Static Output Feedback Control of Switched Nonlinear Systems With Actuator Faults

Improved stability criterion and output feedback control for discrete time-delay systems

This paper considers the problems of designing multivariable proportional-integral-derivative (PID) controllers for discrete-time systems with D-stability and/or performance constraints. First, the PID control problem is cast into a static output feedback (SOF) control problem, and linear matrix inequality (LMI) conditions are presented. Then, a cone complementarity linearisation (CCL) method is used to solve the SOF-stabilisation problem, and a coordinate transformation matrix (CTM) optimisation approach is extended to solve the optimal SOF control problem. Finally, a numerical example is provided to show the effectiveness and advantage of the CTM optimisation approach, and application to the anti-sway and positioning control of an overhead crane demonstrates the validity of the approach.

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.

Robust non-fragile dynamic vibration absorbers with uncertain factors

Output feedback [formula omitted] finite-time control of switched positive delayed systems with MDADT

In order to improve the trajectory tracking accuracy and stability of intelligent vehicles, this paper proposes a vehicle trajectory tracking control method based on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{H_{\infty}}$</tex> proportional-differential (PD) control. Taking the two-degree-of-freedom vehicle model considering lateral motion and yaw motion as the research object, we establish the state space model based on tracking error. Then, the PD control problem of the model is transformed into a static output feedback (SOF) control problem, and the coordinate transformation matrix (CTM) method is used to solve the problem by multiple iterative optimizations. Finally, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{H_{\infty}}$</tex> PD controller satisfying pole configuration constraints and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{H_{\infty}}$</tex> performance constraints is obtained. The co-simulation of MATLAB/Simulink and Carsim shows that the controller has high tracking accuracy based on ensuring vehicle stability in both the double lane-change condition and the serpentine condition.

This paper presents a method for designing a static output feedback integrated path tracking controller for autonomous vehicles. For path tracking, state–space model-based control methods, such as linear quadratic regulator, H∞ control, sliding mode control, and model predictive control, have been selected as controller design methodologies. However, these methods adopt full-state feedback. Among the state variables, the lateral velocity, or the side-slip angle, is hard to measure in real vehicles. To cope with this problem, it is desirable to use a state estimator or static output feedback (SOF) control. In this paper, an SOF control is selected as the controller structure. To design the SOF controller, a linear quadratic optimal control and sliding mode control are adopted as controller design methodologies. Front wheel steering (FWS), rear wheel steering (RWS), four-wheel steering (4WS), four-wheel independent braking (4WIB), and driving (4WID) are adopted as actuators for path tracking and integrated as several actuator configurations. For better performance, a lookahead or preview function is introduced into the state–space model built for path tracking. To verify the performance of the SOF path tracking controller, simulations are conducted on vehicle simulation software. From the simulation results, it is shown that the SOF path tracking controller presented in this paper is effective for path tracking with limited sensor outputs.

This paper presents a method to design a static output feedback active suspension controller for ride comfort improvement and motion sickness reduction in a real vehicle system. Full-state feedback controller has shown good performance for active suspension control. However, it requires a lot of states to be measured, which is very difficult in real vehicles. To avoid this problem, a static output feedback (SOF) controller is adopted in this paper. This controller requires only three sensor outputs, vertical velocity, roll and pitch rates, which are relatively easy to measure in real vehicles. Three types of SOF controller are proposed and optimized with linear quadratic optimal control and the simulation optimization method. Two of these controllers have only three gains to be tuned, which are much smaller than those of full-state feedback. To validate the performance of the proposed SOF controllers, a simulation is carried out on a vehicle simulation package. From the results, the proposed SOF controllers are quite good at improving ride comfort and reducing motion sickness.

This thesis is concerned with the dissipative control and filtering problems of singular systems. Four classes of singular systems are considered: delay-free singular systems, singular systems with constant time-delay, uncertain singular systems with time-varying delay and sensor failures, and singular Markovian jump systems with actuator failures.&#13;\nFor delay-free singular systems, the system augmentation approach is employed to study the dissipative control and filtering problems. First, the approach is used to solve the dissipative control problem by static output-feedback for standard state-space systems which are the special cases of singular systems. For a continuous-time standard state-space system, the closed-loop system is represented in an augmented system form. Based on the augmented system, a necessary and sufficient dissipativity condition is proposed, which decouples the Lyapunov matrix and controller matrix. To further separate the Lyapunov matrix and the system matrices, an equivalent condition is obtained by introducing some slack matrices. Then, a necessary and sufficient condition for the existence of a static output-feedback controller is proposed, and an iterative algorithm is given to solve the condition. For discrete-time singular systems, by giving an equivalent representation of the solution set, a necessary and sufficient dissipativity condition is proposed in terms of strict linear matrix inequality (LMI) which can be easily solved by standard commercial software. Then a state-feedback controller design method is given based on the augmentation system approach. The method is extended to the static output-feedback control problem and the reduced-order dissipative filtering problem.&#13;\nFor continuous-time singular time-delay systems, the problem of state-feedback dissipative control is considered. An improved delay-dependent dissipativity condition in terms of LMIs is established by employing the delay-partitioning technique, which guarantees a singular system to be admissible and dissipative. Based on this, a delay-dependent sufficient condition for the existence of a state-feedback controller is proposed to guarantee the admissibility and dissipativity of the closed-loop system. In addition to delay-dependence, the obtained results are also dependent on the level of dissipativity. Moreover, the results obtained unify existing results on H∞ performance analysis and passivity analysis for singular systems.&#13;\nFor discrete-time singular systems with polytopic uncertainties, time-varying delay and sensor failures, the problem of robust reliable dissipative filtering is considered. The filter is designed by the reciprocally convex approach such that the filtering error singular system is admissible and strictly (Q, S, R)-dissipative. For singular systems with time-varying delay and sensor failures, a sufficient condition of reliable dissipative analysis is obtained in terms of LMIs. Then the result is extended to the uncertain case by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, a desired filter for uncertain singular systems with time-varying delay and sensor failures is obtained by solving a set of LMIs.&#13;\nFor continuous-time singular Markovian jump systems with actuator failures, the problem of reliable dissipative control is addressed. Attention is focused on the state-feedback controller design method such that the closed-loop system is admissible and strictly (Q, S, R)-dissipative. A sufficient condition is obtained in terms of strict LMIs. Moreover, the results obtained unify existing results on H∞control and passive control on singular Markovian jump systems.

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

This paper considers the problem of static output feedback (SOF) control for discrete-time switched linear systems under arbitrary switching. By the aid of switched quadratic Lyapunov functions combined with Finsler’s lemma, new sufficient conditions for SOF stabilization are obtained which guarantee a γ-performance of the closed-loop switched systems subject to input disturbances. The proposed method can work successfully in situations where the existing ones fail. Three examples are given to illustrate its effectiveness.

We investigate the design of a static output feedback control for switching discrete time systems. Looking at the problem of stability analysis, we give two conditions allowing to check the existence of a particular class of Lyapunov functions. Although one can recover the first condition as a particular case from the second one, it is proved that the two conditions are equivalent for stability analysis. Then we show that when one is faced with a static output feedback control problem, the second condition leads to a sufficient solution to build a stabilizing static output feedback controller which is less conservative than the solution based on the first condition.

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.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Robust Finite Frequency ℋ∞ Passive Fault Tolerant Static Output Feedback Control with Application to Active Vibration Attenuation