Design of stabilizing controllers for uncertain time-delay systems via output feedback

Stabilization of fractional-order singular uncertain systems

This work eonsiden the H, norm control of structural systems with collocated sensors and actuators using an analytical upper bound approach. A parametrization of the output feedback control gains that achieve a desired H, norm bound is obtained using an analytical solution of the Bounded Real Lemma. This approach is verified experimentally on a cantilevered aluminum beam with two collocated pairs of piezoceramic patches that serve as sensors and actuators. The finite element model of this beam is developed and the simulations show a drop of -6 dB in the H, norm of the closed loop system. Experimental results verify the simulated results and demonstrate the effectiveness of this method. The proposed control methodology has obvious computational advantages compared to traditional H, control design methods, especially for lnrge scale systems. The control of structural systems with collocated sensors and actuators has been shown to provide great advantages from a stability, passivity, robustness and an implementation viewpoint. For example, collocated control can easily be achieved in a space structure when an attitude rate sensor is placed at the same point as a torque actuator.(l)(2) The actuator placement and sizing optimization for vibration sup pression of a collocated beam structure is discussed in Ref. (3).Collocation of sensors and actuators leads to symmetric transfer functions. Several other classes of engineering sys- tems, such as circuit systems, chemical reactors and power networks, can be modelled as systems with symmetric trans- fer functions. Stabilization, robustness, model reduction and control of such systems has been examined recently.(4)(5) The H, norm control of structural systems has attracted a lot of attention recently due to the interpretation of the H, norm in the frequency domain. In early work, D-K iteration method was used to design H, controllers for a non-collocated flexible shucture. Now state space H, control based on the standard Riccati equation approach or the linear matrix inequality (LMI) formulation is a well developed control synthesis tool. The optimal static state feedback and full-order dynamic output feedback H, con- trol synthesis problems can be solved using iterations on the corresponding Riccati solutions or via the computational solution of a convex LMI optimization problem.(7)(8) On the other hand, the static output feedback and the fixed-order dynamic output feedback H, control synthesis problems are difficult computational problems since they require the

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

In this paper, linear systems working over networks with event driven controller are studied for asymptotic stability. A scheme is presented for the stable operation of such systems in which the control signal update is transmitted over the communication line, only in the case of occurrence of an event. This scheme is useful in reducing the data load on the transmission line. The uncertainty associated with the transmission line is the time delay and is taken into account. Conditions for asymptotic stability are derived for system working with the static output feedback and the dynamic output feedback controllers. The developed designed schemes are demonstrated by simulation of a numerical example and a quadruple-tank system.

Input-Output Decoupling of Nonlinear Systems by Output Feedback

A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems

On the stability of certain systems under resonance conditions

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

We present new several sufficient conditions for the robust stability of uncertain time-delay systems. These conditions represent the delay-independent asymptotic stability and the decaying rate for uncertain single time-delay systems. These results are then extended to uncertain composite linear systems with time delays. The superiority of these results is demonstrated by comparing them to those given by Wang et al. (1987).

SummaryThis paper studies the bipartite output synchronization problem of general linear heterogeneous multiagent systems on signed digraphs. We first show that, for heterogeneous multiagent systems, the bipartite output synchronization over the structurally balanced signed digraphs and the conventional output synchronization over the associated nonnegative digraphs are equivalent. Then, 3 different control protocols, using full‐state feedback, static output feedback, and dynamic output feedback are designed at each agent to solve the bipartite output synchronization problem based on solutions to the corresponding output regulator equations. Explicit local design procedures are proposed for all 3 control protocols. The compensators employed in these protocols incorporate only one copy of the virtual exosystem's dynamics, regardless of the dimensions of the outputs. This results in lower‐dimensional compensators and controllers and, hence, is more computationally tractable compared to the popular internal model principle‐based control protocols. Numerical simulations over 3 different signed communication digraphs validate the proposed control protocols.

This paper studies the output feedback stochastic linear quadratic (LQ) optimal control with state and control dependent noise. Firstly, some necessary/sufficient conditions for the static output feedback stabilizability are given. Secondly, infinite horizon static and dynamic output feedback LQ control are studied, respectively.

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

This paper is concerned with the use of output static feedback in linear time-invariant finite dimensional systems. We consider here the use of an extra relaxation constraint as a mean to obtain efficiently computable (sufficient) conditions for the synthesis of output static stabilizing controllers. We present novel necessary and sufficient conditions for output static feedback stabilizability, that are computable in terms of the solvability of a concave programming problem. We add an extra relaxation constraint to the above conditions, to define a new concept: output static stabilization in the relaxed sense. This (conservative) stabilization concept is fully characterized in terms of the LQR problem. The dependence of the above stabilization concept on the state-space representation of a system is analyzed. We show that for a particular class of plants, the stabilization problem in the above sense can be cast as a convex programming problem. We fully characterize a particular class of plants that are stabilizable in the above sense. A consequence of this characterization is somehow surprising: the identification of a class of plants stabilize via output static feedback, for which stabilizing feedback matrices can be (almost) expressed in analytic closed form. A result which is indeed a generalization of a well-known fact for SISO systems.

Delay-independent robust stability of uncertain linear systems