Delay-dependent H ∞ controller design for linear neutral systems with discrete and distributed delays

This article considers the delay-dependent H _∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H _∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H _∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.     

H ∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation

In this article, H _∞ structured model reduction is addressed for linear discrete systems. Two important classes of systems are considered for structured model reduction, i.e. Markov jump systems and uncertain systems. The problem we deal with is the development of algorithms with the flexibility to allow any structure in the reduced-order system design, such as the structure of an original system, decentralisation of a networked system, pole assignment of the reduced system, etc. The algorithms are derived such that an associated model reduction error guarantees to satisfy a prescribed H _∞ norm-bound constraint. A new condition for the existence of desired reduced-order models preserving a certain structure is presented in a set of linear matrix inequalities (LMI) and non-convex equality constraints. Effective computational algorithms involving LMI are suggested to solve the matrix inequalities characterising a solution of the structured model reduction problem. Numerical examples demonstrate the advantages of the proposed model reduction method.     

Delay-dependent observer-based stabilizing controller design for linear multiple state-delayed systems

This article concerns a coupled LMIs approach to delay-dependent observer-based output feedback stabilizing controller design for linear continuous-time systems with multiple state delays. The advantage of our proposed delay-dependent coupled LMIs criterion lies in that: (1) it can optimize one of multiple time delays with others selected properly, and at the same time, the feedback-gain and observer-gain can be obtained, respectively. (2) it is less conservative than the existing delay-independent ones in the literature. Algorithm to solve the coupled LMIs is also given. Numerical examples illustrate the effectiveness of our method.     

H∞ controller design for linear systems with time-invariant uncertainties

This paper considers the problem of designing robust H _∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H _∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H _∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.     

Adaptive robust H ∞ filter design for linear systems with time-varying uncertainty

This article studies the problem of designing robust H _∞ filters for linear uncertain systems. The uncertainty parameters are assumed to be time-varying, unknown, but bounded, which appear affinely in the matrices of system models. An adaptive mechanism is introduced to construct novel filters with variable gains, which can reduce the conservativeness of the traditional robust H _∞ filters. The proposed adaptive filter design conditions are given in terms of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed strategy.     

On the design of a reduced-order H ∞ controller for nonlinear sampled-data systems

In this paper, the problem of designing reduced-order H ^∞ controllers is studied for nonlinear continuous-time systems with sampled measurements. Using the concepts of dissipativity and differential game, sufficient conditions are derived for the existence of such reduced-order H ^∞ controllers. These conditions are expressed in terms of the solutions of two Hamilton–Jacobi inequalities, comprising a standard Hamilton–Jacobi inequality and a differential Hamilton–Jacobi inequality with jumps. These Hamilton–Jacobi inequalities are exactly those used in the construction of full-order H ^∞ controllers. When these conditions hold, state-space formulae are also given for such reduced-order controllers. An illustrative example is also included.     

Robust H∞ controller design for dynamic consensus networks

This paper studies an H_∞ suboptimal control problems of consensus networks whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. We apply model, orthogonal and diagonal transformations to a dynamic consensus network in order to reduce the overall system into N ? 1 independent subsystems. We then establish a generalised methodology for designing a controller for a dynamic consensus network in the presence of external disturbances, focusing especially on using decentralised controllers that achieve consensus in the absence of disturbances and attenuation of disturbances to a prescribed H_∞ performance level. A design example is given to illustrate our results.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

Relaxed stability condition and state feedback H ∞ controller design for T-S fuzzy systems

In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback H _∞ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback H _∞ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better H _∞ performance. The effectiveness of the proposed approach is shown through two numerical examples. Recommended by Editor Young-Hoon Joo. Xiao-Heng Chang received the B.E. and M.S. degrees from Liaoning Technical University, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, China, in 2007. He is currently a Lecturer in the School of Information Science and Engineering, Bohai University, China. His research interests include fuzzy control and robust control as well as their applications. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

H ∞ filtering for Markovian jump linear systems

The problem of H X filtering for continuous-time linear systems with Markovian jump is investigated. It was assumed that the jumping parameter was available. This paper develops necessary and sufficient conditions for designing a Markovian jump linear filter that ensures a prescribed bound on the L 2 -induced gain from the noise signals to the estimation error. The main result is tailored via linear matrix inequalities.     

Quantised H ∞ filter design for discrete-time systems

This article is concerned with the quantised H _∞ filtering problem for discrete-time systems. The quantiser considered here is dynamic and composed of a dynamic scaling and a static quantiser. Motivated by practical transmission channels requirements, the static quantiser ranges are fully considered in this article. A quantised H _∞ filter design strategy is proposed, taking quantiser errors into account, where a convex optimisation method is developed to minimise static quantiser ranges with meeting H _∞ performance requirement for quantised augmented systems. A numerical example is given to illustrate the effectiveness of the proposed filter design method.     

New results on robust H ∞ filtering design for discrete-time piecewise linear delay systems

This paper revisits the problem of robust H _∞ filtering design for a class of discrete-time piecewise linear state-delayed systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel delay-dependent piecewise Lyapunov–Krasovskii functional combined with Finsler's Lemma, a new delay-dependent sufficient condition for robust H _∞ performance analysis is first derived and then the filter synthesis is developed. It is shown that by using a new linearisation technique, a unified framework can be developed so that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.