Static Output Feedback Control Law Research Articles

Robust H∞ Static Output Feedback Control for TCP/AQM Routers Based on LMI Optimization

This paper proposes a new static output feedback control method to address the congestion control problem in transmission control protocol networks using active queue management routers. Based on linear matrix inequality optimization, this method determines a static output feedback control law to minimize the norm of the transfer function between the controlled queue length of the buffer and the exogenous disturbance affecting the available link bandwidth. A linear matrix inequality formulation is presented as a sufficient condition to guarantee the closed-loop system’s asymptotic stability while maintaining disturbance rejection within a specified level, regardless of round-trip time delays. The proposed robust static output feedback control eliminates the need to measure or estimate all system states, thus simplifying practical implementation. The effectiveness of the proposed design method is demonstrated by applying it in a practical process, as illustrated through a numerical example.

A novel semi-active control of an integrated chassis and seat quasi-zero stiffness suspension system for off-road vehicles

This article introduces an innovative semi-active suspension system for off-road vehicles, incorporating a quasi-zero stiffness suspension to enhance driver comfort. The system includes a central pneumatic spring, double-acting pneumatic linear actuators for adjustable stiffness, and magnetorheological dampers for controlled damping. Using Lyapunov stability theory, a static output feedback control law is designed to address uncertainties in road profiles, driver body parameters, and actuator saturation, relying on measured variables as feedback. Performance constraints focus on driver head acceleration, suspension displacement, and dynamic tire load. The control law problem is converted into a convex optimization problem with linear matrix inequalities. The new semi-active QZSS system is theoretically tested via Matlab simulations and validated through hardware-in-the-loop testing. Comparative analysis between passive QZSS and the new semi-active QZSS on different roads, and vehicle speeds closely aligns with simulation results, with minor disparities attributable to network discrepancies and signal interruptions. Impressively, the semi-active QZSS system reduces driver head vertical acceleration between 26.53 and 35.0% compared to passive air QZSS, showing potential for significantly improving ride comfort, reducing vibration transfer, and enhancing driver wellbeing with minimal energy requirement.

Static Output Feedback Control for Nonlinear Time-Delay Semi-Markov Jump Systems Based on Incremental Quadratic Constraints

This paper is concerned with the problem of static output feedback control for a class of continuous-time nonlinear time-delay semi-Markov jump systems with incremental quadratic constraints. For a class of time-delay semi-Markov jump systems satisfying incremental quadratic constrained nonlinearity, an appropriate mode-dependent Lyapunov–Krasovskii functional is constructed. Based on the matrix transformation, projection theorem and convex set principle, the mode-dependent static output feedback control laws are designed. The feedback control law is given in the form of a linear matrix inequality, which is convenient for a numerical solution. Finally, two practical examples are given to illustrate the effectiveness and superiority of the proposed method.

An Output-Feedback Design Approach for Robust Stabilization of Linear Systems With Uncertain Time-Delayed Dynamics in Sensors and Actuators

In this paper, we propose a control approach for the robust stabilization of linear time-invariant (LTI) systems with non-negligible sensor and actuator dynamics subject to time-delayed signals. Our proposition is based on obtaining an augmented model that encompasses the plant, sensor, and actuator dynamics and also the time-delay dynamic effect. We make use of the Padé Approximation for modeling the time-delay impact on the feedback loop. Since the actual plant state variables are not available for feedback, the sensor outputs, which represent a subset of the augmented system state variables, are used for composing a static output-feedback control law. The robust controller gains are computed by means of a two-stage strategy based on linear matrix inequalities (LMI). For obtaining less conservative conditions we consider the use of homogeneous-polynomial Lyapunov functions (HPLF)– and other decision variables– of arbitrary degree. In our proposition, we also take into account the inclusion of a minimum decay rate criterion in order to improve closed-loop system transient response. Disturbance rejection is also addressed through extensions to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathscr {H}_{2}$ </tex-math></inline-formula> guaranteed cost minimization. The effectiveness of the proposed strategy is attested in the design of a controller for the lateral axis dynamics of an aircraft and other academic examples.

Finite-Time Static Output-Feedback H∞ Control for Discrete-Time Singular Markov Jump Systems Based on Event-Triggered Scheme

The problem of finite-time static output feedback H∞ control for a class of discrete-time singular Markov jump systems is studied in this paper. With the consideration of network transmission delay and event-triggered schemes, a closed-loop model of a discrete-time singular Markov jump system is established under the static output feedback control law, and the corresponding sufficient condition is given to guarantee this system will be regular, causal, finite-time bounded and satisfy the given H∞ performance. Based on the matrix decomposition algorithm, the output feedback controller can be reduced to a feasible solution of a set of strict matrix inequalities. A numerical example is presented to show the effectiveness of the presented method.

A Characterization of approximate decentralized fixed modes of time‐delay systems

AbstractThe concept of decentralized fixed mode (DFM) is crucial in determining the output feedback stabilizability by linear time‐invariant (LTI) decentralized controllers. However, in some cases, although a system has no DFMs, some of its modes may be very close to being fixed. It is thus important to characterize these modes, which are called approximate DFMs (ADFMs). In this paper, the characterization of ADFMs is discussed for LTI neutral (possibly descriptor‐type) time‐delay systems under static and dynamic decentralized output feedback control laws, and a mode mobility measure is proposed to provide quantitative information about ADFMs. To analytically compare the proposed measure, some of the commonly used quantitative measures for the characterization of ADFMs of finite‐dimensional systems have also been extended to the considered type of systems. The herein proposed approach allows multiple time delays and does not require additional expansions or preliminaries for multi‐input multi‐output systems, like some other commonly used methods. Thus, characterization with this measure, in general, requires less computational load, while it can provide more explicit information about the controller effort than the other considered measures.

Robust H∞ output feedback control of uncertain fractional-order systems subject to input saturation

This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0&lt;α&lt;1 subject to input saturation with convex polytopic uncertainties, by a kind of [Formula: see text]–proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ([Formula: see text]) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism.

Static boundary feedback stabilization of an anti-stable wave equation with both collocated and non-collocated measurements

In this paper, we consider the stabilization of a wave equation with an unknown anti-stable injection on the left boundary and the control input on the right boundary, where there are both collocated and non-collocated measurements. A static output feedback control law is designed to stabilize the wave equation. The value ranges of the feedback gains are given, such that all eigenvalues of the closed-loop system are shown to be inside the left-half complex plane by applying the Nyquist criterion for distributed parameter systems. Then the exponential stability of the closed-loop system is established. Numerical simulations are presented to verify the effectiveness of the proposed feedback control law.

Static output feedback control of a chain of integrators with input constraints using multiple saturations and delays

Using multiple saturations and delays, we present a time-domain static output feedback control approach for global stabilization of a chain of integrators with input constraints. In lieu of estimating the state by observers, we utilize the output with distinct delays to construct static output feedback control laws. A nested saturation design technique is employed to handle the nonlinearity in the control. An appealing feature of the proposed nonlinear controllers is that no observer is needed. The bounded and static output feedback control scheme is validated by an application to the triple integrators.

Resilient Event-Triggered Control for LFC-VSG Scheme of Uncertain Discrete-Time Power System under DoS Attacks

This paper is concerned with resilient triggered control problem for load frequency control and virtual synchronous generation (LFC-VSG) scheme of discrete-time multi-area power system with parameter uncertainty, governor dead band (GDB), and low inertia under time delay and aperiodic Denial-of-Service (DoS) attacks. To reduce communication load of sleep intervals, event triggered mechanism (ETM) is introduced. A discrete-time switched delay system model is established to describe the dynamic of multi-area power system under resilient static output feedback control law. Combining piecewise Lyapunov–Krasovskii functional (LKF) method with switched system theory, a criterion is derived that the tolerant bound of attack duration and attack frequency can be estimated explicitly. Meanwhile, some sufficient conditions are obtained which can preserve weighted H ∞ performance. By using linear matrix inequalities (LMIs) techniques, a co-design method is proposed to solve the control gains and trigger parameters. A simulation example of a two-area power system was carried out to verify the efficiency of our proposed resilient event based LFC-VSG scheme.

선적분 퍼지 리아푸노프 함수를 이용한 연속시간 T-S 퍼지 시스템에 대한 정적 출력궤환 제어

The problem of static output feedback control design for continuous-time Takagi-Sugeno (T-S) fuzzy systems is addressed. The proposed stabilizing condition is based on a line-integral fuzzy Lyapunov function and a non-parallel distributed compensation (non-PDC). The existence condition of the stabilizing static output feedback control law is represented in terms of linear matrix inequalities (LMIs) without any transformation matrices and equality conditions. The proposed sufficient stabilizing condition is less conservative than previous results in the literature. An example is illustrated to verify this.

Static output feedback control design for constrained linear discrete‐time systems using data cluster analysis

Methods for the design of static output feedback controllers for linear discrete-time systems subject to state and control constraints, additive disturbance and measurement noise are proposed in this study. First, the authors show how the design can be performed through the construction of an output feedback controlled invariant set together with the solution of several multiparametric linear programming (mp-LP) problems. This technique is commonly used to characterise the optimal control action as a piecewise affine (PWA) function over polyhedral regions. However, when applied to constrained multiple output systems, it may require high online computational cost and large memory capacity, due to the number of polyhedral regions resulting from the mp-LP solution. Within this context, the authors present a new approach to compute a PWA static output feedback control law over a smaller number of polyhedral regions using the K q-flat data cluster analysis algorithm. Optimisation problems to compute PWA sub-optimal static output feedback control laws over an even smaller number of regions are also proposed, and illustrated by numerical examples.

Robust fault-tolerant control for networked control systems subject to random delays via static-output feedback

This paper focuses on the problem of fault-tolerant controller (FTC) design for uncertain networked control systems (NCSs) with random delays and actuator faults. A new fault model is proposed to represent more class of actuator faults. More precisely, the NCSs with random delays and the possible actuator faults are modeled as a Markovian jump system (MJS) with incomplete transition probabilities (TPs) and then LMI-based sufficient conditions are derived to ensure the stochastic stability of the closed-loop system. The sufficient conditions are constructed to synthesize the mode-dependent static-output feedback (SOF) control laws. Feasibility and reliability of the proposed FTC against actuator faults are indicated through simulation results.

Cooperative Output Regulation of Singular Multi-Agent Systems Under Switching Network by Standard Reduction

The cooperative output regulation problem for singular multi-agent systems subject to static networks was studied recently under the assumption that each follower system satisfies the standard assumption. In this paper, we further study the same problem for singular multi-agent systems subject to jointly connected switching networks. First, by introducing a static output feedback control, we remove the unnecessary standard assumption on the singular system in the existing result. Then, we derive a reduced-order normal multi-agent system and obtain a distributed output measurement feedback control law based on the existing result on the normal multi-agent system. Finally, we show that the composition of the static output feedback control law and the distributed output measurement feedback control law solves the cooperative output regulation problem for the original singular multi-agent system. Our result enlarges the class of systems whose cooperative output regulation problem is solvable.

Active control of transonic buffet flow

Transonic buffet is a phenomenon of aerodynamic instability with shock wave motions which occurs at certain combinations of Mach number and mean angle of attack, and which limits the aircraft flight envelope. The objective of this study is to develop a modelling method for unstable flow with oscillating shock waves and moving boundaries, and to perform model-based feedback control of the two-dimensional buffet flow by means of trailing-edge flap oscillations. System identification based on the ARX algorithm is first used to derive a linear model of the input–output dynamics between the flap rotation (the control input) and the lift and pitching moment coefficients (system outputs). The model features a pair of unstable complex-conjugate poles at the characteristic buffet frequency. An appropriate reduced-order model (ROM) with a lower dimension is further obtained by a balanced truncation method that keeps the pair of unstable poles in the unstable subspace but truncates the dynamics in the stable subspace. Based on this balanced ROM, two kinds of feedback control are designed by pole assignment and linear quadratic methods respectively. These independent designs, however, result in similar suboptimal static output feedback control laws. When introduced in numerical simulations, they are both able to completely suppress the buffet instability. Furthermore, the resulting controllers are even able to stabilize buffet flows with nonlinear disturbances and in off-design flow conditions, thus implying their robustness. The analysis of the feedback control laws indicates that parameters (frequency and phase) corresponding to the ‘anti-resonance’ of the linear input–output model are vital for optimal control. The best performance is obtained when the control operates close to the ‘anti-resonance’, which is supported by the optimal frequency and the phase of the open-loop control as well as by the optimal phase of the closed-loop control.

Non-fragile quantized H∞ output feedback control for nonlinear systems with quantized inputs and outputs

This paper is concerned with non-fragile H∞ control problems for a class of continuous-time nonlinear systems with unknown nonlinearity and quantized inputs and outputs. The construction of both static output feedback (SOF) and observer-based output feedback (OBOF) control laws in the presence of additive interval-bounded controller coefficient variations can be divided into two parts, linear and nonlinear parts. The linear part plays a role in achieving the H∞ performance, while the nonlinear part is used to reduce the quantization effect. However, it should be pointed out that the effect of input and output quantization can be eliminated fully for SOF case by requiring knowledge of all signs of the states, but only the effect of input quantization can be eliminated for OBOF case. It is worth mentioning that three novel alternative methods with strict linear matrix inequality (LMI) conditions are proposed to design both SOF and OBOF controllers. In particular, these three new methods do not introduce any other auxiliary constraints as many existing results do where a matrix equality constraint between system matrix and Lyapunov matrix is often inserted. Finally, the effectiveness and advantages of the proposed control methods are demonstrated by a numerical example.

Synthesis of fault-tolerant static output feedback controllers for networked control systems

This paper is concerned with the design of static output feedback control laws for stabilizing a networked control system under possible element failures. Multiple faults can occur on sensors, actuators, or other electrical or mechanical componentes. With considering consecutive packet loss and time-varying network-induced delay, the closed-loop system is modeled as an equivalent time-delay system with several possible modes. By constructing a Lyapunov–Krasovskii function, sufficient conditions for the existence of static output feedback fault-tolerant stabilizing controllers are derived. Moreover, by the simultaneous stabilization approach, it is shown that a static output feedback fault-tolerant controller can be obtained by solving linear matrix inequalities (with equality constraints). Simulation results are presented to validate the theoretical results.

Discretization and event triggered digital output feedback control of LPV systems

This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.

Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator

The quantized output feedback stabilization problem for nonlinear discrete-time systems with saturating actuator is investigated. The nonlinearity is assumed to satisfy the local Lipschitz condition. Different from the previous results where the Lipschitz constant is predetermined, a more general case is considered, where the maximum admissible Lipschitz constant through convex optimization is obtained. In this framework, two kinds of quantizations are derived simultaneously: quantized control input and quantized output. Furthermore, sufficient conditions for the existence of static output feedback control laws are given. The desired controllers ensure that all the trajectories of the closed-loop system will converge to a minimal ellipsoid for every initial condition emanating from a large admissible domain. Finally, four illustrative examples are provided to show the effectiveness of the proposed approach.

Memoryless Static Output Feedback Sliding Mode Control for Nonlinear Systems With Delayed Disturbances

In this technical note, a local stabilization problem for nonlinear systems with disturbances which are dependent on time-varying delay phenomena, is studied. An appropriate transformation is introduced to express the system in regular form which facilitates both design and analysis. Then, sufficient conditions are developed based on a Lyapunov-Razumikhin approach such that the sliding motion is uniformly asymptotically or exponentially stable. A static output feedback control law, independent of the time delay, is synthesized to guarantee reachability of the sliding mode. The accessible bounds on the disturbances are fully used in the control design to reduce the conservatism. A simulation example shows the effectiveness of the approach.