Stabilization via static output feedback

Necessary and sufficient conditions for the existence of a stabilizing static output feedback gain matrix are presented. It is shown that any such gain matrix is the solution of some linear quadratic control problem where the cost functional has a suitable cross term     

Finite-time stabilization via dynamic output feedback

In this paper the finite-time stabilization of continuous-time linear systems is considered; this problem has been previously solved in the state feedback case. In this work the assumption that the state is available for feedback is removed and the output feedback problem is investigated. The main result provided is a sufficient condition for the design of a dynamic output feedback controller which makes the closed loop system finite-time stable. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multi-objective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time stability together with some pole placement requirements.     

Robust output feedback stabilization via risk-sensitive control

We consider a problem of robust linear quadratic Gaussian (LQG) control for discrete-time stochastic uncertain systems with partial state measurements. For a finite-horizon case, the problem was recently introduced by Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398). In this paper, an infinite horizon extension of the results of Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398) is discussed. We show that for a broad class of uncertain systems under consideration, a controller constructed in terms of the solution to a specially parameterized risk-sensitive stochastic control problem absolutely stabilizes the stochastic uncertain system.     

Simultaneous stabilization via linear state feedback control

The problem of simultaneously stabilizing a finite collection of plants via a single compensator utilizing full state information is considered. The authors assume that the complete state can be measured and seek a (static) linear state feedback control law. Sufficient conditions for such full state gains to exist are given and they show via several examples how stabilizing compensators can be designed     

Hankel/Toeplitz matrices and the static output feedback stabilization problem

The static output feedback (SOF) stabilization problem for general linear, continuous-time and discrete-time systems is discussed. A few novel necessary and sufficient conditions are proposed, and a modified SOF stabilization problem with performance is studied. For multiple-input single-output (or single-input multiple-output) systems the relation with a class of Hankel matrices, and their inverses, in the continuous-time case and with a class of Toeplitz matrices, in the discrete-time case, is established. These relationships are used to construct conceptual numerical algorithms. Finally, it is shown that, in the continuous-time case, the problem can be recast as a concave–convex programming problem. A few worked out examples illustrate the underlying theory.     

Robust output feedback stabilization via a small gain theorem

In this paper, we give sufficient conditions for designing robust globally stabilizing controllers for a class of uncertain systems, consisting of ‘nominal’ nonlinear minimum phase systems perturbed by uncertainties which may affect the equilibrium point of the nominal system (‘biased’ systems). The constructive proof combines a systematic step-by-step procedure, based on H_∞ arguments, with a small gain theorem, recently proved for nonliner systems. At each step, one finds two Lyapunov functions, one for a state-feedback problem and the other one for an output injection problem. Combining these two functions, one derives at each step a Lyapunov function candidate for solving an ouptut feedback stabilization problem. This approach allows one to put into a unified framework many existing results on robust output feedback stabilization. © 1998 John Wiley & Sons, Ltd.     

Fixed-structure robust controller synthesis via decentralized static output feedback

This paper describes and illustrates a unified methodology for robust, fixed-structure controller synthesis. The approach is based upon direct fixed-structure controller synthesis using a decentralized static output feedback formulation as a general framework for representing a large class of controller structures. Scaled Popov bounds for the real structured singular value are used to account for real parameter uncertainty and provide the means for optimizing a worst-case ℋ︁₂ cost bound with respect to the free parameters of the controller. Quasi-Newton optimization algorithms are used to solve the resulting numerical optimization problem. Initial stability multiplier and scaling matrices needed in scaled Popov synthesis are obtained by solving an LMI feasibility problem. Using both centralized and decentralized controller structures, numerical results are obtained for a 16th-order acoustic duct model with uncertain damped natural frequencies and for a two-dimensional beam-spring model with uncertain actuator locations. © 1998 John Wiley & Sons, Ltd.     

On static output feedback stabilization of systems with stable generalized zero dynamics

In this note, we define generalized zero dynamics, introduce a generalized zero dynamics algorithm, and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback.     

A new approach to static output feedback stabilization of linear dynamic systems

The topic of this study is output feedback control of linear control system with output. Use of condensed forms of the linear system under static output feedback (SOF) control is made to derive sufficient conditions for stabilization. A minimal-order control-free observer is presented.     

Optimal controllers and output feedback stabilization

In this paper the output feedback stabilizability problem is explored in terms of control Lyapunov functions. Sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem. Our main results extends those developed in [31] and generalize a theorem due to Sontag [23].     

Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Semi-global stabilization and output regulation of linear systems subject to state and/or input constraints have been studied in our earlier work by using state feedback. For the same problems, observer based measurement feedback control designs are the topics of this paper. High-gain observers are used in the feedback design in order to obtain accurate estimates of the state so that the constraint violation can be avoided. Due to the peaking phenomenon associated with a high-gain observer, a special saturation protection is built in the control laws to avoid possible constraint violation. The results in this paper show that the semi-global stabilization and semi-global output regulation problems for constrained linear systems are solvable via measurement feedback under solvability conditions similar to those in the state feedback.     

Asymptotic output stabilization for nonlinear systems via dynamical variable-structure feedback control

In this article, the problem of asymptotic output stabilization in nonlinear controlled systems is approached from the perspective of dynamical sliding-mode control. The proposed controller is based on Fliess's Generalized Observability Canonical Form, recently derived from the differential algebraic approach to system dynamics.     

Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback

This paper proposes a systematic approach for the static output feedback control design for discrete-time uncertain linear systems. It is shown that if the open-loop system satisfies some particular structural conditions and the uncertainty has a specific structure, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and nonsquare systems are considered. The performance problem through a quadratic criterion is also discussed (guaranteed cost control).     

Robust stabilization of T-S fuzzy systems: Fuzzy static output feedback under parametric uncertainty

This paper addresses robust static output-feedback control problems for a nonlinear system with uncertain fuzzy output in Takagi-Sugeno’s (T-S) form. Two cases of the T-S fuzzy system, both continuous- and discrete-time cases are considered. In both cases, sufficient design conditions are derived for asymptotic stabilization in the sense of Lyapunov, in terms of linear matrix inequalities. Results are extended to retain ℋ_∞ disturbance attenuation performance. An illustrative example on the permanent magnet synchronous motor equipped with uncertain nonlinear output and disturbance is provided to illustrate the effectiveness of the proposed methodology.     

Stability and static output feedback stabilization for a class of nonlinear discrete-time singular switched systems

In this paper, the stability and static output feedback stabilization problems for a class of nonlinear discrete-time singular switched systems are discussed. First, based on Lyapunov theory and the implicit function theorem, linear matrix inequalities sufficient conditions are developed which guarantee that the nonlinear discrete-time singular switched systems are regular, causal, have unique solution in a neighborhood of the origin, and are uniformly asymptotically stable. Then, with these conditions, and based on singular value decomposition approach, the design method of static output feedback controllers is given. Last, numerical examples are provided to illustrate the effectiveness of the proposed methods.     

Dynamic output feedback linearization and global stabilization

We present a class of single-input single-output nonlinear systems which are globally transformable by a dynamic output feedback control and a time-varying state space transformation into a linear, observable and minimum phase system. We then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well.     

Robust semiglobal stabilization of minimum-phase input-outputlinearizable systems via partial state and output feedback

In this paper we consider the problem of robust semiglobal stabilization and/or semiglobal practical stabilization of minimum-phase input-output linearizable systems. The results of this paper significantly extend the recent work of Teel and Praly (1993) on SISO (single-input/single-output) minimum-phase systems in several directions. Among these directions are the development of MIMO (multi-input/multi-output) theory and the relaxation of the restriction on the interaction between nonlinear zero dynamics and the state of the linearizable part of the system     

Stabilization for state/input delay systems via static and integral output feedback

This paper addresses the static and integral output feedback stabilization problems of continuous-time linear systems with an unknown state/input delay. By combining an augmentation approach and the delay partitioning technique, criteria for static and integral output feedback stabilizability are proposed in terms of nonlinear matrix inequalities with a free parameter matrix introduced. These new characterizations possess a special structure, which leads to linearized iterative computation. The effectiveness and merits of the proposed approach are shown through numerical examples.     

LQG optimal scalar static output feedback

An eigenproblem-based technique is given for computing the stabilizing scalar static output feedback gain that minimizes the standard linear quadratic performance index in the presence of a Gaussian white-noise disturbance. The method adapts recent work on eigenproblem-based computation of _∞-norms.