### ${\mathscr{H}}_{\infty}$ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process.

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We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded ${H}^{\infty}$-calculus and is based on elementary analysis.

In this paper, we study decentralized ${H}_{\infty}$ feedback control systems with quantized signals in local input-output (control) channels. We first assume that a decentralized output feedback controller has been designed for a multi-channel continuous-time system so that the closed-loop system is Hurwitz stable and a desired ${H}_{\infty}$ disturbance attenuation level is achieved. However, since the local measurement outputs are quantized by a general quantizer before they are passed to the controller, the system’s...

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of ${H}_{2}$ and ${H}_{\infty}$ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in ${H}_{2}$ and ${H}_{\infty}$ are introduced and solved.

This paper deals with some state-feedback ${H}_{2}/{H}_{\infty}$ control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in ${H}_{2}$, ${H}_{\infty}$ and mixed ${H}_{2}/{H}_{\infty}$ are introduced and solved.

This paper addresses the problems of stability analysis and decentralized control of interconnected linear systems with constant time-delays in the state of each subsystems as well as in the interconnections. We develop delay- dependent methods of stability analysis and decentralized stabilization via linear memoryless state-feedback. The proposed methods are given in terms of linear matrix inequalities. Extensions of the decentralized stabilization result to more complex control problems, such...

In this paper, we consider the design of interconnected ${H}_{\infty}$ feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired ${H}_{\infty}$ disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters...

This paper is concerned with the exponential ${H}_{\infty}$ filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and ${H}_{\infty}$ control problem. Then, a mean-square...

This paper is concerned with the flexibility in the closed loop pole location when solving the ${H}_{2}$ optimal control problem (also called the ${H}_{2}$ optimal disturbance attenuation problem) by proper measurement feedback. It is shown that there exists a precise and unique set of poles which is present in the closed loop system obtained by any measurement feedback solution of the ${H}_{2}$ optimal control problem. These “${H}_{2}$ optimal fixed poles” are characterized in geometric as well as structural terms. A procedure...

Mathematics Subject Classification: 26A33; 93C15, 93C55, 93B36, 93B35, 93B51; 03B42; 70Q05; 49N05This paper proposes a novel method to design an H∞ -optimal fractional order PID (FOPID) controller with ability to control the transient, steady-state response and stability margins characteristics. The method uses particle swarm optimization algorithm and operates based on minimizing a general cost function. Minimization of the cost function is carried out subject to the H∞ -norm; this norm is also...

This paper examines the problem of designing a robust ${}_{\infty}$ fuzzy controller with -stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust ${}_{\infty}$ fuzzy controller that guarantees (i) the ₂-gain of the mapping from the exogenous input noise to the...

The synthesis of a feedforward unit for ${H}_{2}$ optimal decoupling of measurable or previewed signals in discrete-time linear time-invariant systems is considered. It is shown that an ${H}_{2}$ optimal compensator can be achieved by connecting a finite impulse response (FIR) system and a stable dynamic unit. To derive the FIR system convolution profiles an easily implementable computational scheme based on pseudoinversion (possibly nested to avoid computational constraints) is proposed, while the dynamic unit...