Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

This paper is concerned with the finite-time quantized H_∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H_∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.     

Stability and stabilization by output feedback control of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays

This paper deals with the problem of stabilization by output feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with a fixed delay by linear programming (LP) and cone complementarity while imposing positivity in closed-loop. The stabilization conditions are derived using the single Lyapunov–Krasovskii Functional (LKF). An example of a real plant is studied to show the advantages of the design procedure.     

Observer-based reliable exponential stabilization and H∞ control for switched systems with faulty actuators: An average dwell time approach

This paper deals with the problem of reliable stabilization and $H_{\infty }$ control for a class of continuous-time switched Lipschitz nonlinear systems with actuator failures. We consider the case that actuators suffer “serious failure”—the never failed actuators cannot stabilize the given system. The differential mean value theorem (DMVT) allows transforming the switched Lipschitz nonlinear systems into switched linear parameter varying (LPV) systems. Based on average dwell time scheme and under the condition that activation time ratio between stabilizable subsystems and unstabilizable ones is not less than a specified constant, sufficient conditions for reliable exponential stabilization of the switched systems are derived by hybrid observer-based output feedback control. The result is also extended to the reliable $H_{\infty }$ control problem.     

Robust H∞ nonlinear modeling and control via uncertain fuzzy systems

In theory, an Algebraic Riccati Equation (ARE) scheme applicable to robust H^∞ quadratic stabilization problems of a class of uncertain fuzzy systems representing a nonlinear control system is investigated. It is proved that existence of a set of solvable AREs suffices to guarantee the quadratic stabilization of an uncertain fuzzy system while satisfying H^∞-norm bound constraint. It is also shown that a stabilizing control law is reminiscent of an optimal control law found in linear quadratic regulator, and a linear control law can be immediately discerned from the stabilizing one. In practice, the minimal solution to a set of parameter dependent AREs is somewhat stringent and, instead, a linear matrix inequalities formulation is suggested to search for a feasible solution to the associated AREs. The proposed method is compared with the existing fuzzy literature from various aspects.     

A novel feedforward–feedback suboptimal control of linear time-delay systems

This paper presents a new approach for solving the optimal control problem of linear time-delay systems with a quadratic cost functional. In this approach, a method of successive substitution is employed to convert the original time-delay optimal control problem into a sequence of linear time-invariant ordinary differential equations (ODEs) without delay and advance terms. The obtained optimal control consists of a linear state feedback term and a forward term. The feedback term is determined by solving a matrix Riccati differential equation. The forward term is an infinite sum of adjoint vectors, which can be obtained by solving recursively the above-mentioned sequence of linear non-delay ODEs. A fast-converging iterative algorithm for this purpose is presented which provides a promising possible reduction of computational efforts. Numerical examples demonstrating the efficiency, simplicity and high accuracy of the suggested technique have been included. Simulation results reveal that just a few iterations of the proposed algorithm are required to find an accurate enough feedforward–feedback suboptimal control.     

Optimal ℋ∞-state feedback control for continuous-time linear systemsfeedback control for continuous-time linear systems

This paper proposes a convex programming method to achieve optimal -state feedback control for continuous-time linear systems. State space conditions, formulated in an appropriate parameter space, define a convex set containing all the stabilizing control gains that guarantee an upper bound on the -norm of the closed-loop transfer function. An optimization problem is then proposed, in order to minimize this upper bound over the previous convex set, furnishing the optimal -control gain as its optimal solution. A limiting bound for the optimum -norm can easily be calculated, and the proposed method will achieve minimum attenuation whenever a feasible state feedback controller exists. Generalizations to decentralized and output feedback control are also investigated. Numerical examples illustrate the theory.This research has been supported in part by grants from Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP and Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq—Brazil. The authors are grateful to the anonymous referees for their useful comments on this paper.