Stability and performance analysis for linear systems with actuator and sensor saturations subject to unmodeled dynamics

This study addresses the control of linear systems subject to both sensor and actuator saturations and additive ℒ2-bounded disturbances. Supposing that only the output of the linear plant is measurable, the synthesis of stabilising output feedback dynamic controllers, allowing to ensure the internal closed-loop stability and the finite ℒ2-gain stabilisation, is considered. In this case, it is shown that the closed-loop system presents a nested saturation term. Therefore, based on the use of some modified sector conditions and appropriate variable changes, synthesis conditions in a ‘quasi’- linear matrix inequality (LMI) form are stated in both regional (local) as well as global stability contexts. Different LMI-based optimisation problems for computing a controller in order to maximise the disturbance tolerance, the disturbance rejection or the region of stability of the closed-loop system are proposed.

In this paper, the $\boldsymbol{L}_{\infty}$ control synthesis problem for linear systems subject to actuator saturation and persistent bounded disturbance is studied. An $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator are simultaneously designed. First, by using the quadratic Lyapunov function technique, a sufficient condition on the existence of the $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator is established via linear matrix inequalities (LMIs). Such an integrated controller is able to guarantee the regional stabilization and the $\boldsymbol{L}_{\infty}$ performance of linear systems with actuator saturation and external persistent bounded disturbance. Second, novel algorithms are developed to optimize the upper bound on the $\boldsymbol{L}_{\infty}$ performance, the event-triggered threshold and the domain of attraction. Moreover, an output-based event-triggered mechanism applying to the anti-windup dynamic output feedback control design is provided, which reduces the number of control actuation updates and information transmission with respect to the traditional time-triggered control scheme.

This paper proposes dynamic output-feedback networked control with actuator saturation and sensor failure for Markovian jump descriptor systems (MJDS). First, the mode-dependent dynamic output-feedback controller is described as a quasi-linear parameter varying system. Then, the stochastic admissibility criterion for the closed-loop system with sensor failure and actuator saturation is obtained as matrix inequalities. To obtain the feasible solution of the non-convex condition, this paper successfully obtains the equivalent condition in terms of strict linear matrix inequalities (LMIs) and the controller gains. A numerical example shows the validity of the proposed result.

On robustness in system identification

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

SummaryIn this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

The paper mainly deals with the problem of finite-time stabilization of linear time-varying systems. A dynamic output feedback controller is designed, which is able to stabilize the linear time-varying systems in finite time. By virtue of extended piecewise constant method, novel criteria for the existence of a dynamic output feedback controller is established in terms of linear matrix inequalities. Compared with the existing method, the proposed method is more efficient from a computational point of view. A simulation is given to illustrate the effectiveness of the obtained result.

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced l 2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

In this paper, both problems of the stability and stabilization analysis for linear neutral time-delay systems are respectively investigated. The time-delays considered here are assumed bounded but no information to be available. Using Lyapunov functional method, delay-dependent conditions for the stability and stabilization of the systems are presented in terms of linear matrix inequality (LMI). A numerical example is given to illustrate the main results of this paper and make a comparison with the results presented in literatures

Stabilization of linear discrete-time systems with actuator saturation

The robust stabilization problem for a class of uncertain linear time-delay systems containing sector saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. The new criterion of delay-dependent robust stabilizability for uncertain time-delay systems is presented and the corresponding robust memoryless state feedback controller is derived in terms of the solutions of several linear matrix inequalities (LMIs). Numerical example is presented to illustrate the obtained results.

In this paper, we consider a continuous-time linear system with finite jumps at discrete instants of time. An iterative method to compute the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -induced norm of a linear system with jumps is presented. Each iteration requires solving an algebraic Riccati equation. We also show that a linear feedback interconnection of a continuous-time finite dimensional linear time- invariant (FDLTI) plant and a discrete-time finite dimensional linear Shift-invariant (FDLSI) controller can be represented as a linear system with jumps. This leads to an iterative method to compute the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -induced norm of a sampled-data system.

Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality

This paper considers the problem of local reliable control for continuous-time linear systems with saturating actuators and disturbance. The local stability and the performance of the designed closed-loop system is guaranteed not only when all the control components are operational, but also in the case of actuator outages in the preselected subset of actuators. The linear matrix inequality (LMI) method and iterative LMI method are proposed to design state-feedback controllers. The effectiveness of our methods is shown by an example.