Static Output-feedback Controller Synthesis for Positive Systems under ℓ∞ Performance

ℓ∞-induced output-feedback controller synthesis for positive nonlinear systems via T–S fuzzy model 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.

In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions for mean-square strong stabilization via a state feedback controller and an output feedback controller are obtained. Furthermore, explicit expressions for the state feedback controller and static output feedback controller are obtained. Finally, two examples are given to illustrate the validity of the above results.

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.

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

It is known that collocated dynamical systems can be robustly stabilized by using symmetric static output feedback controllers and some optimization methods of the feedback gain matrices have been proposed for symmetric systems. This paper extends the result to the asymmetric gyroscopic systems. We first show that static output feedback controllers having asymmetric gains are appropriate for optimal disturbance attenuation in the sense of H∞ control, and provide an optimization method using LMIs. Then it is shown that the obtained optimal controller works to cancel the gyroscopic term included in the system. We further propose to construct dynamic output feedback controllers based on the static optimal gain matrices. Finally, some numerical study results are shown to verify the effectiveness.

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

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

This paper discusses the problems of the finite-time annular domain stability (FTAD-stability) and stabilization of discrete-time stochastic systems (DTSS). First, a definition of FTAD-stability for DTSS is given and a stability criterion is also proposed. Second, we respectively give some sufficient conditions for the existence of state feedback controller (SFC), static output feedback controller (SOFC) and dynamic output feedback controller (DOFC). Finally, a numerical example is utilized to show the effectiveness of proposed method.

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.

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.

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.

Diabetes is a long-term disease during which the body's production and use of the insulin are impaired, causing glucose concentration level to increase in the bloodstream. The blood glucose dynamics is described using the generalized minimal model structure for the intravenously infused insulin-blood glucose, which can represent a wide variety of diabetic patients. In this paper, it is an attempt to incorporate fractional-order derivative into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to determine, mathematically, how the order of a fractional differential system affects the dynamics of system. The paper presents the asymptotical stabilization problem of nonlinear fractional-order glucose-insulin systems. A static output feedback control is considered for the problem. Sufficient conditions for the asymptotical stabilization of the nonlinear fractional-order glucose-insulin system are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belonging to 0 < α < 1. Finally, numerical simulations are carried out to illustrate our proposed results. These numerical simulations show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer order counterpart.

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 paper investigates the static output feedback control problem for discrete-time positive linear systems subject to state delay, actuator constraints, and resource limitations in communication. To address these challenges simultaneously, an event-triggered control framework is developed. A novel event-triggering condition is proposed, based on a component-wise comparison where the triggering error is checked against state-dependent bounds. Sufficient conditions for ensuring positivity, exponential stability, and satisfaction of input constraints are derived. Crucially, these design conditions are formulated as a set of solvable linear programming problems, making the approach computationally tractable. Furthermore, conditions are established to demonstrate a provably reduced control update frequency compared to traditional time-triggered control, quantifying the resource-saving benefits of the proposed approach. Two numerical examples, including one based on a population dynamics model, illustrate the effectiveness of the proposed approach.