Solution Of LMIs Research Articles

Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions

This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

Observer analysis and design for nonlinear bounded Lipschitz systems

Abstract The design of dynamic observers for nonlinear Lipschitz systems has considered great attention in past decades. Instead of applying the standard strictly explicit designs or LMI-based heuristic solutions, in this paper, an efficient systematic method is deployed by considering the existence of some arbitrary bounds on the nonlinear Lipschitz terms. The method enables to relax the observer design from the conventional restrictions and it is easily solved analytically without needing the solution of LMIs. As proven in the paper by a detailed and rigorous analysis, its main advantage is that it guarantees global asymptotic stability and ensures the observer response with desired decay characteristics satisfying simultaneously the Lyapunov equation.

New H∞ dynamic observer design for time-delay systems subject to disturbances

This paper presents a new approach to design an H dynamic observer (DO) for multi-delayed linear systems subject to -norm disturbances. This observer generalises the existing results on the proportional observer (PO), the proportional integral observer (PIO), and the DO. The proposed design approach is derived from the solution of LMIs based on the parametrization results of algebraic constraints. These algebraic constraints can be easily obtained from the unbiasedness conditions of the estimation error. The obtained results are illustrated by a numerical example to show the performances of the proposed observer.

Asynchronous H∞ fixed-order filtering for LPV switched delay systems with mode-dependent average dwell time

This paper investigates the problem of robust H∞ fixed-order filtering for a class of linear parameter-varying (LPV) switched delay systems under asynchronous switching that the system parameter matrices and the time delays are dependent on the real-time measured parameters. The so-called asynchronous switching means that there are time delays between the switching of filters and the switching of system modes. By constructing the parameter-dependent and mode-dependent Lyapunov-Krasovskii functional which is allowed to increase during the running time of active subsystem with the mismatched filter, and using the mode-dependent average dwell time (MDADT) switching method, the sufficient conditions for exponential stability and satisfying a novel weighted H∞ criterion are derived. As there exist couplings between Lyapunov-Krasovskii functional matrices and system parameter matrices, we utilize slack matrices to decouple them. Based on the above results, a suitable weighted H∞ fixed-order filter can be obtained in the form of the parameter linear matrix inequalities (PLMIs). By virtue of approximate basis function and gridding technique, the design of weighted H∞ fixed-order filter can be transformed into the solution of the finite dimensional LMIs. Finally, a numerical example is presented to verify both the effectiveness and the low conservatism of the parameter-dependent and mode-dependent fixed-order filtering method proposed in this paper.

Adaptive output regulation of right-invertible MIMO LTI systems, with application to vessel motion control

The problem of robust output regulation for MIMO linear time-invariant systems with harmonic exogenous inputs and parameter uncertainties is addressed. We discuss two methods to handle stability in the presence of plant uncertainties, that take full advantage of all controls and all available measurements. One method, appeals to a general notion of “robust” minimum-phase. The other method, that addresses the case of unstructured uncertainties, reposes on the solution of appropriate LMIs. In both cases, the critical issue is to show how adaptive tuning of the internal model can be implemented, so as to obtain a controller that guarantees asymptotic convergence of the regulated output to zero. A numerical example of vessel motion control is given to illustrate one of the proposed approaches.

New Approach to Exponential Stability Analysis and Stabilization for Delayed T-S Fuzzy Markovian Jump Systems

This paper is concerned with delay-dependent exponential stability analysis and stabilization for continuous-time T-S fuzzy Markovian jump systems with mode-dependent time-varying delay. By constructing a novel Lyapunov-Krasovskii functional and utilizing some advanced techniques, less conservative conditions are presented to guarantee the closed-loop system is mean-square exponentially stable. Then, the stabilization conditions are derived and the fuzzy controller can be obtained by solving a set solutions of LMIs. The upper bound of time-delay that the system can be stabilized is given by using an optimal algorithm. Two examples are presented to illustrate the effectiveness and potential of our methods.

Stochastic stability analysis for joint process driven and networked hybrid systems

The stochastic stability and impulsive noise disturbance attenuation in a class of joint process driven and networked hybrid systems with coupling delays (JPDNHSwD) has been investigated. In particular, there are two separable processes monitoring the networked hybrid systems. One drives inherent network structures and properties, the other induces random variations in the control law. Continuous dynamics and control laws in networked subsystems and couplings among subsystems change as events occur stochastically in a spatio-temporal fashion. When an event occurs, the continuous state variables may jump from one value to another. Using the stochastic Lyapunov functional approach, sufficient conditions on the existence of a remote time-delay feedback controller which ensures stochastic stability for this class of JPDNHSwD are obtained. The derived conditions are expressed in terms of solutions of LMIs. An illustrative example of a dynamical network driven by two Markovian processes is used to demonstrate the satisfactory control performance.

Design of Anti-Windup Compensators for a Class of Nonlinear Control Systems with Actuator Saturation

This paper addresses the design of static anti-windup compensators for a class of nonlinear systems subject to actuator saturation. Considering that a (possibly nonlinear) dynamic output feedback control law has been previously designed disregarding the saturation, a method to compute a static anti-windup gain which ensures the local stability of the closed-loop system is proposed. The results are based on a differential algebraic representation of rational systems and on a modified version of the generalized sector condition to deal with the saturation effects. From these elements, an algorithm based on the solution of LMIs is proposed to calculate an anti-windup gain to enlarge the region of attraction of the closed-loop system. Moreover, extensions of the results are presented to deal with parameter uncertainty and the presence of energy bounded disturbances. A numerical example is presented to illustrate the proposed method.

Resilient static output feedback power system stabiliser using PSO-LMI optimisation

In this paper, two new power system stabiliser PSS designs are proposed. The first one is based on a combined particle swarm optimisation PSO with linear matrix inequality LMI optimisation thereby improving previous existing results. The property of PSO of not sticking into a local minimum is used to eliminate the conservativeness of the design result utilising the static output feedback SOF stabiliser within an iterative solution of LMIs. The proposed design provides robustness against uncertainties wherein power systems operations are changing continuously due to load changes. In addition to load variations, the second controller is based on a derived sufficient condition using PSO-LMIs optimisation in order to obtain a resilient PSS that takes into consideration controller's parameters uncertainty as well. The effectiveness of the algorithm is shown for a single machine infinite bus power system.

Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties

In this paper, the design problem of state estimator for genetic regulatory networks with time delays and randomly occurring uncertainties has been addressed by a delay decomposition approach. The norm-bounded uncertainties enter into the genetic regulatory networks (GRNs) in random ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the uncertain GRNs. Delay-dependent stability criteria are obtained in terms of linear matrix inequalities by constructing a Lyapunov–Krasovskii functional and using some inequality techniques (LMIs). Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs. Finally, a numerical example is provided to demonstrate the feasibility of the proposed estimation schemes.

Finite time chaos control for a class of chaotic systems with input nonlinearities via TSM scheme

This paper investigates nonsingular terminal sliding mode control for a class of uncertain systems with nonlinear inputs and its application in chaos control. When some of the system states are finite-time stable, the nonlinear items that coupled with these states may come into zeros in other subsystems. This will simplify the stability analysis of the whole system greatly. Compared with the traditional finite-time stabilization design method, the introduction of the terminal sliding mode can reduce the input dimensions. Only one control input is requested to realize chaos control of the Liu system when unmatched uncertainties and input nonlinearity coexist. The parameter matrices in the TSM can be determined through the solution of LMIS. Simulation results are given to demonstrate the effectiveness of the proposed method.

Robust Control for Uncertain Switched Systems with Interval Nondifferentiable Time‐Varying Delays

This paper addresses the conditions for robust stabilization of a class of uncertain switched systems with delay. The system to be considered is autonomous and the state delay is time‐varying. Using Lyapunov functional approach, restriction on the derivative of time‐delay function is not required to design switching rule for the robust stabilization of switched systems with time‐varying delays. The delay‐dependent stability conditions are presented in terms of the solution of LMIs which can be solved by various available algorithms. A numerical example is given to illustrate the effectiveness of theoretical results.

Robust Reliable Sliding Mode H<sub>∞</sub> Control for Uncertain Stochastic Nonlinear Jump Systems with Actuator Failures

The problems of stochastic stability and robust reliable sliding mode H∞ control for a class of nonlinear matched and mismatched uncertain systems with stochastic jumps are considered in this paper. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix. The transition of the jumping parameters in the systems is governed by a finite-state markov process. A sufficient condition is given for the existence of integral sliding surface in terms of linear matrix inequalities (LMIs). Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in finite time. Moreover, a state feedback controller is also constructed by using the solution of LMIS. Finally, we give a design example in order to show the effectiveness of our method.

On Delay-Dependent Robust Stability under Model Transformation of Some Neutral Systems

This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the “state” and norm bounded time varying quasi-linear uncertainties in the delayed “state” and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability are given in terms of the existence of positive definite solutions of LMIs.

RobustH ∞ controller design for a class of uncertain systems

TheH ∞ control problem for a class of systems with time-varying and nonlinear uncertainties is considcred. A new sufficient condition based on LMI is provided to judge their robust stability andL 2-gain finiteness. Solvability conditions are presented for both state feedback and output feedback cases, which are all reduced to solutions of LMIs. The design procedure is also discussed via LMI approach.

Reduced-order output feedback controllers for the robust H∞ performance problem

This note considers robust H∞ control problems for a class of systems with time-varying uncertainty lying in a hyperrectangle. It has two features: (i) Output feedback controllers are discussed instead of the state feed-back ones. It is proved that the problem can be reduced to finite-dimensional convex programming problems of finite vertex LMIs. All desired output feedback controllers can be parameterized based on the solutions of 2m LMIs. (ii) Reduced-order controller design is considered and the design idea is also formulated as solutions to LMIs. These results are also an extension of the main theorems about reduced-order controllers discussed in ref. [8] for uncertain systems. Based on the approaches presented here, similar problems in the discrete-time case could be dealt with.