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The diesel engines are emitting toxic gases which affect the greenhouse gases. In this research, the methyl esters were extracted from waste papaya seed oil using transesterification process. The Direct Injection Kirloskar diesel engine at constant speed of 1500 rpm and compression ratio of 17.5:1 was used to test the fuel. The injection nozzle holes were varied from 3 to 4 holes. The emissions were recorded using AVL gas analyser. The 20% blend with 4-hole nozzle shows reduction in NOx, CO and CO2 emissions at full load. The performance is increased for 30% blend at full load.

This article deals with the relationship between rational representations of linear differential systems and their state representations. In particular we study the relationship between rational representations on the one hand, and output nulling and driving variable representations on the other. In the input output framework it is well-known that every controllable and observable realization of the transfer matrix of the system yields a minimal input/state/output representation. If a proper rational matrix is used for a rational kernel or image representation of the system, then the question arises under what conditions realizations of this rational matrix give rise to state representations. We will establish conditions under which realizations of the proper rational matrix appearing in a rational image representation yield minimal driving variable representations of the system. Likewise, we find conditions under which realization leads from rational kernel representations to minimal output nulling representations. We also study the converse problem, namely state elimination from driving variable and output nulling representations. We will establish closed form expressions for kernel and image representations of the external behaviors associated with these particular state representations. (C) 2013 Elsevier B.V. All rights reserved.

Given a nominal plant, together with a fixed neighborhood of this plant, the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood (in an appropriate sense). If a controller achieves this design objective, we say that it robustly stabilizes the nominal plant. In this paper we formulate the robust stabilization problem in a behavioral framework, with control as interconnection. We also formulate a relevant behavioral $\mathcal{H}_{\infty}$ synthesis problem, which will be instrumental in solving the robust stabilization problem. We use both rational and polynomial representations for the behaviors under consideration. Necessary and sufficient conditions for the existence of robustly stabilizing controllers are obtained using the theory of dissipative systems. We will also find the optimal stability radius, i.e., the smallest upper bound on the radii of the neighborhoods for which there exists a robustly stabilizing controller. This smallest upper bound is expressed in terms of certain storage functions associated with nominal control system.

This paper deals with the problems of regular imple- mentability and stabilization of a given plant in the context of finite- dimensional linear differential system behaviors. In particular we solve the problems of regular implementability and stabilization using controllers in which a pre-specified subset of the plant con- trol variables is free. We will also extend the results to the situation in which the set of plant control variables is partitioned into two complementary subsets. Variables from one subset should become controller inputs, while variables from the other should become controller outputs. In other words, we consider the problems of regular implementability and stabilization using controllers with a priori given input/output structure.

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well-known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the main result of this paper, we will derive a new condition for equivalence of rational kernel representations of possibly noncontrollable behaviors. This paper also deals with the equivalence of polynomial as well as rational image representations.

Given a nominal plant, together with a fixed neighborhood of this plant, the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood (in an appropriate sense). If a controller achieves this design objective, we say that it robustly stabilizes the nominal plant. In this paper we formulate the robust stabilization problem in a behavioral framework, with control as interconnection. We use both rational as well as polynomial representations for the behaviors under consideration. We obtain necessary and sufficient conditions for the existence of robustly stabilizing controllers using the theory of dissipative systems. We will also find the smallest upper bound on the radii of the neighborhoods for which there exists a robustly stabilizing controller. This smallest upper bound is expressed in terms of certain storage functions associated with nominal plant.

Given a nominal plant, together with a fixed neighborhood of this plant, the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood (in an appropriate sense). If a controller achieves this design objective, we say that it robustly stabilizes the nominal plant. In this paper we formulate the robust stabilization problem in a behavioral framework, with control as interconnection. We use both rational as well as polynomial representations for the behaviors under consideration. We obtain a behavioral version of the ‘small gain theorem’ and then obtain necessary and sufficient conditions for the existence of robustly stabilizing controllers using the theory of dissipative systems. We will also find the smallest upper bound on the radii of the neighborhoods for which there exists a robustly stabilizing controller. This smallest upper bound is expressed in terms of certain storage functions associated with the nominal control system.

In this paper we deal with the problem of finding necessary and sufficient conditions for a behavior to be regularly implementable using controllers in which an a priori given part of the control variables is free or maximally free. We will solve the above problems in both the full and the partial interconnection case.