Robust Stability Of System Research Articles

LMI-based robust stability and stabilization analysis of fractional-order interval systems with time-varying delay

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results, a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in LMI form, which is more suitable to check due to various existing efficient convex optimization parsers and solvers. Finally, some numerical examples have shown the effectiveness of our results.

Fault-Tolerant Robust Model-Predictive Control of Uncertain Time-Delay Systems Subject to Disturbances

Time delays, model uncertainties, faults, and disturbances are frequently the main causes of performance degradation and instability in industrial process control. This article presents a fault-tolerant robust model-predictive control design for processes that involve the above effects and process constraints. The uncertainties are modeled into a polytopic affine form based on variations in the system's parameters. A new model based on augmentation of the state variables and tracking error is used that provides increased degrees of freedom for the control design and guarantees tracking performance. A parameter-dependent Lyapunov-Krasovskii functional is used to design a state-feedback control that reduces the conservatism of the conventional approach and ensures robust stability and tracking performance of the closed-loop system. At each sampling instant, a control action is computed by solving an online constrained optimization problem that minimizes the upper bound of the “worst-case” performance index. Finally, the proposed framework is employed for the fault-tolerant control of a continuous stirred tank reactor to demonstrate its effectiveness in mitigating actuator faults and tracking the desired set point.

Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

Robust stability and stabilization of fractional-order systems with polytopic uncertainties via homogeneous polynomial parameter-dependent matrix forms

This paper addresses the robust stability and stabilization problems for fractional-order systems with polytopic uncertainties. By introducing homogeneous polynomial parameter-dependent matrix forms, the robust stability and stabilization conditions can be expressed as square matricial representation (SMR) of matrix forms, which is finally reduced to solving linear matrix inequalities (LMIs). Since the auxiliary matrices are all homogeneous polynomial parameter-dependent, the proposed method is effective and less conservative than the existing results, which is illustrated by the final numerical examples.

New results on robust finite-time stability of singular large-scale complex systems with interconnected delays

In this paper, we provide an efficient approach based on combination of singular value decomposition (SVD) and Lyapunov function methods to finite-time stability of linear singular large-scale complex systems with interconnected delays. By representing the singular large-scale system as a differential-algebraic system and using Lyapunov function technique, we provide new delay-dependent conditions for the system to be regular, impulse-free and robustly finite-time stable. The conditions are presented in the form of a feasibility problem involving linear matrix inequalities (LMIs). Finally, a numerical example is presented to show the validity of the proposed results.

Robust adaptive stabilization of nonlinear systems with mismatched time delays

For a class of nonlinear systems with mismatched time delays and disturbances, robust adaptive stabilization control is studied. The control law is split into two terms. One is used to cope with the delayed states, and the other is to handle the disturbance. The improved robust adaptive laws with control gain function and time-varying σ-modification are constructed to estimate the unknown integrated parameters. It is proved that the designed adaptive controller can ensure the asymptotic convergence of the closed-loop system states. Another adaptive algorithm is also proposed to ensure the asymptotic stability of the closed delayed nonlinear system without external disturbance.

Fuzzy adaptive fault diagnosis and compensation for variable structure hypersonic vehicle with multiple faults.

Based on the type-II fuzzy logic, this paper proposes a robust adaptive fault diagnosis and fault-tolerant control (FTC) scheme for multisensor faults in the variable structure hypersonic vehicles with parameter uncertainties. Type-II fuzzy method approximates the original models while eliminating the parameter uncertainties. Hence the sensor faults are detected and isolated by the multiple output residuals and thresholds considering nonlinear approximation errors and disturbance. Based on the fuzzy adaptive augmented observer, the faults and disturbance are all estimated accurately by an improved proportional-differential part. Then a variable structure FTC scheme repairs the faults by the estimation, the fast-varying disturbance is considered in FTC scheme and is compensated by the control parameters designed based on its derivative function, thereby enhancing the output robust tracking accuracy of the variable structure hypersonic vehicles. The Lyapunov theory proves the system robust stability, semi-physical simulation verifies the validity of the proposed method and the superiority compared with the traditional method.

An explicit robust stability condition for uncertain time-varying first-order plus dead-time systems

First-order plus dead-time (FOPDT) models are broadly used in process control to represent damped dynamic processes with time delays. An explicit condition for parameter- and delay-dependent robust stability of FOPDT systems with varying uncertain parameters and delay is derived in this paper. An internal model control (IMC) approach is proposed to parameterize stabilizing controllers that satisfy the output tracking objective in time-varying FOPDT systems represented by an uncertain first-order dynamic model with a time-varying delay in the control input. The small-gain theorem is used to derive an explicit necessary and sufficient parameter-dependent robust stability condition as a function of the nominal system gain, nominal varying delay, nominal time constant, and the bounds of the parameter uncertainties. An equivalent proportional-integral-derivative (PID) controller is then extracted to facilitate the implementation of the proposed IMC-based robust control. The application of the proposed explicit robust stability condition is studied in the context of air-fuel ratio (AFR) control in lean-burn spark ignition (SI) engines with a large time-varying transport delay in the control loop due to the placement of the universal exhaust gas oxygen (UEGO) sensor downstream the catalytic converter.

Robust stability of stochastic systems with varying delays: Application to RLC circuit with intermittent closed-loop

This paper characterizes the robust second-moment stability of stochastic linear systems subject to varying delays. The delays assume a particular form suitable to represent packet loss in networked control systems, under the zero-order hold feedback. The proposed robust stability condition requires checking the spectral radius of an appropriate matrix that that depends on uncertain parameters belonging to a polytope. Due to this polytope’s dependence, checking the spectral radius is difficult from the numerical viewpoint. As an attempt to solve the problem, we convert the polytope-based condition into a randomized approach. Namely, we present probability bounds that help us certificate the robust second-moment stability under high probability. A real-time electronic application illustrates the potential benefits of our approach.

Multivariable State-Feedback Controller Design for PV Inverter Connected to a Weak Grid

This paper presents a robust multi-input multi-output (MIMO) state-feedback control scheme for a photovoltaic (PV) inverter connected to a weak grid. For a weak grid, the point of common coupling (PCC) voltage is very sensitive to the power disturbances and it is dynamically coupled to the PLL dynamics. So far, most of the control methods do not take into accounts these couplings. Therefore, in this paper, the MIMO controller was designed taking into account the dynamics of the phase-locked loop (PLL) and coupling effects between PCC voltage and the active power to enhance the system’s robustness. As result, the robust performance of the PV inverter interfaced to a weak grid was yielded. In addition, the sensitivity of the system to PLL was eliminated, allowing the use of larger PLL bandwidth even in a very weak grid. Based on the eigenvalues analysis method, a comparative study between the proposed control method and the conventional vector control method was performed. The proposed method is verified with simulations in PLECS and real-time simulations in the RT Box. The results show that the proposed MIMO control method preserves the system stability robustness against any change of grid strength, generated power and PLL bandwidth.

Robust Stability of Time-Varying Markov Jump Linear Systems with Respect to a Class of Structured, Stochastic, Nonlinear Parametric Uncertainties

This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.

Robust Stabilization of High-Order Nonlinear Systems With Unknown Sensitivities and Applications in Humanoid Robot Manipulation

This article is concerned with the improvement of robust control methodology and its application in stabilizing a class of high-order nonlinear systems with multiple unknown time-varying sensitivities, and discusses how to use the proposed control strategy on humanoid robot manipulation. The novel design approach successfully breaks through the limitation of the neural network technique; that is, state variables must be located in some compact sets. The remarkable feature of the systems under investigation lies in the presence of measurement sensitivities and higher powers, which makes the nonlinear systems essentially different from the related works. By reductio and the introduction of a modified tuning function, an appropriate controller is constructed to render that all the state variables belong to a predetermined bounded set. Finally, an example is provided to illustrate the effectiveness of the proposed control strategy.

Robust stability criteria for linear impulsive delay systems

AbstractThis article is concerned with robust stability for linear impulsive delay systems with polytope uncertainties. For the linear impulsive delay systems without uncertainties, the stability is addressed by employing a Lyapunov‐Krasovskii‐like functional, which is comprised of a Lyapunov‐Krasovskii functional and an auxiliary functional. By introducing integrals of the state, an augmented Lyapunov‐Krasovskii‐like functional is constructed. With an integral inequality proposed to deal with the derivative of the Lyapunov‐Krasovskii‐like functional, a stability criterion is derived for the impulsive delay system. Then the stability criterion is extended to linear impulsive delay systems with polytope uncertainties, and a robust stability criterion is obtained. Examples are given to illustrate the stability results are valid or of less conservatism than some existing ones.

Robust Load-Frequency Control in Islanded Microgrids: Virtual Synchronous Generator Concept and Quantitative Feedback Theory

Increasing penetration of renewable energy sources based on power electronic interfaces in traditional power systems reduces the inertia constant and damping coefficient. It also increases uncertainty and the sensitivity of the system to disturbances. The concept of the virtual synchronous generator (VSG) is used to emulate the inertia constant and damping property like a synchronous generator. It can be shown that all given VSG structures have the same dynamics as the proportional-integral-derivative (PID) controller. In this paper, the quantitative feedback theory (QFT) is used to tune the VSG parameters such that robust system stability and performance are guaranteed. Moreover, the desired disturbance attenuation is also taken into account. Through frequency response analysis and time-domain simulations, it is shown that the proposed strategy can be successfully used to solve the load-frequency control problem in islanded microgrids (MGs). In addition, the proposed QFT-based VSG is compared with another robust VSG designed by the well-known <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> technique to illustrate its better performance against disturbances.

Convergence of coprime factor perturbations for robust stabilization of Oseen systems

&lt;p style='text-indent:20px;'&gt;Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard robust controller designs can compensate small uncertainties if they can be qualified as a coprime factor perturbation of the plant. We show that for the linearized Navier-Stokes equations, a linearization error can be expressed as a coprime factor perturbation and that this perturbation smoothly depends on the size of the linearization error. In particular, improving the linearization makes the perturbation smaller so that, eventually, standard robust controller will stabilize the system.&lt;/p&gt;

Output-feedback anti-disturbance predictor-based control for discrete-time systems with time-varying input delays

This paper investigates the robust stabilization of discrete-time systems with time-varying input delays and model uncertainties by predictor-based anti-disturbance output-feedback control strategies. Here, a novel predictor-feedback control combined with an extended state observer is proposed. The objective is to counteract the negative effects of input delays while actively rejecting disturbance signals typically encountered in engineering practice, such as steps or harmonics. Differently from previous approaches, unknown but bounded time-varying delays are taken into consideration. Moreover, the complexity of the algorithm for control synthesis is notably reduced. Finally, an illustrative example from the literature is provided to show that better robust performance can be achieved with the proposed method.

Dynamic robust stabilization of fractional-order linear systems with nonlinear uncertain parameters: an LMI approach

ABSTRACT This paper presents a dynamic output feedback controller with determined order for the stabilization of a class of fractional-order system with nonlinear uncertain parameters with fractional order . Using stability theories of fractional-order systems and linear matrix inequalities (LMIs), some sufficient conditions in the LMI form are deduced to guarantee the robustness and asymptotic stabilization of the system. Designing a dynamic robust controller, along with all its useful features, leads to more unknown parameters in comparison with a static controller and makes controller design procedure more difficult due to more complex constraints that must be solved. In this paper, using proper lemmas and theorems, LMI techniques, and suitable solvers and parsers the difficulty of designing such controllers has been overcome. Simulation results of three different numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems.

The modal sensitivity, robustness and roughness of dynamic systems (review article)

The review focuses on the development of theories of sensitivity and modal sensitivity, robustness and roughness of dynamic systems. In modern theory of dynamic systems and automatic control systems, there is a need to study the properties of sensitivity, robustness and roughness of systems in their interconnection. An import application of sensitivity theory is associated with the design and creation of high-precision and low-sensitivity systems. The most significant results were achieved in the development of differential methods for the analysis and synthesis of low-sensitivity systems. One approach to the analysis and synthesis of linear systems of low parametric sensitivity in the space of states was developed using the functions of modal sensitivity or, in other words, the method of modal sensitivity. A review of robustness theory considers methods of studying and ensuring the robust stability of interval dynamical systems, paying attention to both algebraic and frequency directions of robust stability. The work presents the main results of the original algebraic method of robust stability of interval dynamical systems for continuous and discrete time. The section “Basic development stages of the theory of roughness of systems” describes the main principles of the theory and method of topological roughness of dynamical systems, based on the concept of roughness according to Andronov–Pontryagin. Applications of the topological roughness method to synergetic systems and chaos have been used to investigate many systems, such as the Lorenz and Rössler attractors, the Belousov–Zhabotinsky, Chua, predator-prey, Hopf bifurcation, Schumpeter and Caldor economic systems, etc. The review proposes applying the approach of analogies of theoretical-multiple topology and the abstract method for studying weakly formalized and informal systems. Further research suggests the development of theories of sensitivity, robustness, roughness and bifurcation for complex nonlinear dynamic

Adaptive fractional-order non-singular terminal sliding mode control based on fuzzy wavelet neural networks for omnidirectional mobile robot manipulator

This paper studies a novel adaptive fractional-order non-singular terminal sliding mode (FO-NTSM) control strategy for omnidirectional mobile robot manipulator (OMRM) with unknown parameters and external disturbances. Firstly, we adopt the fuzzy wavelet neural networks (FWNNs) to estimate the dynamic uncertainty of the OMRM because it has superior function approximation capability. Secondly, we design the adaptive NTSM controller to attenuate external disturbances by virtue of adjusting the weights of the FWNNs online. Moreover, we obtain a fractional-order (FO) control criterion, which speed up the convergence of the algorithm. In addition, we prove the globally robust stability of the OMRM control system through a designed Lyapunov function. Finally, simulation and experiment researches indicate the feasible and validity of the presented method.

Investigation of the Robust Absolute Stability of the Tunnel Kiln Control System with Delay

The paper considers the system of automatic control of the tunnel kiln temperature conditions. The investigation of a delay influence on the transition process has been carried on. The transfer function of the object under control with interval coefficients taking into account possible effects of the parametric uncertainty has been obtained. A graphical method of representing the obtained results in the form of displaying the modified amplitude-phase characteristics on a complex plane has been applied which obviously demonstrates a robust absolute stability of the system under investigation. The simulation performed in the Matlab environment has proved the correctness of the results obtained.