Robust Static Output Feedback Control Research Articles

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.

Robust Reduced-order Output-feedback H∞ Control

The problem of robust H∞ reduced-order control design for linear systems in presence of polytopic type uncertainties is addressed. The controller is obtained by transforming the problem into a robust static output-feedback control design problem. Applying a recent method for solving the latter by means of linear matrix inequalities, a sufficient condition is obtained for the existence of a solution to the problem. A simple method for deriving the reduced-order controller is given in the case where the latter condition is satisfied.

Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H 2 and H ∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

Static Output Feedback Control Synthesis for Linear Systems With Time-Invariant Parametric Uncertainties

This technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous-time systems with time-invariant polytopic uncertainties. Sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities. Furthermore, the results are also extended to H2 static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

ROBUST STATIC OUTPUT FEEDBACK ℋ∞ CONTROL OF A CLASS OF STOCHASTIC HYBRID SYSTEMS IN NOISY ENVIRONMENT: LMI FORMULATION

In this paper, we address the robust static output feedback control problem of continuous time active fault tolerant control system with Markovian parameters (AFTCSMP) subject to structured parameter uncertainties, in noisy environnement. We will first derive a necessary and sufficient condition for the robust internal exponential stability in the mean square of the uncertain AFTCSMP in terms of nonlinear matrix inequalities. Then, an LMI relaxation scheme is presented to eliminate the nonlinearities, yielding a new easily tractable sufficient condition. Having obtained this result, we can move on the control problem and write the robust output feedback ℋ∞ control problem of the uncertain continuous time AFTCSMP in terms of an LMI optimization problem. The convex approach naturally leads to powerful numerical algorithms to solve these problematic. A numerical example is presented to illustrate the theoretical results.

Ellipsoidal sets for resilient and robust static output-feedback

The implementation of a controller, if not exact, may lead to the so-called fragility problem, i.e., the loss of expected closed-loop properties. In the present note, this difficult problem is dealt with considering robust static-output feedback (SOF) control for uncertain linear time-invariant systems. By analogy with robust analysis theory based on quadratic separation, a new formulation for the SOF design is shown to be a valuable way to tackle fragility issues. Indeed, the use of a quadratic separator for design purpose allows to define a whole resilient (nonfragile) set of SOF control laws. Results are formulated as matrix inequalities one of which is nonlinear. A numerical algorithm based on nonconvex optimization is provided ant its running is illustrated on classical examples from literature.

Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach

This paper addresses the problem of designing robust static output-feedback controllers for nonlinear discrete-time interval systems with time delays both in states and in control input. In the approach, we do not directly employ the Lyapunov approach, as do in most of traditional fuzzy control design approaches. Instead, sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed-loop fuzzy system. The stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the Matlab linear matrix inequality (LMI) toolbox. Finally, an example is provided to illustrate the effectiveness of the proposed approach.

Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach

This paper discusses a robust stabilization problem for a class of multi-input and multi-output (MIMO) discrete-time non-linear systems with both state and control inputs containing non-linear perturbations. The problem is solved via static output feedback and dynamic output feedback, respectively. A unified approach is used to cast the problem into a convex optimization involving linear matrix inequalities (LMI), all the controllers can robustly stabilize the systems and maximize the bound on the non-linear perturbations. This paper also extends the output feedback centralized design approach to a class of discrete-time MIMO non-linear decentralized systems, both robust static and dynamic output feedback controllers are obtained.

Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback

This paper is concerned with the design of robust static and dynamic output feedback controllers for a class of uncertain linear systems with norm-bounded uncertainty. The uncertainty is assumed to enter into both the state and input matrices. However, the output matrix is assumed to be free of uncertain parameters. Necessary conditions are given for the existence of a static output feedback controller that quadratically stabilizes the system and minimizes a bound on the quadratic function. Our results may be considered as an extension of the optimal output feedback LQR problem to the case of uncertain systems with norm-bounded uncertainty. The problem of full-order and reduced-order dynamic output feedback is also considered using the static output feedback results.