Static Output Feedback Stabilization Research Articles

Optimal Static Output Feedback Stabilization of Fractional-Order Systems With Caputo Derivative Order 1 ≤ α < 2

Optimal Static Output Feedback Stabilization of Fractional-Order Systems With Caputo Derivative Order 1 ≤ α < 2

New Relaxed Static Output Feedback Stabilization of T–S Fuzzy Systems with Time-Varying Delays

This paper investigates the imperfect premise matching-based (IPMB) static output feedback (SOF) controller for T–S fuzzy systems with time-varying delays. Firstly, by employing integral inequality techniques, the membership-function-independent fuzzy SOF design methods in terms of LMIs are presented based on imperfect premise matching (IPM) strategy. The obtained stabilization conditions do not contain equality constraints, and the output matrices do not have rank constraints. Secondly, some suitable relaxation variables are employed, and more relaxed membership-function-dependent (MFD) stabilization conditions are obtained by considering the local boundary information of membership functions (MFs). Finally, two simulation examples are given to show the progressiveness of the proposed methods in this paper.

Hyperparameter Selection in Deep Unfolding-based Static Output Feedback Stabilization

Hyperparameter Selection in Deep Unfolding-based Static Output Feedback Stabilization

Static output feedback global asymptotic stability of limit cycles for discrete-time switched affine systems

This paper deals with static output feedback stabilisation of suitable limit cycles for discrete-time switched affine systems. In a first step, a limit cycle is determined according to a performance criterion specified by the designer related to the steady-state response of interest as, for instance, the maximum allowed ripple. Afterwards, based on a time-varying convex Lyapunov function, a min-type switching rule is designed through sufficient conditions expressed in terms of linear matrix inequalities that ensure global asymptotic stability of the limit cycle and an H2 or H∞ minimum guaranteed cost. A practical application example concerning the voltage regulation of a DC-DC multicellular converter is used for validation and comparison.

Invariant output feedback stabilisability: the scalar case

In this paper we prove that stabilisability is a static output feedback (SOF) invariant, for scalar and multivariable systems. Then we examine scalar stabilisability, from an invariant viewpoint. We prove that the signature of Hermite’s Bezoutian is constant within certain intervals that we call critical, and we give a very simple algebraic stabilisability criterion, consisted of a finite number of stability checks, one for each critical interval. We establish the validity of this criterion with Routh, Hurwitz and Lyapunov methods. We prove that the winding number of the Nyquist plot around points of the real axis, is constant within critical intervals. We correlate the stabilisability within critical intervals with the stability of corresponding critical polynomials defined at their limits. Finally, we discuss why our findings constitute a decisive step towards the analytical solution for the persisting problem of static output feedback stabilizability of linear time invariant multivariable systems.

Static output feedback stabilization of uncertain rational nonlinear systems with input saturation

In this paper, the notion of robust strict QSR-dissipativity is applied to solve the static output feedback control problem for a class of continuous-time nonlinear rational systems subject to input saturation and bounded parametric uncertainties. A local dissipativity condition is combined with generalized sector conditions to formulate the synthesis of a stabilizing controller in terms of linear matrix inequalities. Furthermore, an iterative algorithm based on linear matrix inequalities is proposed in order to compute the feedback gain matrix that maximizes the estimate of the closed-loop region of attraction. Numerical examples are provided to illustrate the applicability of this new approach in examples borrowed from the literature.

Asynchronous output feedback control for Markov jump systems under dynamic event‐triggered strategy

AbstractThis article addresses the synthesis of static output feedback stabilization via employing event‐based control, for discrete‐time Markov jump systems subject to limited bandwidth and mismatched modes. The event‐triggered communication strategy with an extra dynamic variable is considered in the design of controller to alleviate transmission burden. Then, for the purpose of further improving system performance, a special triggering threshold constructed as a diagonal matrix is introduced. Asynchronous behavior caused by mismatched modes between the controller and controlled systems is depicted by utilizing a hidden Markov model. With the assistance of output feedback theory, an asynchronous event‐based output feedback control law is sufficiently formulated to achieve the stochastic stabilization with desired performance. Ultimately, an illustrative example is implemented to verify the feasibility of theoretical results.

Nearest neighbor control for practical stabilization of passive nonlinear systems

This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with m-dimensional input space, it is sufficient to have m+1 discrete input points (other than zero for general passive systems or the target constant input for constant-incrementally passive systems). Furthermore, we present a constructive algorithm to design such m+1 nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control.

Output feedback controller design for discrete LTI systems with polytopic uncertainty via direct searching of the design space

AbstractThis paper concerns static output feedback stabilization of polytopic discrete linear time‐invariant (LTI) systems. The previous related studies were mainly based on linear matrix inequality (LMI) approaches which are naturally conservative. In this paper, a novel design algorithm is presented that iteratively partitions a primary design space to subspaces. Then, by assessing stabilizability status of each generated subspace, the algorithm determines the total stabilizable parts and removes the undesired parts of the design space. Mathematical theories are developed to determine the total de‐stabilizability or stabilizability of a given subspace. These subspaces' properties are detected through checking the existence of critical polynomials (which have roots on the unit circle of the complex plane) on their exposed edges. By omitting the undesired parts of the design space, the algorithm just searches the desired parts which are far smaller than the primary design space. This strategy improves the feasibility performance of the algorithm. Some illustrating examples are provided to show the steps of the design algorithm. Furthermore, 100 random models are generated to evaluate the feasibility performance of the proposed algorithm as compared to some existing methods. The results reveal the superiority of the proposed algorithm.

Static output feedback stabilization of T-S fuzzy active suspension systems

This paper investigates, a new methodology for non-linear active suspension systems (ASS) with static output feedback (SOF) control. The nonlinear ASS is represented by a Takagi–Sugeno fuzzy control ASS in continuous time. A SOF control presented by a family of linear matrix inequalities (LMIs) guarantees the asymptotic stability and ensures certain an H∞ performance level. This methodology motivated this research, where in the context of active suspension (AS) systems, the guaranteed performance correspond to ride comfort in the presence of road disturbances. Thus, a controller is developed for a quarter-car model with active suspension. The Simulated results with root-mean-square (RMS) values illustrate the effectiveness of the proposed approach.

Dynamic output feedback stabilization of deterministic finite automata via the semi-tensor product of matrices approach

This paper deals with the dynamic output feedback stabilization problem of deterministic finite automata (DFA). The static form of this problem is defined and solved in previous studies via a set of equivalent conditions. In this paper, the dynamic output feedback (DOF) stabilization of DFAs is defined in which the controller is supposed to be another DFA. The DFA controller will be designed to stabilize the equilibrium point of the main DFA through a set of proposed equivalent conditions. It has been proven that the design problem of DOF stabilization is more feasible than the static output feedback (SOF) stabilization. Three simulation examples are provided to illustrate the results of this paper in more details. The first example considers an instance DFA and develops SOF and DOF controllers for it. The example explains the concepts of the DOF controller and how it will be implemented in the closed-loop DFA. In the second example, a special DFA is provided in which the DOF stabilization is feasible, whereas the SOF stabilization is not. The final example compares the feasibility performance of the SOF and DOF stabilizations through applying them to one hundred random-generated DFAs. The results reveal the superiority of the DOF stabilization.

Static output feedback stabilization for second-order singular systems using model reduction methods

Static output feedback stabilization for second-order singular systems using model reduction methods

Static output feedback negative imaginary controller synthesis with an [formula omitted] norm bound

A large number of practical systems can be modeled as negative imaginary (NI) systems. In this paper, we investigate the problem of static output feedback (SOF) NI controller design with H∞ performance. Motivated by the two-stage framework for SOF stabilization, a sufficient condition is derived for the SOF controller synthesis. An iterative LMI-based algorithm is suggested to find an SOF controller. The algorithm consists of two stages: (1) finding an initial output injection controller; (2) computing a desired SOF controller. In addition, a numerical example is provided to verify the proposed method.

Iterative LMI approach to robust static output feedback control of uncertain polynomial systems with bounded actuators

This paper presents a novel static output feedback stabilization of polynomial systems with bounded actuators. We propose a new sufficient condition for static output feedback design for nominal polynomial systems with constraints on input magnitudes. In the proposed stabilization condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the controller is independent of the Lyapunov matrices. The main result is the novel parameter-dependent Lyapunov functions that are readily applied to robust static output feedback design of polynomial systems subject to parametric uncertainty. The proposed design conditions are bilinear in the decision variables. Hence, we provide iterative algorithms to solve the design problems. At each iteration, the design condition is cast as parameter-dependent linear matrix inequalities using the sum-of-squares technique and can be efficiently solved. The proposed approach leads to enhanced static output feedback design with computationally tractable formulation. Effectiveness of the proposed approach is demonstrated by numerical examples.

On LMI conditions to design robust static output feedback controller for continuous-time linear systems subject to norm-bounded uncertainties

This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results.

Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming

This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

Static output feedback stabilization for a linear parabolic PDE system with time-varying delay via mobile collocated actuator/sensor pairs

This paper addresses a static output feedback (SOF) stabilization problem for a linear parabolic partial differential equation (PDE) system with time-varying delay via mobile collocated actuator/sensor pairs. Initially, an SOF stabilization scheme via mobile actuator/sensor pairs is proposed for the delayed PDE system, where the spatial domain is divided into multiple subdomains according to the number of actuator/sensor pairs and the projection modification algorithm is employed to ensure each collocated actuator/sensor pair only can move within the respective subdomain. Subsequently, the well-posedness of the closed-loop delayed PDE system is analyzed using the operator semigroup theory. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate, a delay-dependent control-plus-guidance design is developed in the form of bilinear matrix inequalities (BMIs), such that the resulting closed-loop system is exponentially convergent and the mobile actuator/sensor guidance can improve the transient response of closed-loop state. Moreover, an iterative algorithm based on linear matrix inequalities is provided to solve the BMIs. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed method.

Static Sliding Mode Control of Systems With Arbitrary Relative Degree by Using Artificial Delay

Static output-feedback stabilization of systems with relative degree n with matched disturbances is considered. Assuming that the system is controllable, a static output-feedback sliding mode controller is designed, where the output derivatives up to the order (n-1) are approximated by using the current and the delayed values of the output. Numerical examples illustrate the efficiency of the method.

Network-based control of a semilinear damped beam equation under point and pointlike measurements

We consider distributed static output-feedback stabilization of a damped semilinear beam equation. Distributed in space measurements are either point or pointlike, where a pointlike measurement is the state value averaged on a small subdomain. Network-based implementation of the control law which enters the PDE through shape functions is studied, where variable sampling intervals and transmission delays are taken into account. Our main objective is to derive and compare the results under both types of measurements in terms of the upper bound on the delays and sampling intervals that preserve the stability for the same (as small as possible) number of sensors/actuators. For locally Lipschitz nonlinearities, regional stabilization is achieved. Numerical results show that the pointlike measurements lead to larger delays and samplings, provided the subdomains, where these measurements are averaged, are not too small.

Robust Static Output Feedback Stabilization of Continuous-Time Linear Systems via Enhanced LMI Conditions

This paper addresses the problem of Static Output Feedback (SOF) stabilization for continuous-time linear systems subject to norm-bounded parameter uncertainties. Usually this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearize to get non conservative Linear matrix inequality (LMI) conditions. In this paper, by means of some technical lemmas, we transform the BMI into a new LMI with a line search over two scalar variables. The obtained LMI conditions are less conservative than those existing in the literature. Numerical evaluations are presented to show the superiority of the proposed method.