Design of Controllers for Quadratic Stability and Disturbance Attenuation of Uncertain Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 594-598
Author(s):  
Faryar Jabbari ◽  
I˙. Emre Ko¨se
Keyword(s):  
Output Feedback ◽  
Uncertain Systems ◽  
Disturbance Attenuation ◽  
Time Varying ◽  
Quadratic Stability ◽  
Structured Uncertainty ◽  
Attenuation Level ◽  
Convex Problem ◽  
Disturbance Attenuation Level ◽  
Two Stages

In this paper, we discuss the design of controllers that provide quadratic stability and a desirable disturbance attenuation level (through an appropriately small L2 gain) for systems with time varying, real and structured uncertainty. It is shown that for a class of systems, the problem of designing dynamic output feedback can be separated into two stages, each an easily solvable convex problem. This information could be used in system design and configuration. Two examples are presented to illustrate the proposed approach.

scholarly journals Multicriteria Adaptive Observers for Singular Systems with Unknown Time-Varying Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Wookyong Kwon ◽  
Jaepil Ban ◽  
Soohee Han ◽  
Chong Soo Lee ◽  
Sangchul Won
Keyword(s):  
Singular Systems ◽  
Disturbance Attenuation ◽  
Estimation Accuracy ◽  
Time Varying ◽  
Varying Parameters ◽  
Integral Action ◽  
Attenuation Level ◽  
Adaptive Observers ◽  
Time Varying Parameters ◽  
Disturbance Attenuation Level

This paper proposes multicriteria adaptive observers for a class of singular systems with unknown time-varying parameters. Two criteria for theH∞disturbance attenuation level and the upper bound of an ultimate invariant set are scalarized into a single cost function and then it is minimized by varying the weight parameter, which creates the optimal trade-off curve or Pareto optimal points. The proposed multicriteria adaptive observers are shown to be able to easily include integral action for better robust performance. It is demonstrated with numerical simulations that the proposed multicriteria adaptive observers provide the good estimation accuracy and allow effective and compromising design by considering two different cost functions simultaneously.

Robust stability and stabilization of networked control systems with stochastic time-varying network-induced delays

2020 ◽  
Vol 42 (10) ◽  
pp. 1782-1796 ◽  
Author(s):  
Mohamed Rouamel ◽  
Sofiane Gherbi ◽  
Fayçal Bourahala
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Networked Control Systems ◽  
Feedback Controller ◽  
Disturbance Attenuation ◽  
Time Varying ◽  
Lower And Upper Bounds ◽  
State Feedback Controller ◽  
Attenuation Level ◽  
Disturbance Attenuation Level

This paper investigates the robust stability analysis and state feedback controller design of networked control systems (NCSs). A stochastic network-induced delay in given interval with known lower and upper bounds is considered. Therefore, the NCS is modeled as linear system with probabilistic time-varying delay distribution. Then, the Lyapunov-Krasovskii functional (LKF) is formulated using probabilistic informations of both lower and upper bounds of the time-varying network-induced delay, and Wirtinger-based integral inequalities are used to estimate the accuracy of the resulting time derivatives and also to reduce conservatism by introducing some new cross terms. Afterwards, stability condition based on [Formula: see text] disturbance attenuation level is expressed in terms of a set of linear matrix inequalities (LMIs), and Finsler’s lemma is used to relax it by adding slack decision variables and decoupling the systems matrices from those of Lyapunov-Krasovskii. This procedure makes the state feedback controller design as simple as a variables change. Finally, a maximum allowable upper bound of the network-induced delay and state feedback controller gains are calculated by resolving the above relaxed LMIs’ convex optimization problem. Practical numerical examples are provided to validate the proposed approach; the results show that the negative effects of the unpredictable network-induced delays are compensated and the stability of NCSs with high disturbance attenuation level is guaranteed. A comparative study with other results in recent researches is also given and the superiority of the proposed method in terms of robustness and conservatism reduction is shown.

Dual-finite distributed H∞ filtering in sensor networks

2021 ◽  
pp. 095965182199758
Author(s):  
Changshuo Wang ◽  
Jiwei Wen ◽  
Xiaoli Luan
Keyword(s):  
Sensor Networks ◽  
Disturbance Attenuation ◽  
Time Interval ◽  
Frequency Range ◽  
Frequency Scale ◽  
Attenuation Level ◽  
Exogenous Noise ◽  
Disturbance Attenuation Level ◽  
Reference Input ◽  
Filtering Approach

Generally, distributed H∞ filtering approach achieves a certain disturbance attenuation level in the full frequency range. However, the energy of system noise or reference input usually limits in a specified frequency range. To reduce such a design conservatism, this article develops a distributed filtering approach based on dual scale, that is, filtering over a finite-time interval from time scale and also on a specified finite-frequency region from the frequency scale. Our target is to make the filtering error under sensor networks monitoring be relaxed into an ellipsoid bound rather than asymptotically converging to zero for exogenous noise in a specified frequency range. Finally, two illustrative examples demonstrate the strength of the developed filtering approach.

scholarly journals NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
T. Osuna ◽  
O. E. Montano ◽  
Y. Orlov
Keyword(s):  
Sliding Mode ◽  
Numerical Study ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Sliding Modes ◽  
Time Dynamics ◽  
Attenuation Level ◽  
Disturbance Factor ◽  
Disturbance Attenuation Level ◽  
The Impact

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

Stabilization via output feedback for a type of uncertain time-varying port-controlled Hamiltonian system based on linear matrix inequality approach

2019 ◽  
Vol 41 (15) ◽  
pp. 4387-4397 ◽  
Author(s):  
Tianyi Zhao ◽  
Guangren Duan
Keyword(s):  
Output Feedback ◽  
Control Method ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Varying ◽  
Quadratic Stability ◽  
Pch System ◽  
Uncertain Time ◽  
Necessary And Sufficient ◽  
Output Equation

In this paper, the control of a type of uncertain time-varying port-controlled Hamiltonian (PCH) systems is investigated. As a matter of fact, the control method proposed in this paper is not based on passivity of PCH systems, but a general output equation is introduced inspired by the measured “information” in the systems in traditional control system theory and the problem of output feedback is considered. In this paper, a conception of p-quadratic stability of the type of PCH system is introduced, and the relationship between p-quadratic stability and Lyapunov stability is pointed out. Then, the problem for p-quadratic stabilization of the proposed system via static output feedback is solved in the following two cases, respectively. For the case of unperturbed output equation, a necessary and sufficient condition for the problem is derived in terms of two groups of linear matrix inequalities (LMIs); for the general case that the output equation also has time-varying perturbations, a sufficient condition for p-quadratic stable of closed-loop system is also given in terms of LMIs. It is also shown that conservatism can be greatly reduced when the perturbation variables in the uncertain PCH systems are restricted to vary within certain intervals. Finally, a numerical example is proposed in the end followed by a simulation to verify the effectiveness of the method proposed in this paper.

Robust Delay-Dependent H∞ Control for Uncertain Structural Systems With Actuator Delay

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Hakan Yazici ◽  
Rahmi Guclu ◽  
Ibrahim B. Kucukdemiral ◽  
M. N. Alpaslan Parlakci
Keyword(s):  
Optimization Technique ◽  
Time History ◽  
Disturbance Attenuation ◽  
Structural Systems ◽  
Attenuation Level ◽  
Uncertainty Bound ◽  
Disturbance Attenuation Level ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper is concerned with the design of a robust, state-feedback, delay-dependent H∞ controller for an active vibration control of seismic-excited structural systems having actuator delay, norm bounded uncertainties, and L2 disturbances. The norm bounded uncertainties are assumed to exist in variations of structural stiffness and damping coefficients. Based on the selection of Lyapunov–Krasovskii functional, first a bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H∞ stabilization criteria are easily extended by employing a well-known bounding technique. Then, a cone complementary algorithm is also utilized to solve the nonconvex optimization problem. By use of the proposed method, a suboptimal controller with maximum allowable delay bound, uncertainty bound and minimum allowable disturbance attenuation level can be easily obtained by solving the proposed convex optimization technique. A four-degree-of-freedom uncertain structural system subject to seismic excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results, obtained by using real time-history data of Kobe and Kocaeli earthquakes show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay and parametric uncertainty bound.

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