Decay rate constrained stabilization of positive systems using static output feedback

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

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 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.

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 article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

Combined input–output finite-time stability condition with static output-feedback H ∞ control is proposed in this work to effectively attenuate the short-duration road disturbance. The control problem is formulated based on the pre-defined condition of input–output finite-time stability with H ∞ bound along with pre-established quarter-car active suspension model. Then, a feasible static output-feedback controller is designed via variable substitution approach and linear matrix inequalities. Output-feedback control’s initial infeasibility issue is solved by state-feedback technique. The controller is specifically designed for the system which exposed with short-duration exogenous disturbances hence, this work prefers finite-time approach instead Lyapunov asymptotic stability condition. To enumerate the significance of the proposed controller numerical examples are presented and its response is effectively analyzed in distinct domains (time and frequency). The theoretical results denote that the combined input–output finite-time stability condition with static output-feedback H ∞ control can enhance the vehicle performance better when compared with passive and conventional static output-feedback control scheme. Additionally, the controller robustness is verified.

An LMI-Based Approach to Static Output Feedback Stabilization of T—S Fuzzy Systems

ROBUST H∞ STATIC OUTPUT FEEDBACK CONTROL OF FUZZY SYSTEMS: AN ILMI APPROACH

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

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 paper describes an output feedback control with input constraints for a lateral and roll vehicle dynamics model in critical motions. The variation of the road adhesion coefficient is considered. To this, a T-S disturbed model is proposed and a static output feedback control is designed with assuming that the lateral velocity and the roll angle are unavailable for measurement. The designed controller not only ensures the stability of the resulting closed loop system but also the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performances. Based on Lyaponov theory, the controller gains are obtained by solving a set of Linear matrix inequalities (LMIs) constraints. The proposed techniques have been evaluated using a bicycle model with four degrees of freedom using Matlab software.

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

ABSTRACTThis paper investigates the robust control of discrete‐time switched systems in the presence of parametric uncertainty and time‐varying delays. To accommodate a more general model, nonlinear Lipschitz functions are incorporated. Additionally, the system is modeled with constraints on both control inputs and outputs. To achieve the control objectives, static and dynamic output feedback controllers are designed using the robust model predictive control (RMPC) framework. The underlying optimization problem is formulated and solved, leveraging Lyapunov‐Krasovskii functionals (LKF) and switched Lyapunov functions (SLF). The asymptotic stability of the closed‐loop system under arbitrary switching signals is ensured by satisfying sufficient conditions expressed as linear matrix inequalities (LMIs). A key advantage of the proposed method lies in its low conservatism. Moreover, the time delay and state variables are assumed unknown, and they ensure an acceptable transient response of the closed‐loop system. To demonstrate the effectiveness of the designed controllers, simulation results are provided and compared against prior related works, highlighting the improvements achieved.

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.

This paper investigates the problems of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback (SOF) control of two-dimensional (2-D) discrete systems described by the Roesser model and Fornasini-Marchesini second model, respectively. By applying the 2-D Bounded Real Lemma combined with a slack variable technique, some sufficient linear matrix inequality (LMI)-based conditions for the existence of SOF controllers are established. Numerical examples are given to illustrate the effectiveness of the proposed LMI-based design method.