LMI Conditions Research Articles

<i>H</i>∞ performance analysis and switching control design for uncertain discrete switched time-delay systems

The H∞ performance analysis and switching control of uncertain discrete switched time-delay systems with linear fractional perturbations are studied in this paper. The design of a simple switching signal is developed to acquire LMI conditions which achieve H∞ performance and switching control of discrete switched time-delay system. The conservativeness of obtained results can be improved by using the delay-partitioning approach. The using LMI variables number is less than our past proposed non-negative inequality approach. Finally, we use some numerical examples to illustrate the major improvement of the developed results.

Delay-Dependent State-Feedback Dissipative Control for Suspension Systems With Constraints Using a Generalized Free-Weighting-Matrix Method

This paper presents a novel delay-dependent dissipative control synthesis technique with a state-feedback structure for input-delayed suspension systems using a tighter bounding technique. By more accurately estimating the derivative of the LKF, we focus on reducing the conservatism of the state-feedback control synthesis for suspension systems with strict design constraints. New LMI conditions for a desired state-feedback controller are developed by employing a generalized free-weighting-matrix (GFWM) method. By solving the LMIs, the proposed controller for active suspension systems is obtained such that the closed-loop systems have asymptotic stability with guaranteed $(\mathcal {Q},\mathcal {S},\mathcal {R})$ -dissipative performances, while also satisfying the design constraint conditions. Numerical simulations effectively confirm the benefits of the proposed control synthesis technique for the design of state-feedback control.

Stability analysis of LPV systems under aperiodic sampled-data dynamic output feedback control

Abstract This paper addresses the problem of asymptotic stability assessment of LPV systems under aperiodic sampled-data dynamic output feedback control. Based on a looped-functional approach to deal with the aperiodic sampling effects, the continuous and discrete-time behaviors of the plant and controller, respectively, are taken into account. For a given discrete-time stabilizing controller, the obtained LMI conditions can be used to directly certify the stability of the closed-loop system considering the sampling interval in a given range. Moreover, they can be incorporated into an optimization problem to obtain the maximal bounds on the sampling interval for which stability of the closed-loop system is guaranteed. A numerical example with the application of the proposed method is shown.

<i>H</i>∞ performance analysis and switching control design for uncertain discrete switched time-delay systems

The H∞ performance analysis and switching control of uncertain discrete switched time-delay systems with linear fractional perturbations are studied in this paper. The design of a simple switching signal is developed to acquire LMI conditions which achieve H∞ performance and switching control of discrete switched time-delay system. The conservativeness of obtained results can be improved by using the delay-partitioning approach. The using LMI variables number is less than our past proposed non-negative inequality approach. Finally, we use some numerical examples to illustrate the major improvement of the developed results.

Line Integral Approach to Extended Dissipative Filtering for Interval Type-2 Fuzzy Systems

This article is concerned with the problems of extended dissipativity analysis and filter design for interval type-2 (IT2) fuzzy systems. Based on the line integral Lyapunov function, a sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established. A LMI-based equivalent condition to the obtained one in a nonlinear form is provided by combining congruence transformation with change of variables. This LMI condition obtained is more general than the one which is based on the common quadratic Lyapunov function. Meanwhile, in terms of parameterization, the extended dissipative filter is developed which guarantees the asymptotic stability and extended dissipativity for the filtering error system. Furthermore, our filter obtained by the parameterization method includes the one obtained by the equivalent transformation method as a special case. Two simulation examples are provided to show the merits and effectiveness of the proposed approach.

LMI conditions for output feedback control of switched systems based on a time-varying convex Lyapunov function

This paper proposes novel sufficient conditions expressed in terms of linear matrix inequalities for the dynamical output feedback control design of discrete-time switched linear systems. More specifically, an output-dependent switching function together with a full order switched controller are determined in order to assure exponential stability and a guaranteed H2 performance level. The proposed output feedback conditions have some useful properties: (a) they are based on a time-varying convex Lyapunov function, which contributes to reducing conservatism, (b) the controller parameters are independent of the Lyapunov matrices, which lead to time-invariant controller matrices, and (c) the conditions are expressed in terms of linear matrix inequalities being easier to solve, but not necessarily more conservative than other techniques available in the literature. Two academic examples are used for validation and comparison with other techniques from the literature.

Decentralized Suboptimal State Feedback Integral Tracking Control Design for Coupled Linear Time-Varying Systems

In this paper, a suboptimal state feedback integral decentralized tracking control synthesis for interconnected linear time-variant systems is proposed by using orthogonal polynomials. Particularly, the use of operational matrices allows, by expanding the subsystem input states and outputs over a shifted Legendre polynomial basis, the conversion of time-varying parameter differential state equations to a set of time-independent algebraic ones. Hence, optimal open-loop state and control input coefficients are forwardly determined. These data are used to formulate a least-square problem, allowing the synthesis of decentralized state feedback integral control gains. Closed-loop asymptotic stability LMI conditions are given. The proposed approach effectiveness is proved by solving a nonconstant reference tracking problem for coupled inverted pendulums.

Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems

Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems

Switching fuzzy modelling and control scheme using T-S fuzzy systems with nonlinear consequent parts

This paper extends the idea of switching T-S fuzzy systems with linear consequent parts to nonlinear ones. Each nonlinear subsystem is exactly represented by a T-S fuzzy system with Lure’ type consequent parts, which allows to model and control wider classes of switching systems and also reduce the computation burden of control synthesis. With the use of a switching fuzzy Lyapunov function, the LMI conditions for asymptotic stability of the system with maximum decay-rate and disturbance attenuation properties under arbitrary switching law are derived. Moreover, several numerical examples are provided to demonstrate the effectiveness of the proposed approaches to reduce the computational burden of control synthesis and improving the closed-loop performance of the system.

Global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays

This paper focus on the problem of global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays. By choosing a proper variable substitution, an inertial neural network consisting of second-order differential equations can be converted into a first-order differential model. The sufficient conditions of the inertial neural network with neutral delay are derived by constructing suitable Lyapunov-Krasovskii functional candidates, introducing new free weighting matrices, utilizing inequality techniques and analytical method. Through the LMI condition, we analyze the global exponential stability of the delayed inertial neural networks in Lagrange sense. Meanwhile, the global exponential attractive set is also given. Finally, some example is given to illustrate our theoretical results.

Intermediate variable observer based fault estimation and fault-tolerant control for nonlinear stochastic system with exogenous disturbance

This paper focuses on the problems of fault estimation and fault-tolerant control for a class of nonlinear system with noise and exogenous disturbance. A novel intermediate variable observer and a disturbance observer are designed to estimate the system state, actuator fault, sensor fault and exogenous disturbance, simultaneously. Based on the estimation information, an observer based fault-tolerant controller is proposed. The LMI conditions are obtained to ensure that the whole closed-loop system is mean-square exponentially stable with the H∞ performance. At last, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

Robust control with an anti-windup technique based in relaxed LMI conditions for LTV system

Robust control with an anti-windup technique based in relaxed LMI conditions for LTV system

Robust control with an anti-windup technique based in relaxed LMI conditions for LTV system

This paper proposes a new technique to address the anti-windup (AW) with model predictive control (MPC) scheme for linear time-varying (LTV) systems. The main advantage of this new approach is the reduced conservativeness compared with other well-known anti-windup techniques and to prevent integration windup in MPC controllers when the actuators are saturated. The control with AW is applied in a three-state switching cell (3SSC) DC-DC converter operating under saturation conditions. The MPC with proposed anti-windup is compared with the MPC technique and with MPC-AW without relaxation. The MPC-AW with relaxation improves the performance when the converter operated in the saturated mode and allows the rational use of the converter. The simulation results validated the efficiency of the proposed approach and showed that the proposed approach not only allows working better with the polytope modeling but also improves the response under LTV disturbance.

Robust Sliding Window Observer-Based Controller Design for Lipschitz Discrete-Time Systems

The aim of this paper is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. The observer and the controller are enriched with sliding windows of measurements and estimated states, respectively. This technique allows to increase the number of decision variables and thus get less restrictive and more general LMI conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI). The obtained constraint is transformed, through a useful approach, to a more suitable one easily tractable by standard software algorithms. Numerical example is given to illustrate the performances of the proposed approach.

Gain-scheduled ℋ∞ controller synthesis for LPV systems subject to multiplicative noise

This paper proposes LMI conditions to design parameter-dependent (i.e. gain-scheduled) state-feedback controllers that ensure closed-loop stability with guaranteed ℋ∞ performance for both continuous and discrete-time LPV systems with state multiplicative noise. The state-space matrices and the multiplicative noise matrix are considered polytopic and independent. The time-varying parameters can be considered time-invariant, arbitrarily fast or with bounded rates of variation. The advantages of the proposed technique are illustrated by numerical examples borrowed from the literature.

Monotonically Convergent Iterative Learning Control for Piecewise Affine Systems

Piecewise affine (PWA) systems enable modelling of systems that encompass hybrid dynamics and nonlinear effects. The aim of this paper is to develop an ILC framework for PWA systems. A new approach to analyse monotonic convergence is developed for PWA systems. This is achieved by exploiting the incremental l2-gain leading to sufficient LMI conditions guaranteeing monotonic convergence. An example confirms the monotonic convergence property for ILC applied to a mass-spring-damper system with a one-sided spring.

Sensor blending and Control allocation for non-square linear systems to achieve negative imaginary dynamics

This paper deals with the design of static pre- and post- compensators to transform stable, non-square LTI systems into the class of strongly strict negative imaginary systems. The pre-compensator plays the role of a control allocator while the post-compensator does sensor blending in order to make a non-square system square along with satisfying the strongly strict negative imaginary property. A specific structure of the post-compensator is also given that guarantees a feasible solution of the LMI conditions when applied to systems with number of outputs greater than or equal to number of inputs. The proposed pre- and post- compensators can also stabilize a non-square plant in closed-loop upon satisfying a particular DC-gain condition and furthermore, they can be utilized to develop a simple constant input tracking framework for non-square systems. The LMI-based design methodology offers a numerically tractable solution framework and hence the easy implementation of the proposed scheme in practical applications. Illustrative examples are provided throughout the paper to demonstrate the usefulness of the proposed results in widening the scope of the negative imaginary theory to non-square LTI systems (e.g. safety-critical systems having redundant sensors and actuators).

On a new generalised LMI condition and randomised algorithm for robust stabilisation via static-output-feedback

ABSTRACTFor a given system with time-invariant affine uncertainties, ranging in a unit hypercube or, equivalently, in a hyper-rectangle, new LMI sufficient conditions for the verification of a given simultaneous static-output-feedback for hypercube nodes, being robust static-output-feedback for the whole system, are proved. The conditions generalise previous results in the sense that we do not assume that the state-to-measurement or the input-to-state matrix is constant. Based on the LMI conditions, a randomised algorithm is suggested. The effectiveness of the method is reinforced through experiments on real-life systems.

Finite-Time $$L_\infty $$ Performance State Estimation of Recurrent Neural Networks with Sampled-Data Signals

This paper, by proposing a sampled-data control scheme, we investigate the finite-time $$L_\infty $$ performance state estimation of recurrent neural networks. By constructing a novel Lyapunov functional, new stability and stabilization conditions are derived. By utilizing integral inequality techniques, sufficient LMI conditions are derived to ensure the finite-time stability of considered neural networks. Furthermore, finite-time observer gain analysis of recurrent neural networks is set up to measure its disturbance tolerance capability in the fixed time interval. Numerical examples are given to verify the effectiveness of the proposed approach.

The Lyapunov-based stability analysis of reduced order micro-grid via uncertain LMI condition

This paper proposed a new three-step method for studying dynamic stability of an islanded micro-grid (MG). In conventional methods, state-space model linearization around an operating point and modal analysis are utilized. Due to lower inertia and operation of MG in islanding mode, MG is more sensitive to changes of parameters and contingencies. Therefore, small signal stability (sss) analysis has a very limited validity range and large signal studies should be also performed to get an appropriate perception of the system stability. In this paper, beside sss study to determine network stability status around a dominant operating point, an algorithm based on multi-time scale systems theory is suggested to detect slow and fast modes which can be used for system decomposition into fast and slow subsystems. Fast modes have large negative real values and/or damping ratios, which can be eliminated in large signal stability analysis with an appropriate approximation. Therefore, singular perturbation theory is used to reduce the model order and extract the network slow subsystem. Then, the Lyapunov function can be applied to reduced model. In addition, continuous load and the renewable distributed generators power variations in the system cause to wide range of changes in the operating point and state space model of the system. Therefore, the copula distribution is proposed to model the uncertainties. Then, the uncertain LMI condition based on scenarios extracted from the copula is used to determination of the Lyapunov function and the attraction domain. Finally, the attraction domain sensitivity to MG parameters change is studied to achieve sufficient insight about the system stability margins.