Some New Results on Strong $gamma_k$ -$gamma_{cl} H_{infty}$ Stabilization

The strong $gamma_k{hbox{-}}gamma_{cl}~ H_{infty}$ stabilization problem is addressed in this paper. Based on the bounded real lemma, an improved sufficient condition on strong $H_{infty}$ stabilization as well as its dual form is derived, which extends the ARE constraint in the former results into an inequality constraint. Two path-following algorithms are proposed to solve the associated optimization problems with BMI constraints, which lead to full order controllers. A numerical example is presented to demonstrate the effectiveness of the result.      

Network-Based ${{cal H}}_{!!!infty }$ Output Tracking Control

This paper is concerned with the problem of H_infin output tracking for network-based control systems. The physical plant and the controller are, respectively, in continuous time and discrete time. By using a sampled-data approach, a new model based on the updating instants of the holder is formulated, and a linear matrix inequality (LMI)-based procedure is proposed for designing state-feedback controllers, which guarantee that the output of the closed-loop networked control system tracks the output of a given reference model well in the H_infin sense. Both network-induced delays and data packet dropouts have been taken into consideration in the controller design. The network-induced delays are assumed to have both an upper bound and a lower bound, which is more general than those used in the literature. The introduction of the lower bound is shown to be advantageous for reducing conservatism. Moreover, the controller design method is further extended to more general cases, where the system matrices of the physical plant contain parameter uncertainties, represented in either polytopic or norm-bounded frameworks. Finally, an illustrative example is presented to show the usefulness and effectiveness of the proposed H_infin output tracking design.     

${cal L}_1$ Adaptive Output Feedback Controller for Systems of Unknown Dimension

This note presents novel adaptive output feedback control methodology for systems of unknown dimension in the presence of unmodeled dynamics and time-varying uncertainties. The adaptive output feedback controller ensures uniformly bounded transient and asymptotic tracking for the system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation rate. Simulations of an unstable nonminimum phase system verify the theoretical findings.     

Design of Observer-Based $H_infty$ Control for Fuzzy Time-Delay Systems

This paper addresses the problem of observer-based H_infin control for nonlinear systems with time-varying delay represented by Takagi-Sugeno (T-S) fuzzy model. It presents a single-step linear matrix inequality (LMI) method for the fuzzy control design, which overcomes the drawback of the two-step LMI approach often encountered in the literature. The derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict LMIs. When restricted to delay-free fuzzy systems, the present results improve or reduce to existing ones. Illustrative examples show the effectiveness and merits of the present results.     

Relaxed ${cal H}_{infty }$ Stabilization Conditions for Discrete-Time Fuzzy Systems With Interval Time-Varying Delays

To derive less-conservative delay- and range-dependent ${cal H}_{infty }$ stabilization conditions for discrete-time Takagi–Sugeno (T–S) fuzzy systems with interval time-varying delays, the use of a fuzzy-weighting-dependent Lyapunov–Krasovskii functional (FWLKF), in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions, is proposed. Subsequently, parameterized linear matrix inequality (PLMI)-based ${cal H}_infty$ stabilization conditions are derived by following the free-weighting matrix approach. To fully exploit the convexity of fuzzy weighting functions, the derived PLMIs are sequentially replaced by a finite set of LMIs by considering all possible conditions associated with fuzzy weighting functions.      

Simultaneous $H^{infty}$ Control for Nonlinear Systems

This note develops a novel method for designing simultaneous $H^{infty}$ state feedback controllers for a collection of single-input nonlinear systems. Based on the Kalman—Yakubovich—Popov Lemma, necessary and sufficient conditions for the existence of simultaneous $H^{infty}$ controllers are derived by the control storage function approach. A universal formula for constructing continuous, time-invariant, simultaneous $H^{infty}$ state feedback controllers is presented.      

${cal H}_{infty}$ Filtering of Discrete-Time Markov Jump Linear Systems Through Linear Matrix Inequalities

This technical note addresses the discrete-time Markov jump linear systems ${cal H}_{infty}$ filtering design problem. First, under the assumption that the Markov parameter is measurable, the main contribution is the linear matrix inequality (LMI) characterization of all linear filters such that the estimation error remains bounded by a given ${cal H}_{infty}$ norm level, yielding the complete solution of the mode-dependent filtering design problem. Based on this result, a robust filter design able to deal with polytopic uncertainty is considered. Second, from the same LMI characterization, a design procedure for mode-independent filtering is proposed. Some examples are solved for illustration and comparisons.      

$K$ Constrained Shortest Path Problem

Motivated by a real project for a sophisticated automated storage and retrieval system (AS/RS), we study the problem of generating K shortest paths that are required to satisfy a set of constraints. We propose a structural branching procedure that decomposes the problem into at most K|N| subproblems, where |N| is the number of nodes in the network. By using a Network Modification procedure, each subproblem can be transformed into a constrained shortest path problem (CSP). When these constraints satisfy a so called separable property, the subproblem can be further simplified. Based on this branching procedure, we propose a specific algorithm for an application where resource and loopless constraints have to be respected. Numerical results show that our algorithm is very efficient and robust.     

An Improved Path-Following Method for Mixed ${H} _{2} /{H}_{infty}$ Controller Design

Among the few methods available to solve bilinear matrix inequalities (BMIs) occurring in control design, the path-following method, published some years ago, appears to be one of the best ones, as far as linearization methods are concerned. However, few details are given in the literature about its implementation and limits. In this technical note, this method is applied to the design of mixed H ₂/H _infin controllers with full details of the algorithm and some improvements over the one which has been published a few years ago. The results obtained with the numerical example given in that same publication, as well as with some other examples, are compared with those given by other methods, including a direct BMI-solving program.     

Delay-Dependent $hbox{H}_{infty }$ Filter Design for Discrete-Time Fuzzy Systems With Time-Varying Delays

This paper investigates delay-dependent $hbox{H}_{bminfty }$ filter design problems for discrete-time fuzzy systems with time-varying delays. First, a novel delay-dependent piecewise Lyapunov–Krasovskii functional (DDPLKF) is proposed in which both the upper bound of delays and the delay interval are considered. Based on this DDPLKF, the delay-dependent stability criteria for discrete-time systems with constant or time-varying delays are obtained, respectively. Then, delay-dependent full-order and reduced-order $hbox{H}_{bminfty }$ filter design approaches are proposed. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Simulation examples are also given to illustrate the performance of the proposed approaches. It is shown that our approaches are less conservative and that the corresponding $hbox{H}_{bminfty }$ filters can achieve better performance than the existing approaches.      

Decentralized $H_{infty }$ Filter Design for Discrete-Time Interconnected Fuzzy Systems

This paper describes a decentralized $H_{infty }$ filter design for discrete-time interconnected fuzzy systems based on piecewise-quadratic Lyapunov functions. The systems consist of $J$discrete-time interconnected Takagi–Sugeno (T–S) fuzzy subsystems, and a decentralized $H_infty$ filter is designed for each subsystem. It is shown that the stability of the overall filtering-error system with $H_{infty }$ performance can be established if a piecewise-quadratic Lyapunov function can be constructed. Moreover, the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Two simulation examples are given to show the effectiveness of the proposed approach.      

Design and Analysis of a Novel ${cal L}_1$ Adaptive Control Architecture With Guaranteed Transient Performance

This paper presents a novel adaptive control architecture that adapts fast and ensures uniformly bounded transient response for system's both signals, input and output, simultaneously. This new architecture has a low-pass filter in the feedback loop and relies on the small-gain theorem for the proof of asymptotic stability. The tools from this paper can be used to develop a theoretically justified verification and validation framework for adaptive systems. Simulations illustrate the theoretical findings.     

$H_{infty}$ Filtering for Fuzzy Singularly Perturbed Systems

This paper considers the problem of designing $H_{infty}$ filters for fuzzy singularly perturbed systems with the consideration of improving the bound of singular-perturbation parameter $epsilon$. First, a linear-matrix-inequality (LMI)-based approach is presented for simultaneously designing the bound of the singularly perturbed parameter $epsilon$, and $H_{infty}$ filters for a fuzzy singularly perturbed system. When the bound of singularly perturbed parameter $epsilon$ is not under consideration, the result reduces to an LMI-based design method for $H_{infty}$ filtering of fuzzy singularly perturbed systems. Furthermore, a method is given for evaluating the upper bound of singularly perturbed parameter subject to the constraint that the considered system is to be with a prescribed $H_{infty}$ performance bound, and the upper bound can be obtained by solving a generalized eigenvalue problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.      

New Approach on Robust Delay-Dependent ${H}_infty$ Control for Uncertain T--S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust ${H}_{infty }$ control for Takagi--Sugeno (T--S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.      

Characterization of High-Pressure $hbox{XeF}_{2}$ Vapor-Phase Silicon Etching for MEMS Processing

Typical release for structures in microelectromechanical systems (MEMS) devices requires the use of sacrificial layers and wet etchants. As an alternative, bulk Si can be utilized for nonsilicon MEMS or structures as the sacrificial material when exposed to vapor-phase XeF₂ . This paper presents the results of using relatively high pressures (> 3.0 torr) for the purpose of MEMS processing, while characterizing the physical etching mechanism and its effects on the working Si substrate in relation to the allowed processing time. The observed etch rates for high-pressure release varied from 1.6 to 1.9 mum/min for applied pressures of 4.5-5.5 torr. The resulting roughness is shown to be primarily dependent on time, where the maximum average roughness is approximately 1.4 mum after 3000 s at 5.5 torr. Slightly anisotropic results are produced by the increased pressures, showing a 0.7 : 1.0 (vertical : lateral) etch rate, as well as some detrimental effects to the released structures. Furthermore, the use of etch windows are investigated in relation to etch rate when subjected to these high pressures.     

$H_{infty }$ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links

This paper investigates the problem of H _infin fuzzy control of nonlinear systems under unreliable communication links. The nonlinear plant is represented by a Takagi--Sugeno (T-S) fuzzy model, and the control strategy takes the form of parallel distributed compensation. The communication links existing between the plant and controller are assumed to be imperfect (that is, data packet dropouts occur intermittently, which appear typically in a network environment), and stochastic variables satisfying the Bernoulli random binary distribution are utilized to model the unreliable communication links. Attention is focused on the design of H _infin controllers such that the closed-loop system is stochastically stable and preserves a guaranteed H _infin performance. Two approaches are developed to solve this problem, based on the quadratic Lyapunov function and the basis-dependent Lyapunov function, respectively. Several examples are provided to illustrate the usefulness and applicability of the developed theoretical results.     

Observer-Based Relaxed ${{cal H}}_{infty }$ Control for Fuzzy Systems Using a Multiple Lyapunov Function

This short paper proposes a method of designing a fuzzy observer-based H _infin controller for discrete-time Takagi-Sugeno (T-S) fuzzy systems. To enhance the applicability of the output-feedback controller and improve its performance, this short paper first builds a set of fuzzy control rules with premise variables different from those of the T-S fuzzy system, and sets the overall controller to be dependent on not only the current time but also the one-step-past information on the estimated fuzzy weighting functions. Then, based on the fuzzy control rules, this short paper establishes a less conservative H _infin stabilization condition incorporated with a multiple Lyapunov function dependent on the estimated fuzzy weighting functions. Through a two-step design procedure, the H _infin stabilization condition is formulated in terms of parameterized linear matrix equalities (PLMIs), which are reconverted into LMIs with the help of an efficient and effective relaxation scheme.     

${cal H}_{infty}$ State-Feedback Control Design for Fuzzy Systems Using Lyapunov Functions With Quadratic Dependence on Fuzzy Weighting Functions

This paper proposes a method for designing an ${cal H}_{infty}$ state-feedback fuzzy controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems. To derive less conservative ${cal H}_{infty}$ stabilization conditions, this paper enhances the interactions among the fuzzy subsystems using a multiple Lyapunov function with quadratic dependence on fuzzy weighting functions. Besides, for more allocation of the nonlinearity to the fuzzy control system, this paper introduces a slack variable that is quadratically dependent on the one-step-past fuzzy weighting functions as well as the current ones. In the derivation, the ${cal H}_{infty}$ stabilization conditions are formulated in terms of parameterized linear matrix inequalities (PLMIs), which are reconverted into LMI conditions with the help of an efficient relaxation technique.