control scheme combining the disturbance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of complex continuous models with disturbances. The disturbances are supposed to include two parts. One part in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other part is supposed to have the bounded H₂‐norm. Parametric uncertainties exist both in concerned plant and in exogenous subsystem. The disturbance observers based on regional pole placement and D‐stability theory are designed and integrated with conventional H_∞ control laws. The new composite DOBC and H_∞ control scheme is applied to complex continuous models for the case with known and unknown nonlinearity, respectively. Then the first type of disturbances can be estimated and rejected, and the second type can be attenuated; simultaneously, the desired dynamic performances can be guaranteed. Simulations for a flight control system are given to demonstrate the effectiveness of the results and compare the proposed results with the previous schemes. Copyright © 2009 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.     

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.     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems

This paper investigates the robust H_∞ control problem for stochastic systems with a delay in the state. Sufficient delay‐dependent conditions for the existence of state‐feedback controllers are proposed to guarantee mean‐square asymptotic stability as well as the prescribed H_∞ performance for the closed‐loop systems. Moreover, the results are further extended to the stochastic time‐delay systems with parameter uncertainties, which are assumed to be time‐varying norm‐bounded appearing in both the state and the input matrices. The appealing idea is to partition the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust passivity‐based H∞ control for uncertain switched nonlinear systems

In this paper, we investigate the H_∞ control problem for uncertain switched nonlinear systems with passive and non‐passive subsystems. For any given average dwell time, any given passivity rate and any given disturbance attenuation level, we design feedback controllers of subsystems, which may depend on the pre‐given constants, to solve the H_∞ control problem for the uncertain switched nonlinear systems for all admissible uncertainties. For linear systems, the exponential small‐time norm‐observability is shown to be preserved under disturbance. Two examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

H∞ filtering for singular systems with time‐varying delay

This paper is concerned with the delay‐dependent H_∞ filtering problem for singular systems with time‐varying delay in a range. In terms of linear matrix inequality approach, the delay‐range‐dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H_∞ performance level. The sufficient conditions are proposed for the existence of linear H_∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

This paper presents fault tolerant controllers for a class of one‐sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H_∞ filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H_∞ ‐SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one‐sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed‐loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.     

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.     

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.     

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.     

Robust H∞ controller design for continuous‐time piecewise time‐delay systems

This paper investigates the robust H_∞ control problem for continuous‐time piecewise time‐delay systems by using piecewise continuous Lyapunov function. The uncertainties of the systems under consideration are expressed in a linear fractional form. A strict linear matrix inequality approach is developed to obtain delay‐dependent asymptotic stability conditions and H_∞ performance. The H_∞ controller design problem is solved by exploiting the cone complementarity linearization (CCL) method. Finally an example is given to illustrate the application of the proposed approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H2/H∞ control for time‐delay systems with polytopic uncertainty

In this paper, new separated H_∞ and H₂ performance criteria are derived for a class of time‐delay systems. When used in robust performance analysis and synthesis for real polytopic uncertainty and in multiobjective controller synthesis, they can partially rule out the technical restriction of using a single Lyapunov function, and therefore, lead to potentially less conservative linear matrix inequality (LMI) characterizations. Based on the criteria, robust multiobjective H₂/H_∞ controller is designed for time‐delay systems with polytopic uncertainty. All the conditions are given in terms of LMIs. Numerical examples are given to illustrate the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

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.     

Stability analysis and H∞ control design for a class of nonlinear time‐delay systems

This paper investigates the stability and H_∞ control problem for a class of nonlinear time‐delay systems with a nonsingular Jacobian matrix, and provides a number of new results regarding stability analysis and control design. Firstly, an equivalent form is obtained for this class of systems by means of coordinate transformation and/or orthogonal decomposition of vector fields. Then, based on the equivalent form and free‐weighting matrix method, several sufficient conditions, in terms of nonlinear matrix inequalities, are derived for the stability analysis of the time‐delay systems by constructing suitable Lyapunov functionals. Finally, we use the equivalent form and the obtained stability results to investigate the H_∞ control problem, and present a control design procedure for this class of time‐delay systems. A study of illustrative examples shows that the results obtained in this paper have less conservatism, and work very well in the stability analysis and control design of some nonlinear time‐delay systems. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐dependent adaptive reliable H∞ control of linear time‐varying delay systems

This paper considers the problem of delay‐dependent adaptive reliable H_∞ controller design against actuator faults for linear time‐varying delay systems. Based on the online estimation of eventual faults, the parameters of adaptive reliable H_∞ controller are updating automatically to compensate the fault effects on the system. A new delay‐dependent reliable H_∞ controller is established using a linear matrix inequality technique and an adaptive method, which guarantees the stability and adaptive H_∞ performance of closed‐loop systems in normal and faulty cases. A numerical example and its simulation results illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust stability and H∞ control for uncertain discrete Markovian jump singular systems with mode‐dependent time‐delay

The robust stochastic stability, stabilization and H_∞ control for mode‐dependent time‐delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a standard linear system, and delay‐dependent linear matrix inequalities (LMIs) conditions for the mode‐dependent time‐delay discrete Markovian jump singular systems to be regular, causal and stochastically stable, and stochastically stable with γ‐disturbance attenuation are obtained, respectively. With these conditions, robust stabilization problem and robust H_∞ control problem are solved, and the LMIs sufficient conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper. Copyright © 2008 John Wiley & Sons, Ltd.